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Watteaux, R., G. Sardina, L. Brandt, and D. Iudicone. "On the time scales and structure of Lagrangian intermittency in homogeneous isotropic turbulence." Journal of Fluid Mechanics 867 (March 25, 2019): 438–81. http://dx.doi.org/10.1017/jfm.2019.127.
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We present a study of Lagrangian intermittency and its characteristic time scales. Using the concepts of flying and diving residence times above and below a given threshold in the magnitude of turbulence quantities, we infer the time spectra of the Lagrangian temporal fluctuations of dissipation, acceleration and enstrophy by means of a direct numerical simulation in homogeneous and isotropic turbulence. We then relate these time scales, first, to the presence of extreme events in turbulence and, second, to the local flow characteristics. Analyses confirm the existence in turbulent quantities of holes mirroring bursts, both of which are at the core of what constitutes Lagrangian intermittency. It is shown that holes are associated with quiescent laminar regions of the flow. Moreover, Lagrangian holes occur over few Kolmogorov time scales while Lagrangian bursts happen over longer periods scaling with the global decorrelation time scale, hence showing that loss of the history of the turbulence quantities along particle trajectories in turbulence is not continuous. Such a characteristic partially explains why current Lagrangian stochastic models fail at reproducing our results. More generally, the Lagrangian dataset of residence times shown here represents another manner for qualifying the accuracy of models. We also deliver a theoretical approximation of mean residence times, which highlights the importance of the correlation between turbulence quantities and their time derivatives in setting temporal statistics. Finally, whether in a hole or a burst, the straining structure along particle trajectories always evolves self-similarly (in a statistical sense) from shearless two-dimensional to shear bi-axial configurations. We speculate that this latter configuration represents the optimum manner to dissipate locally the available energy.
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Bos, Wouter J. T. "On the anisotropy of the turbulent passive scalar in the presence of a mean scalar gradient." Journal of Fluid Mechanics 744 (March 10, 2014): 38–64. http://dx.doi.org/10.1017/jfm.2014.60.
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AbstractWe investigate the origin of the scalar gradient skewness in isotropic turbulence on which a mean scalar gradient is imposed. The problem of the advection of an anisotropic scalar field is reformulated in terms of the advection of an isotropic vector field. For this field, triadic closure equations are derived. It is shown how the scaling of the scalar gradient skewness depends on the choice of the time scale used for the Lagrangian decorrelation of the vector field. The persistent anisotropy in the small scales for the third-order statistics is shown to be perfectly compatible with Corrsin–Obukhov scaling for second-order quantities, since second- and third-order scalar quantities are governed by a different triad correlation time scale. Whereas the inertial range dynamics of second-order scalar quantities is governed by the Lagrangian velocity correlation time, the third-order quantities remain correlated over a time related to the large-scale dynamics of the scalar field. It is argued that this time is determined by the average time it takes for a fluid particle to travel between ramp-cliff scalar structures.
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Martins, Luís Gustavo N., Gervásio A. Degrazia, Otávio C. Acevedo, Franciano S. Puhales, Pablo E. S. de Oliveira, Claudio A. Teichrieb, and Samuel M. da Silva. "Quasi-Experimental Determination of Turbulent Dispersion Parameters for Different Stability Conditions from a Tall Micrometeorological Tower." Journal of Applied Meteorology and Climatology 57, no. 8 (August 2018): 1729–45. http://dx.doi.org/10.1175/jamc-d-17-0269.1.
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AbstractTurbulent wind data measured by sonic anemometers installed at various heights on a 140-m-tall micrometeorological tower located at a coastal site are used to obtain vertical profiles of the velocity standard deviations σi, Lagrangian decorrelation local time scales TLi, and eddy diffusivities Kα for distinct stability conditions. The novelty of the study lies in the use of turbulent data directly measured over the extension of the atmospheric surface layer at a coastal site for that purpose. Furthermore, the approach employs the Hilbert–Huang transform to determine the wind energy spectral peak frequencies. These are applied to the asymptotic spectral equation from Taylor statistical diffusion theory to obtain the turbulent dispersion parameters, which are shown to generally agree well with those provided by a classical autocorrelation approach. For neutral and stable situations the vertical profiles of momentum eddy diffusivities agree well with those derived from the spectral and autocorrelation method. Additionally, the turbulent integral time scales and eddy diffusivities determined by the method at a coastal location are found to overestimate those predicted from analytical expressions based on continental field observations. The turbulence parameters found are suitable to be employed in air pollution dispersion models.
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Surcel, Madalina, Isztar Zawadzki, and M. K. Yau. "A Study on the Scale Dependence of the Predictability of Precipitation Patterns." Journal of the Atmospheric Sciences 72, no. 1 (January 1, 2015): 216–35. http://dx.doi.org/10.1175/jas-d-14-0071.1.
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Abstract A methodology is proposed to investigate the scale dependence of the predictability of precipitation patterns at the mesoscale. By applying it to two or more precipitation fields, either modeled or observed, a decorrelation scale can be defined such that all scales smaller than are fully decorrelated. For precipitation forecasts from a radar data–assimilating storm-scale ensemble forecasting (SSEF) system, is found to increase with lead time, reaching 300 km after 30 h. That is, for , the ensemble members are fully decorrelated. Hence, there is no predictability of the model state for these scales. For , the ensemble members are correlated, indicating some predictability by the ensemble. When applied to characterize the ability to predict precipitation as compared to radar observations by numerical weather prediction (NWP) as well as by Lagrangian persistence and Eulerian persistence, increases with lead time for most forecasting methods, while it is constant (300 km) for non–radar data–assimilating NWP. Comparing the different forecasting models, it is found that they are similar in the 0–6-h range and that none of them exhibit any predictive ability at meso-γ and meso-β scales after the first 2 h. On the other hand, the radar data–assimilating ensemble exhibits predictability of the model state at these scales, thus causing a systematic difference between corresponding to the ensemble and corresponding to model and radar. This suggests that either the ensemble does not have sufficient spread at these scales or that the forecasts suffer from biases.
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Buligon, Lidiane, Gervásio A. Degrazia, Charles R. P. Szinvelski, and Antonio G. Goulart. "Algebraic Formulation for the Dispersion Parameters in an Unstable Planetary Boundary Layer: Application in the Air Pollution Gaussian Model." Open Atmospheric Science Journal 2, no. 1 (August 12, 2008): 153–59. http://dx.doi.org/10.2174/1874282300802010153.
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An alternative formulation for the dispersion parameters in a convective boundary layer is presented. The development consists of a simple algebraic relation for the dispersion parameters, originated from the fitting of experimental data, in which the turbulent velocity variances and the Lagrangian decorrelation time scales are derived from the turbulent kinetic energy convective spectra. Assuming homogeneous turbulence for elevated regions in an unstable planetary boundary layer (PBL), the present approach, which provides the dispersion parameters, has been compared to the observational data as well as to results obtained by classical complex integral formulations. From this comparison yields that the vertical and lateral dispersion parameters obtained from the simple algebraic formulas reproduce, in an adequate manner, the spread of contaminants released by elevated continuous source in an unstable PBL. Therefore, the agreement with dispersion parameters available by an integral formulation indicates that the hypothesis of using an algebraic formulation as a surrogate for dispersion parameters in the turbulent convective boundary layer is valid. In addition, the algebraic vertical and lateral dispersion parameters were introduced into an air pollution Gaussian diffusion model and validated with the concentration data of Copenhagen experiments. The results of such Gaussian model, incorporating the algebraic dispersion parameters, are shown to agree with the measurements of Copenhagen.
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IJZERMANS, RUTGER H. A., ELENA MENEGUZ, and MICHAEL W. REEKS. "Segregation of particles in incompressible random flows: singularities, intermittency and random uncorrelated motion." Journal of Fluid Mechanics 653 (April 13, 2010): 99–136. http://dx.doi.org/10.1017/s0022112010000170.
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The results presented here are part of a long-term study in which we analyse the segregation of inertial particles in turbulent flows using the so called full Lagrangian method (FLM) to evaluate the ‘compressibility’ of the particle phase along a particle trajectory. In the present work, particles are advected by Stokes drag in a random flow field consisting of counter-rotating vortices and in a flow field composed of 200 random Fourier modes. Both flows are incompressible and, like turbulence, have structure and a distribution of scales with finite lifetime. The compressibility is obtained by first calculating the deformation tensor Jij associated with an infinitesimally small volume of particles following the trajectory of an individual particle. The fraction of the initial volume occupied by the particles centred around a position x at time t is denoted by |J|, where J ≡ det(Jij) and Jij ≡ ∂xi(x0, t)/∂x0,j, x0 denoting the initial position of the particle. The quantity d〈ln|J|〉/dt is shown to be equal to the particle averaged compressibility of the particle velocity field 〈∇ · v〉, which gives a measure of the rate-of-change of the total volume occupied by the particle phase as a continuum. In both flow fields the compressibility of the particle velocity field is shown to decrease continuously if the Stokes number St (the dimensionless particle relaxation time) is below a threshold value Stcr, indicating that the segregation of particles continues indefinitely. We show analytically and numerically that the long-time limit of 〈∇ · v〉 for sufficiently small values of St is proportional to St2 in the flow field composed of random Fourier modes, and to St in the flow field consisting of counter-rotating vortices. If St > Stcr, however, the particles are ‘mixed’. The level of mixing can be quantified by the degree of random uncorrelated motion (RUM) of particles which is a measure of the decorrelation of the velocities of two nearby particles. RUM is zero for fluid particles and increases rapidly with the Stokes number if St > Stcr, approaching unity for St ≫ 1. The spatial averages of the higher-order moments of the particle number density are shown to diverge with time indicating that the spatial distribution of particles may be very intermittent, being associated with non-zero values of RUM and the occurrence of singularities in the particle velocity field. Our results are consistent with previous observations of the radial distribution function in Chun et al. (J. Fluid Mech., vol. 536, 2005, p. 219).
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Buckley, Martha W., Tim DelSole, M. Susan Lozier, and Laifang Li. "Predictability of North Atlantic Sea Surface Temperature and Upper-Ocean Heat Content." Journal of Climate 32, no. 10 (April 30, 2019): 3005–23. http://dx.doi.org/10.1175/jcli-d-18-0509.1.
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Abstract Understanding the extent to which Atlantic sea surface temperatures (SSTs) are predictable is important due to the strong climate impacts of Atlantic SST on Atlantic hurricanes and temperature and precipitation over adjacent landmasses. However, models differ substantially on the degree of predictability of Atlantic SST and upper-ocean heat content (UOHC). In this work, a lower bound on predictability time scales for SST and UOHC in the North Atlantic is estimated purely from gridded ocean observations using a measure of the decorrelation time scale based on the local autocorrelation. Decorrelation time scales for both wintertime SST and UOHC are longest in the subpolar gyre, with maximum time scales of about 4–6 years. Wintertime SST and UOHC generally have similar decorrelation time scales, except in regions with very deep mixed layers, such as the Labrador Sea, where time scales for UOHC are much larger. Spatial variations in the wintertime climatological mixed layer depth explain 51%–73% (range for three datasets analyzed) of the regional variations in decorrelation time scales for UOHC and 26%–40% (range for three datasets analyzed) of the regional variations in decorrelation time scales for wintertime SST in the extratropical North Atlantic. These results suggest that to leading order decorrelation time scales for UOHC are determined by the thermal memory of the ocean.
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Bley, Sebastian, Hartwig Deneke, and Fabian Senf. "Meteosat-Based Characterization of the Spatiotemporal Evolution of Warm Convective Cloud Fields over Central Europe." Journal of Applied Meteorology and Climatology 55, no. 10 (October 2016): 2181–95. http://dx.doi.org/10.1175/jamc-d-15-0335.1.
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AbstractThe spatiotemporal evolution of warm convective cloud fields over central Europe is investigated on the basis of 30 cases using observations from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) on board the geostationary Meteosat platforms. Cloud fields are tracked in successive satellite images using cloud motion vectors. The time-lagged autocorrelation is calculated for spectral reflectance and cloud property fields using boxes of 16 × 16 pixels and adopting both Lagrangian and Eulerian perspectives. The 0.6-μm reflectance, cloud optical depth, and water path show a similar characteristic Lagrangian decorrelation time of about 30 min. In contrast, significantly lower decorrelation times are observed for the cloud effective radius and droplet density. It is shown that the Eulerian decorrelation time can be decomposed into an advective component and a convective component using the spatial autocorrelation function. In an Eulerian frame cloud fields generally decorrelate faster than in a Lagrangian one. The Eulerian decorrelation time contains contributions from the spatial decorrelation of the cloud field advected by the horizontal wind. A typical spatial decorrelation length of 7 km is observed, which suggests that sampling of SEVIRI observations is better in the temporal domain than in the spatial domain when investigating small-scale convective clouds. An along-track time series of box-averaged cloud liquid water path is derived and compared with the time series that would be measured at a fixed location. Supported by previous results, it is argued that this makes it possible to discriminate between local changes such as condensation and evaporation on the one hand and advective changes on the other hand.
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Degrazia, Gervasio, Domenico Anfossi, Haroldo Fraga De Campos Velho, and Enrico Ferrero. "A Lagrangian Decorrelation Time Scale in the Convective Boundary Layer." Boundary-Layer Meteorology 86, no. 3 (March 1998): 525–34. http://dx.doi.org/10.1023/a:1000734626931.
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Sumata, Hiroshi, Frank Kauker, Michael Karcher, Benjamin Rabe, Mary-Louise Timmermans, Axel Behrendt, Rüdiger Gerdes, et al. "Decorrelation scales for Arctic Ocean hydrography – Part I: Amerasian Basin." Ocean Science 14, no. 1 (March 2, 2018): 161–85. http://dx.doi.org/10.5194/os-14-161-2018.
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Abstract. Any use of observational data for data assimilation requires adequate information of their representativeness in space and time. This is particularly important for sparse, non-synoptic data, which comprise the bulk of oceanic in situ observations in the Arctic. To quantify spatial and temporal scales of temperature and salinity variations, we estimate the autocorrelation function and associated decorrelation scales for the Amerasian Basin of the Arctic Ocean. For this purpose, we compile historical measurements from 1980 to 2015. Assuming spatial and temporal homogeneity of the decorrelation scale in the basin interior (abyssal plain area), we calculate autocorrelations as a function of spatial distance and temporal lag. The examination of the functional form of autocorrelation in each depth range reveals that the autocorrelation is well described by a Gaussian function in space and time. We derive decorrelation scales of 150–200 km in space and 100–300 days in time. These scales are directly applicable to quantify the representation error, which is essential for use of ocean in situ measurements in data assimilation. We also describe how the estimated autocorrelation function and decorrelation scale should be applied for cost function calculation in a data assimilation system.
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Romanou, Anastasia, William B. Rossow, and Shu-Hsien Chou. "Decorrelation Scales of High-Resolution Turbulent Fluxes at the Ocean Surface and a Method to Fill in Gaps in Satellite Data Products." Journal of Climate 19, no. 14 (July 15, 2006): 3378–93. http://dx.doi.org/10.1175/jcli3773.1.
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Abstract In the first part of the paper, a high space–time resolution (1° latitude/longitude and daily) dataset of the turbulent fluxes at the ocean surface is used to estimate and study the seasonal to annual near-global maps of the decorrelation scales of the latent and sensible heat fluxes. The decorrelation scales describe the temporal and spatial patterns that dominate the flux fields (within a bandpass window) and hence reveal the dominant variability in the air–sea interaction. Regional comparison to the decorrelation scales of the flux-related variables such as the wind stress, the humidity difference, and the SST identifies the main mechanism responsible for the variability in each flux field. In the second part of the paper, the decorrelation scales are used to develop a method for filling missing values in the dataset that result from the incomplete satellite coverage. Weight coefficients in a linear regression function are determined from the spatial and temporal decorrelations and are functions of zonal and meridional distance and time. Therefore they account for all spatial and temporal patterns on scales greater than 1 day and 1° latitude/longitude and less than 1 yr and the ocean basin scale. The method is evaluated by simulating the missing-value distribution of the Goddard Satellite-Based Surface Turbulent Fluxes, version 2 (GSSTF2) dataset in the NCEP SST, the International Satellite Climatology Project (ISCCP)-FD (fluxes calculated using D1 series) surface radiation, and the Global Precipitation Climatology Project (GPCP) datasets and by comparing the filled datasets to the original ones. Main advantages of the method are that the decorrelation scales are unrestricted functions of space and time; only information internal to the flux field is used in the interpolation scheme, and the computation cost of the method is low enough to facilitate its use in similar large datasets.
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Glowacki, David R., Emanuele Paci, and Dmitrii V. Shalashilin. "Boxed Molecular Dynamics: Decorrelation Time Scales and the Kinetic Master Equation." Journal of Chemical Theory and Computation 7, no. 5 (April 19, 2011): 1244–52. http://dx.doi.org/10.1021/ct200011e.
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Charlton-Perez, Andrew J., and Alan O’Neill. "On the Sensitivity of Annular Mode Dynamics to Stratospheric Radiative Time Scales." Journal of Climate 23, no. 2 (January 15, 2010): 476–84. http://dx.doi.org/10.1175/2009jcli2995.1.
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Abstract Long decorrelation time scales of the annular mode are observed in the lower stratosphere. This study uses a simple dynamical model, which has been used extensively to study stratosphere–troposphere coupling to investigate the origin of the long dynamical time scales. Several long runs of the model are completed, with different imposed thermal damping time scales in the stratosphere. The dynamical time scales of the annular mode are found to be largely insensitive to the input thermal damping time scales, producing similar dynamical time scales in all cases below 50 hPa. This result suggests that the hypothesis that long time scales in the lower stratosphere are due to long radiative time scales in this region is false.
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Hamrud, Mats, and Henning Rodhe. "Lagrangian time scales connected with clouds and precipitation." Journal of Geophysical Research 91, no. D13 (1986): 14377. http://dx.doi.org/10.1029/jd091id13p14377.
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Sheshadri, Aditi, and R. Alan Plumb. "Propagating Annular Modes: Empirical Orthogonal Functions, Principal Oscillation Patterns, and Time Scales." Journal of the Atmospheric Sciences 74, no. 5 (April 10, 2017): 1345–61. http://dx.doi.org/10.1175/jas-d-16-0291.1.
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Abstract The two leading empirical orthogonal functions (EOFs) of zonal-mean zonal wind describe north–south fluctuations, and intensification and narrowing, respectively, of the midlatitude jet. Under certain circumstances, these two leading EOFs cannot be regarded as independent but are in fact manifestations of a single, coupled, underlying mode of the dynamical system describing the evolution in time of zonal wind anomalies. The true modes are revealed by the principal oscillation patterns (POPs). The leading mode and its associated eigenvalue are complex, its structure involves at least two EOFs, and it describes poleward (or equatorward) propagation of zonal-mean zonal wind anomalies. In this propagating regime, the principal component (PC) time series associated with the two leading EOFs decay nonexponentially, and the response of the system to external forcing in a given EOF does not depend solely on the PC decorrelation time nor on the projection of the forcing onto that EOF. These considerations are illustrated using results from an idealized dynamical core model. Results from Southern Hemisphere ERA-Interim data are partly consistent with the behavior of the model’s propagating regime. Among other things, these results imply that the time scale that determines the sensitivity of a model to external forcing might be different from the decorrelation time of the leading PC and involves both the rate of decay of the dynamical mode and the period associated with propagation.
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Schemm, Sebastian, and Tapio Schneider. "Eddy Lifetime, Number, and Diffusivity and the Suppression of Eddy Kinetic Energy in Midwinter." Journal of Climate 31, no. 14 (June 22, 2018): 5649–65. http://dx.doi.org/10.1175/jcli-d-17-0644.1.
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Abstract The wintertime evolution of the North Pacific storm track appears to challenge classical theories of baroclinic instability, which predict deeper extratropical cyclones when baroclinicity is highest. Although the surface baroclinicity peaks during midwinter, and the jet is strongest, eddy kinetic energy (EKE) and baroclinic conversion rates have a midwinter minimum over the North Pacific. This study investigates how the reduction in EKE translates into a reduction in eddy potential vorticity (PV) and heat fluxes via changes in eddy diffusivity. Additionally, it augments previous observations of the midwinter storm-track evolution in both hemispheres using climatologies of tracked surface cyclones. In the North Pacific, the number of surface cyclones is highest during midwinter, while the mean EKE per cyclone and the eddy lifetime are reduced. The midwinter reduction in upper-level eddy activity hence is not associated with a reduction in surface cyclone numbers. North Pacific eddy diffusivities exhibit a midwinter reduction at upper levels, where the Lagrangian decorrelation time is shortest (consistent with reduced eddy lifetimes) and the meridional parcel velocity variance is reduced (consistent with reduced EKE). The resulting midwinter reduction in North Pacific eddy diffusivities translates into an eddy PV flux suppression. In contrast, in the North Atlantic, a milder reduction in the decorrelation time is offset by a maximum in velocity variance, preventing a midwinter diffusivity minimum. The results suggest that a focus on causes of the wintertime evolution of Lagrangian decorrelation times and parcel velocity variance will be fruitful for understanding causes of seasonal storm-track variations.
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Ishihara, Takashi, and Yukio Kaneda. "Time Micro Scales of Lagrangian Strain Tensor in Turbulence." Journal of the Physical Society of Japan 62, no. 2 (February 15, 1993): 506–13. http://dx.doi.org/10.1143/jpsj.62.506.
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Kim, Sung Yong, and P. Michael Kosro. "Observations of near-inertial surface currents off Oregon: Decorrelation time and length scales." Journal of Geophysical Research: Oceans 118, no. 7 (July 2013): 3723–36. http://dx.doi.org/10.1002/jgrc.20235.
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Cancelli, Diana M., Marcelo Chamecki, and Nelson L. Dias. "A Large-Eddy Simulation Study of Scalar Dissimilarity in the Convective Atmospheric Boundary Layer." Journal of the Atmospheric Sciences 71, no. 1 (December 27, 2013): 3–15. http://dx.doi.org/10.1175/jas-d-13-0113.1.
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Abstract A numerical study of the effect of entrainment fluxes at the top of the atmospheric boundary layer (ABL) on dissimilarity between scalars within the mixed and surface layers is conducted. Simulation results clearly show that entrainment fluxes of opposite sign cause decorrelation between the scalars throughout the entire ABL. In the upper part of the mixed layer, this decorrelation is caused by changes in the covariance between the scalars and the scalar variance as well, and is distributed over the entire range of scales resolved in the simulation. Near the surface, the reduction in correlation coefficient originates from an increasing scalar variance, which is present exclusively in the large scales. These effects are noticeable on time scales of about 24 min or longer, and could be interpreted as nonstationarity for the typical 30-min periods used in surface-layer data processing. In addition, it is shown that, for the conditions studied here, the scalar correlation coefficient within the surface layer scales with the measurement height normalized by the ABL depth and not by the Obukhov length.
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Dosio, Alessandro, Jordi Vilá Guerau de Arellano, Albert A. M. Holtslag, and Peter J. H. Builtjes. "Relating Eulerian and Lagrangian Statistics for the Turbulent Dispersion in the Atmospheric Convective Boundary Layer." Journal of the Atmospheric Sciences 62, no. 4 (April 1, 2005): 1175–91. http://dx.doi.org/10.1175/jas3393.1.
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Abstract Eulerian and Lagrangian statistics in the atmospheric convective boundary layer (CBL) are studied by means of large eddy simulation (LES). Spectra analysis is performed in both the Eulerian and Lagrangian frameworks, autocorrelations are calculated, and the integral length and time scales are derived. Eulerian statistics are calculated by means of spatial and temporal analysis in order to derive characteristic length and time scales. Taylor’s hypothesis of frozen turbulence is investigated, and it is found to be satisfied in the simulated flow. Lagrangian statistics are derived by tracking the trajectories of numerous particles released at different heights in the turbulent flow. The relationship between Lagrangian properties (autocorrelation functions) and dispersion characteristics (particles’ displacement) is studied through Taylor’s diffusion relationship, with special emphasis on the difference between horizontal and vertical motion. Results show that for the horizontal motion, Taylor’s relationship is satisfied. The vertical motion, however, is influenced by the inhomogeneity of the flow and limited by the ground and the capping inversion at the top of the CBL. The Lagrangian autocorrelation function, therefore, does not have an exponential shape, and consequently, the integral time scale is zero. If distinction is made between free and bounded motion, a better agreement between Taylor’s relationship and the particles’ vertical displacement is found. Relationships between Eulerian and Lagrangian frameworks are analyzed by calculating the ratio β between Lagrangian and Eulerian time scales. Results show that the integral time scales are mainly constant with height for z/zi < 0.7. In the upper part of the CBL, the capping inversion transforms vertical motion into horizontal motion. As a result, the horizontal time scale increases with height, whereas the vertical one is reduced. Current parameterizations for the ratio between the Eulerian and Lagrangian time scales have been tested against the LES results showing satisfactory agreement at heights z/zi < 0.7.
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Chen, C., H. L. Read, and M. A. Escabi. "Precise Feature Based Time Scales and Frequency Decorrelation Lead to a Sparse Auditory Code." Journal of Neuroscience 32, no. 25 (June 20, 2012): 8454–68. http://dx.doi.org/10.1523/jneurosci.6506-11.2012.
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Nguyen, Vi, and Dimitrios V. Papavassiliou. "Hydrodynamic Dispersion in Porous Media and the Significance of Lagrangian Time and Space Scales." Fluids 5, no. 2 (May 21, 2020): 79. http://dx.doi.org/10.3390/fluids5020079.
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Transport in porous media is critical for many applications in the environment and in the chemical process industry. A key parameter for modeling this transport is the hydrodynamic dispersion coefficient for particles and scalars in a porous medium, which has been found to depend on properties of the medium structure, on the dispersing compound, and on the flow field characteristics. Previous studies have resulted in suggestions of different equation forms, showing the relationship between the hydrodynamic dispersion coefficient for various types of porous media in various flow regimes and the Peclet number. The Peclet number is calculated based on a Eulerian length scale, such as the diameter of the spheres in packed beds, or the pore diameter. However, the nature of hydrodynamic dispersion is Lagrangian, and it should take the molecular diffusion effects, as well as the convection effects, into account. This work shifts attention to the Lagrangian time and length scales for the definition of the Peclet number. It is focused on the dependence of the longitudinal hydrodynamic dispersion coefficient on the effective Lagrangian Peclet number by using a Lagrangian length scale and the effective molecular diffusivity. The lattice Boltzmann method (LBM) was employed to simulate flow in porous media that were constituted by packed spheres, and Lagrangian particle tracking (LPT) was used to track the movement of individual dispersing particles. It was found that the hydrodynamic dispersion coefficient linearly depends on the effective Lagrangian Peclet number for packed beds with different types of packing. This linear equation describing the dependence of the dispersion coefficient on the effective Lagrangian Peclet number is both simpler and more accurate than the one formed using the effective Eulerian Peclet number. In addition, the slope of the line is a characteristic coefficient for a given medium.
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Fung, J. C. H. "The Dependence of the Time Scale of Relative Lagrangian Motion on the Initial Separation." Journal of Applied Mechanics 65, no. 1 (March 1, 1998): 204–8. http://dx.doi.org/10.1115/1.2789027.
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Kinematic simulation of homogeneous isotropic turbulence are used to compute Lagrangian statistics of turbulence and, in particular, its time scales. The computed pseudo-Lagrangian velocity autocorrelation functions Rˆ11L(l,t) compare well with theory for a small initial separation l and short time t. We also demonstrate the feasibility of using kinematic simulation as a means of constructing Lagrangian statistics.
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Tian, Xue, and Yi Zhang. "Time-scales Herglotz type Noether theorem for delta derivatives of Birkhoffian systems." Royal Society Open Science 6, no. 11 (November 2019): 191248. http://dx.doi.org/10.1098/rsos.191248.
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The time-scales theory provides a powerful theoretical tool for studying differential and difference equations simultaneously. With regard to Herglotz type variational principle, this generalized variational principle can deal with non-conservative or dissipative problems. Combining the two tools, this paper aims to study time-scales Herglotz type Noether theorem for delta derivatives of Birkhoffian systems. We introduce the time-scales Herglotz type variational problem of Birkhoffian systems firstly and give the form of time-scales Pfaff–Herglotz action for delta derivatives. Then, time-scales Herglotz type Birkhoff’s equations for delta derivatives are derived by calculating the variation of the action. Furthermore, time-scales Herglotz type Noether symmetry for delta derivatives of Birkhoffian systems are defined. According to this definition, time-scales Herglotz type Noether identity and Noether theorem for delta derivatives of Birkhoffian systems are proposed and proved, which can become the ones for delta derivatives of Hamiltonian systems or Lagrangian systems in some special cases. Therefore, it is shown that the results of Birkhoffian formalism are more universal than Hamiltonian or Lagrangian formalism. Finally, the time-scales damped oscillator and a non-Hamiltonian Birkhoffian system are given to exemplify the superiority of the results.
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Shi, Yufei, and Yi Zhang. "Noether Theorem on Time Scales for Lagrangian Systems in Event Space." Wuhan University Journal of Natural Sciences 24, no. 4 (July 10, 2019): 295–304. http://dx.doi.org/10.1007/s11859-019-1400-z.
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Nardelli, Bruno Buongiorno. "A Novel Approach for the High-Resolution Interpolation of In Situ Sea Surface Salinity." Journal of Atmospheric and Oceanic Technology 29, no. 6 (June 1, 2012): 867–79. http://dx.doi.org/10.1175/jtech-d-11-00099.1.
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Abstract A novel technique for the high-resolution interpolation of in situ sea surface salinity (SSS) observations is developed and tested. The method is based on an optimal interpolation (OI) algorithm that includes satellite sea surface temperature (SST) in the covariance estimation. The covariance function parameters (i.e., spatial, temporal, and thermal decorrelation scales) and the noise-to-signal ratio are determined empirically, by minimizing the root-mean-square error and mean error with respect to fully independent validation datasets. Both in situ observations and simulated data extracted from a numerical model output are used to run these tests. Different filters are applied to sea surface temperature data in order to remove the large-scale variability associated with air–sea interaction, because a high correlation between SST and SSS is expected only at small scales. In the tests performed on in situ observations, the lowest errors are obtained by selecting covariance decorrelation scales of 400 km, 6 days, and 2.75°C, respectively, a noise-to-signal ratio of 0.01 and filtering the scales longer than 1000 km in the SST time series. This results in a root-mean-square error of ~0.11 g kg−1 and a mean error of ~0.01 g kg−1, that is, reducing the errors by ~25% and ~60%, respectively, with respect to the first guess.
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Ullmann, Tobias, Julia Sauerbrey, Dirk Hoffmeister, Simon Matthias May, Roland Baumhauer, and Olaf Bubenzer. "Assessing Spatiotemporal Variations of Sentinel-1 InSAR Coherence at Different Time Scales over the Atacama Desert (Chile) between 2015 and 2018." Remote Sensing 11, no. 24 (December 10, 2019): 2960. http://dx.doi.org/10.3390/rs11242960.
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This study investigates synthetic aperture radar (SAR) time series of the Sentinel-1 mission acquired over the Atacama Desert, Chile, between March 2015 and December 2018. The contribution analyzes temporal and spatial variations of Sentinel-1 interferometric SAR (InSAR) coherence and exemplarily illustrates factors that are responsible for observed signal differences. The analyses are based on long temporal baselines (365–1090 days) and temporally dense time series constructed with short temporal baselines (12–24 days). Results are compared to multispectral data of Sentinel-2, morphometric features of the digital elevation model (DEM) TanDEM-X WorldDEM™, and to a detailed governmental geographic information system (GIS) dataset of the local hydrography. Sentinel-1 datasets are suited for generating extensive, nearly seamless InSAR coherence mosaics covering the entire Atacama Desert (>450 × 1100 km) at a spatial resolution of 20 × 20 meter per pixel. Temporal baselines over several years lead only to very minor decorrelation, indicating a very high signal stability of C-Band in this region, especially in the hyperarid uplands between the Coastal Cordillera and the Central Depression. Signal decorrelation was associated with certain types of surface cover (e.g., water or aeolian deposits) or with actual surface dynamics (e.g., anthropogenic disturbance (mining) or fluvial activity and overland flow). Strong rainfall events and fluvial activity in the periods 2015 to 2016 and 2017 to 2018 caused spatial patterns with significant signal decorrelation; observed linear coherence anomalies matched the reference channel network and indicated actual episodic and sporadic discharge events. In the period 2015–2016, area-wide loss of coherence appeared as strip-like patterns of more than 80 km length that matched the prevailing wind direction. These anomalies, and others observed in that period and in the period 2017–2018, were interpreted to be caused by overland flow of high magnitude, as their spatial location matched well with documented heavy rainfall events that showed cumulative precipitation amounts of more than 20 mm.
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Genthon, Christophe. "Space–time Antarctic surface mass-balance variability from climate models." Annals of Glaciology 39 (2004): 271–75. http://dx.doi.org/10.3189/172756404781814294.
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AbstractThe interannual to interdecadal variability and space–time statistics (including radius of decorrelation) of the Antarctic surface mass balance (SMB) are evaluated from climate models and meteorological analyses. At model resolution scales (>100 km), the interannual relative standard deviation of precipitation ranges from ∼5% (remotest interior) to ∼40% and possibly more. Time variability is spatially coherent at distances of ∼500km on average, less than 300 km in the interior near ridges, but in excess of 700 km in some regions. As far as spatial distributions are concerned, interannual statistics can be broadly transposed to interdecadal time-scales. The amplitude of variability may also be extrapolated across time-scales, using a ‘white’ spectrum hypothesis according to one coupled ocean– atmosphere model, but a significantly ‘red’ spectrum hypothesis according to another. Surface sublimation and blowing-snow processes are estimated to have limited contributions to the statistics of the SMB at model-resolved scales. Precipitation statistics can thus largely be transposed to SMB. The information reported here is expected to be useful for defining the details of field programmes such as the International Trans-Antarctic Scientific Expedition (ITASE), for extrapolating the spatial significance of field SMB data and for better interpreting Antarctic ice-sheet surface elevation changes from satellite altimetry.
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Lumpkin, Rick, Anne-Marie Treguier, and Kevin Speer. "Lagrangian Eddy Scales in the Northern Atlantic Ocean." Journal of Physical Oceanography 32, no. 9 (September 1, 2002): 2425–40. http://dx.doi.org/10.1175/1520-0485-32.9.2425.
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Abstract Eddy time and length scales are calculated from surface drifter and subsurface float observations in the northern Atlantic Ocean. Outside the energetic Gulf Stream, subsurface timescales are relatively constant at depths from 700 m to 2000 m. Length scale and the characteristic eddy speed decrease with increasing depth below 700 m, but length scale stays relatively constant in the upper several hundred meters of the Gulf Stream. It is suggested that this behavior is due to the Lagrangian sampling of the mesoscale field, in limits set by the Eulerian eddy scales and the eddy kinetic energy. In high-energy regions of the surface and near-surface North Atlantic, the eddy field is in the “frozen field” Lagrangian sampling regime for which the Lagrangian and Eulerian length scales are proportional. However, throughout much of the deep ocean interior, the eddy field may be in the “fixed float” regime for which the Lagrangian and Eulerian timescales are nearly equal. This does not necessarily imply that the deep interior is nearly linear, as fixed-float sampling is possible in a flow field of O(1) nonlinearity.
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Raghukumar, Kaustubha, Grace Chang, Frank Spada, Craig Jones, Tim Janssen, and Andrew Gans. "Performance Characteristics of “Spotter,” a Newly Developed Real-Time Wave Measurement Buoy." Journal of Atmospheric and Oceanic Technology 36, no. 6 (June 2019): 1127–41. http://dx.doi.org/10.1175/jtech-d-18-0151.1.
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AbstractThe Spotter is a low-cost, real-time, solar-powered wave measurement buoy that was recently developed by Spoondrift Technologies, Inc. (Spoondrift). To evaluate the data quality of the Spotter device, we performed a series of validation experiments that included comparisons between Spotter-derived motions and prescribed wave motions (monochromatic and random waves) on a custom-built, motion-controlled validation stand and simultaneous in-water measurements using a conventional wave measurement buoy, the Datawell DWR-G4 (Datawell). Spotter evaluations included time-domain validation (i.e., wave by wave) and comparisons of wave spectra, directional moments, and bulk statistical parameters such as significant wave height, peak period, mean wave direction, and directional spread. Spotter wave measurements show excellent fidelity and lend a high degree of confidence in data quality. Overall, Spotter-derived bulk statistical parameters were within 10% of respective Datawell-derived quantities. The Spotter’s low cost and compact form factor enabled unique field deployments of multiple wave measurement buoys for direct measurements of wave characteristics such as ocean wave decorrelation length scales, wave speed, and directional spread. Wave decorrelation lengths were found to be inversely proportional to the width of the spectrum, and wave speeds compared well against linear wave theory.
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Kostrykin, S. V., A. A. Khapaev, V. M. Ponomarev, and I. G. Yakushkin. "Lagrangian structures in time-periodic vortical flows." Nonlinear Processes in Geophysics 13, no. 6 (November 14, 2006): 621–28. http://dx.doi.org/10.5194/npg-13-621-2006.
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Abstract. The Lagrangian trajectories of fluid particles are experimentally studied in an oscillating four-vortex velocity field. The oscillations occur due to a loss of stability of a steady flow and result in a regular reclosure of streamlines between the vortices of the same sign. The Eulerian velocity field is visualized by tracer displacements over a short time period. The obtained data on tracer motions during a number of oscillation periods show that the Lagrangian trajectories form quasi-regular structures. The destruction of these structures is determined by two characteristic time scales: the tracers are redistributed sufficiently fast between the vortices of the same sign and much more slowly transported into the vortices of opposite sign. The observed behavior of the Lagrangian trajectories is quantitatively reproduced in a new numerical experiment with two-dimensional model of the velocity field with a small number of spatial harmonics. A qualitative interpretation of phenomena observed on the basis of the theory of adiabatic chaos in the Hamiltonian systems is given. The Lagrangian trajectories are numerically simulated under varying flow parameters. It is shown that the spatial-temporal characteristics of the Lagrangian structures depend on the properties of temporal change in the streamlines topology and on the adiabatic parameter corresponding to the flow. The condition for the occurrence of traps (the regions where the Lagrangian particles reside for a long time) is obtained.
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Cucco, Andrea, Georg Umgiesser, Cristian Ferrarin, Angelo Perilli, Donata Melaku Canu, and Cosimo Solidoro. "Eulerian and lagrangian transport time scales of a tidal active coastal basin." Ecological Modelling 220, no. 7 (April 2009): 913–22. http://dx.doi.org/10.1016/j.ecolmodel.2009.01.008.
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Chiswell, Stephen M. "Lagrangian Time Scales and Eddy Diffusivity at 1000 m Compared to the Surface in the South Pacific and Indian Oceans." Journal of Physical Oceanography 43, no. 12 (December 1, 2013): 2718–32. http://dx.doi.org/10.1175/jpo-d-13-044.1.
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Abstract Argo floats cannot be regarded as true Lagrangian drifters because they periodically rise to the surface. Hence, previous estimates of eddy diffusivity at depth using single-particle statistics have been limited to one submerged cycle. However, unless the Lagrangian time scale is significantly shorter than the Argo cycle time, this single-particle calculation can have a large bias. Here, eddy diffusivity computed from single-particle statistics using Argo data is compared to that computed by assuming that Eulerian scales at depth are the same as at the surface, and that the relationship between Lagrangian and Eulerian time scales derived by Middleton is valid. If the methods provide the same answer, one can have confidence in both methods. Eddy diffusivity calculated from the single-particle statistics shows the same spatial structure as that computed from inferred time scale, but is smaller by a factor of about 2. It is suggested that this is because the deep Lagrangian time scale over much of the region is comparable to, or longer than, the 10-day Argo submergence cycle.
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YEUNG, P. K. "Lagrangian characteristics of turbulence and scalar transport in direct numerical simulations." Journal of Fluid Mechanics 427 (January 25, 2001): 241–74. http://dx.doi.org/10.1017/s0022112000002391.
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A study of the Lagrangian statistical properties of velocity and passive scalar fields using direct numerical simulations is presented, for the case of stationary isotropic turbulence with uniform mean scalar gradients. Data at higher grid resolutions (up to 5123 and Taylor-scale Reynolds number 234) allow an update of previous velocity results at lower Reynolds number, including intermittency and dimensionality effects on vorticity time scales. The emphasis is on Lagrangian scalar time series which are new to the literature and important for stochastic mixing models. The variance of the ‘total’ Lagrangian scalar value (ϕ˜+, combining contributions from both mean and fluctuations) grows with time, with the velocity–scalar cross-correlation function and fluid particle displacements playing major roles. The Lagrangian increment of ϕ˜+ conditioned upon velocity and scalar fluctuations is well represented by a linear regression model whose parameters depend on both Reynolds number and Schmidt number. The Lagrangian scalar fluctuation is non-Markovian and has a longer time scale than the velocity, which is due to the strong role of advective transport, and is in contrast to results in an Eulerian frame where the scalars have shorter time scales. The scalar dissipation is highly intermittent and becomes de-correlated in time more rapidly than the energy dissipation. Differential diffusion for scalars with Schmidt numbers between 1/8 and 1 is characterized by asymmetry in the two-scalar cross-correlation function, a shorter time scale for the difference between two scalars, as well as a systematic decrease in the Lagrangian coherency spectrum up to at least the Kolmogorov frequency. These observations are consistent with recent work suggesting that differential diffusion remains important in the small scales at high Reynolds number.
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Fasoli, Benjamin, John C. Lin, David R. Bowling, Logan Mitchell, and Daniel Mendoza. "Simulating atmospheric tracer concentrations for spatially distributed receptors: updates to the Stochastic Time-Inverted Lagrangian Transport model's R interface (STILT-R version 2)." Geoscientific Model Development 11, no. 7 (July 13, 2018): 2813–24. http://dx.doi.org/10.5194/gmd-11-2813-2018.
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Abstract. The Stochastic Time-Inverted Lagrangian Transport (STILT) model is comprised of a compiled Fortran executable that carries out advection and dispersion calculations as well as a higher-level code layer for simulation control and user interaction, written in the open-source data analysis language R. We introduce modifications to the STILT-R code base with the aim to improve the model's applicability to fine-scale (< 1 km) trace gas measurement studies. The changes facilitate placement of spatially distributed receptors and provide high-level methods for single- and multi-node parallelism. We present a kernel density estimator to calculate influence footprints and demonstrate improvements over prior methods. Vertical dilution in the hyper near field is calculated using the Lagrangian decorrelation timescale and vertical turbulence to approximate the effective mixing depth. This framework provides a central source repository to reduce code fragmentation among STILT user groups as well as a systematic, well-documented workflow for users. We apply the modified STILT-R to light-rail measurements in Salt Lake City, Utah, United States, and discuss how results from our analyses can inform future fine-scale measurement approaches and modeling efforts.
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Ruzanski, Evan, and V. Chandrasekar. "An Investigation of the Short-Term Predictability of Precipitation Using High-Resolution Composite Radar Observations." Journal of Applied Meteorology and Climatology 51, no. 5 (May 2012): 912–25. http://dx.doi.org/10.1175/jamc-d-11-069.1.
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AbstractThe short-term predictability of precipitation patterns observed by meteorological radar is an important concept as it establishes a means to characterize precipitation and provides an upper limit on the extent of useful nowcasting. Predictability also varies on the basis of spatial and temporal scales of the observed meteorological phenomena. This paper describes an investigation of the short-term predictability of precipitation patterns containing microalpha (0.2–2 km) to mesobeta (20–200 km) scales using high-resolution (0.5 km–1 min–1 dBZ) composite radar reflectivity data, extending the analysis presented in previous work to smaller space and time scales. An experimental approach is used in which continuous and categorical lifetimes of radar reflectivity fields in Eulerian and Lagrangian space are used to quantify short-term predictability. The space–time scale dependency of short-term predictability is analyzed, and a practical upper limit on the extent of Lagrangian persistence-based nowcasting is estimated. Connections to the predictability of larger scales are made within the context of previous work. The results show that short-term predictability estimates in terms of lifetime are approximately 14–15 and 20–21 min in Eulerian and Lagrangian space, respectively, and suggest that a linear relationship exists between predictability and space–time structure from microalpha to macrobeta (2000–10 000 km) scales.
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Zhai, Xiang-Hua, and Yi Zhang. "Lie symmetry analysis on time scales and its application on mechanical systems." Journal of Vibration and Control 25, no. 3 (August 7, 2018): 581–92. http://dx.doi.org/10.1177/1077546318790864.
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The theory of time scales that can unify and extend continuous and discrete analysis has proved to be more accurate in modeling the dynamic process. The Lie symmetry approach, which is an effective way to deal with different kinds of dynamical equations in a variety of areas of applied science, is to be analyzed on time scales. We begin with the Lie group of point infinitesimal transformations on time scales and its corresponding extensions. And the invariance of dynamical equations on time scales under the infinitesimal transformations is discussed. More specifically, the Lie symmetries for dynamical equations of mechanical systems on time scales including Lagrangian systems on time scales, Hamiltonian systems on time scales, and Birkhoffian systems on time scales are investigated as applications. Thus, the corresponding conserved quantities for mechanical systems on time scales are derived by using the Lie symmetries. Examples are given to illustrate the application of the results.
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Bouzaiene, Maher, Milena Menna, Pierre-Marie Poulain, and Dalila Elhmaidi. "Lagrangian Dispersion Characteristics in The Western Mediterranean." Journal of Marine Research 76, no. 5 (September 1, 2018): 139–61. http://dx.doi.org/10.1357/002224018826473290.
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Dispersion characteristics in the Western Mediterranean are analyzed using data from Coastal Ocean Dynamics Experiment (CODE) and Surface Velocity Program (SVP) surface drifters deployed in the period 1986–2017. Results are presented in terms of absolute dispersion A2 (mean-squared displacement of drifter individuals) and of relative dispersion (D2; mean square separation distance of drifter pairs). Moreover, the dispersion characteristics are estimated for different initial separation distances (D0) between particles: smaller, larger, or comparable with the internal Rossby radius of deformation. Results show the presence of a quasiballistic regime for absolute dispersion at small time scales and the nonlocal relative dispersion regime related to the submesoscale activities for scales smaller than the internal Rossby radius. At intermediate times, two anomalous absolute dispersion regimes (elliptic and hyperbolic regimes) related with the flow topology are observed, although the relative dispersion involves the Richardson and shear/ballistic regimes only for D0 smaller than the Rossby radius. During the subsequent 20–30 days, absolute dispersion shows quasirandom walk regime and relative dispersion follows the diffusive regime for scales larger than 100 km for which pair velocities are uncorrelated.
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Berndtsson, Ronny, Kenji Jinno, Akira Kawamura, Magnus Larson, and Janusz Niemczynowicz. "Some Eulerian and Lagrangian statistical properties of rainfall at small space-time scales." Journal of Hydrology 153, no. 1-4 (January 1994): 339–55. http://dx.doi.org/10.1016/0022-1694(94)90198-8.
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Oesterlé, Benoit, and Leonid I. Zaichik. "On Lagrangian time scales and particle dispersion modeling in equilibrium turbulent shear flows." Physics of Fluids 16, no. 9 (July 29, 2004): 3374–84. http://dx.doi.org/10.1063/1.1773844.
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Luo, Jian-ping, Zhi-ming Lu, and Yu-lu Liu. "Lagrangian time scales and its relationship to Eulerian equivalents in turbulent channel flow." Journal of Shanghai University (English Edition) 14, no. 1 (February 2010): 71–75. http://dx.doi.org/10.1007/s11741-010-0114-1.
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Piecuch, Christopher G., and Tatiana A. Rynearson. "Quantifying Dispersal and Connectivity of Surface Waters Using Observational Lagrangian Measurements." Journal of Atmospheric and Oceanic Technology 29, no. 8 (August 1, 2012): 1127–38. http://dx.doi.org/10.1175/jtech-d-11-00172.1.
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Abstract Probability distribution functions of displacement are central to Lagrangian statistics and the study of fluid dispersal. A method for computing marginal probability distributions of passive tracer dispersal from Lagrangian observations is developed. Using a pseudotrack approach, probability distributions for the domain of occupation and transit time are developed, complimenting more frequently used bulk statistics for average transit time and overall crossing probability. To demonstrate application of this technique to observations, likelihoods and time scales of dispersal from the Gulf Stream to the Azores are quantified using World Ocean Circulation Experiment (WOCE) Surface Velocity Program (SVP) near-surface drifter data for the years 1992–2008. Over observable time scales, the transit of a particle in the near-surface ocean from the Gulf Stream to the Azores occurs across a spectrum of time scales, from tens to hundreds of days, with an overall likelihood of 42% ± 4% and a mean time scale of 321 ± 41 days. The exclusion of measurements from drifters released after 1 January 2004 (which have been shown to potentially exhibit bias) slightly increases the overall likelihood of connection (49% ± 6%), consistent with recent surface current shifts in the northern North Atlantic, and increases the mean connection time scale (371 ± 52 days), potentially reflecting spurious acceleration of drifters in recent years. The method presented is general and applicable to a wide range of applications in physical and ecological oceanography.
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McClean, Julie L., Pierre-Marie Poulain, Jimmy W. Pelton, and Mathew E. Maltrud. "Eulerian and Lagrangian Statistics from Surface Drifters and a High-Resolution POP Simulation in the North Atlantic." Journal of Physical Oceanography 32, no. 9 (September 1, 2002): 2472–91. http://dx.doi.org/10.1175/1520-0485-32.9.2472.
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Abstract Eulerian and Lagrangian statistics were calculated from the North Atlantic surface drifter dataset for the years 1993–97 and a high-resolution eddy-resolving configuration of the Los Alamos National Laboratory (LANL) Parallel Ocean Program (POP) model. The main purpose of the study was to statistically quantify the state of the surface circulation in the North Atlantic Ocean for this period and compare it with the equivalent modeled state. Diffusivities and time and length scales are anisotropic over most of the ocean basin, except in most of the subpolar regions. Typical time and length scales are 2–4 days and 20–50 km. Longest timescales are found in the energetically quiescent regions in the south and southeast sectors of the basin. The longest length scales are found in the energetic western boundary current system, the most dispersive region of the domain. In many respects the eddy-resolving model reproduced a surface circulation in good statistical agreement with that depicted by the drifters. Model time and length scales were also anisotropic, with typical timescales of 2–4 days and length scales of 20–50 km in the zonal direction, and 30–50 km in the meridional direction. An eddy-permitting POP simulation produced unrealistic time and length scales that were too long and too short relative to the drifter scales; these were attributed to the model being too stable hydrodynamically.
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Good, P., C. Giannakopoulos, F. M. O’Connor, S. R. Arnold, M. de Reus, and H. Schlager. "Constraining tropospheric mixing timescales using airborne observations and numerical models." Atmospheric Chemistry and Physics Discussions 3, no. 2 (March 5, 2003): 1213–45. http://dx.doi.org/10.5194/acpd-3-1213-2003.
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Abstract. A technique is demonstrated for estimating atmospheric mixing time-scales from in-situ data, using a Lagrangian model initialised from an Eulerian chemical transport model (CTM). This method is applied to airborne tropospheric CO observations taken during seven flights of the Mediterranean Intensive Oxidant Study (MINOS) campaign, of August 2001. The time-scales derived, correspond to mixing applied at the spatial scale of the CTM grid. Specifically, they are upper bound estimates of the mix-down lifetime that should be imposed for a Lagrangian model to reproduce the observed small-scale tracer structure. They are relevant to the family of hybrid Lagrangian-Eulerian models, which impose Eulerian grid mixing to an underlying Lagrangian model. The method uses the fact that in Lagrangian tracer transport modelling, the mixing spatial and temporal scales are decoupled: the spatial scale is determined by the resolution of the initial tracer field, and the time scale by the trajectory length. The chaotic nature of lower-atmospheric advection results in the continuous generation of smaller spatial scales, a process terminated in the real atmosphere by mixing. Thus, a mix-down lifetime can be estimated by varying trajectory length so that the model reproduces the observed amount of small-scale tracer structure. Selecting a trajectory length is equivalent to choosing a mixing timescale. For the cases studied, the results are very insensitive to CO photochemical change calculated along the trajectories. The method is most appropriate for relatively homogeneous regions, i.e. it is not too important to account for changes in aircraft altitude or the positioning of stratospheric intrusions, so that small scale structure is easily distinguished. The chosen flights showed a range of mix-down time upper limits: 1 and 3 days for 8 August and 3 August, due to recent convective and boundary layer mixing respectively, and 7–9 days for 16, 17, 22a, 22c and 24 August. For the flight of 3 August, the observed concentrations result from a complex set of transport histories, and the models are used to interpret the observed structure, while illustrating where more caution is required with this method of estimating mix-down lifetimes.
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YEUNG, P. K., and BRIAN L. SAWFORD. "Random-sweeping hypothesis for passive scalars in isotropic turbulence." Journal of Fluid Mechanics 459 (May 25, 2002): 129–38. http://dx.doi.org/10.1017/s0022112002008248.
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The hypothesis of the small scales being passively swept along by the large-scale motions in turbulent flow is extended to passive scalars in isotropic turbulence. A theory based on strong mutual cancellation between local and advective derivatives and other assumptions is shown to capture the Reynolds and Schmidt number dependence of time scales characterizing Eulerian and Lagrangian rates of change. Agreement with direct numerical simulation data improves systematically with increasing Reynolds number. In accordance with the physics of random sweeping, the Eulerian frequency spectrum is very similar in shape to the wavenumber spectrum, but is broadened at higher frequencies compared to its Lagrangian counterpart. Overall the hypothesis appears to be even more valid for transported scalars than for the velocity field, which gives support to the use of Lagrangian approaches in the study of turbulent mixing.
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Di Bernardino, Annalisa, Paolo Monti, Giovanni Leuzzi, and Giorgio Querzoli. "Eulerian and Lagrangian time scales of the turbulence above staggered arrays of cubical obstacles." Environmental Fluid Mechanics 20, no. 4 (January 23, 2020): 987–1005. http://dx.doi.org/10.1007/s10652-020-09736-8.
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Sukhatme, Jai. "Lagrangian Velocity Correlations and Absolute Dispersion in the Midlatitude Troposphere." Journal of the Atmospheric Sciences 62, no. 10 (October 1, 2005): 3831–36. http://dx.doi.org/10.1175/jas3560.1.
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Abstract Employing daily wind data from the ECMWF, passive particle advection is performed to estimate the Lagrangian velocity correlation functions (LVCF) associated with the midlatitude tropospheric flow. In particular, the velocity field is decomposed into time mean and transient (or eddy) components to better understand the nature of the LVCFs. A closely related quantity, the absolute dispersion (AD), is also examined. Given the anisotropy of the flow, meridional and zonal characteristics are considered separately. The zonal LVCF is seen to be nonexponential. In fact, for intermediate time scales it can either be interpreted as a power law of the form τ−α with 0 < α < 1 or as the sum of exponentials with differing time scales—both interpretations being equivalent. More importantly the long time correlations in the zonal flow result in a superdiffusive zonal AD regime. On the other hand, the meridional LVCF decays rapidly to zero. Before approaching zero the meridional LVCF shows a region of negative correlation—a consequence of the presence of planetary-scale Rossby waves. As a result the meridional AD, apart from showing the classical asymptotic ballistic and diffusive regimes, displays transient subdiffusive behavior.
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Seuront, L., F. Schmitt, D. Schertzer, Y. Lagadeuc, and S. Lovejoy. "Multifractal intermittency of Eulerian and Lagrangian turbulence of ocean temperature and plankton fields." Nonlinear Processes in Geophysics 3, no. 4 (December 31, 1996): 236–46. http://dx.doi.org/10.5194/npg-3-236-1996.
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Abstract. In this paper, we present evidence that intermittency of Eulerian and Lagrangian turbulence of ocean temperature and plankton fields is multifractal and furthermore can be analysed with the help of universal multifractals. We analyse time series of temperature and in vivo fluorescence taken from a drifter in the mixed coastal waters of the eastern English Channel. Two analysis techniques are used to compute the fundamental universal multifiractal parameters, which describe all the statistics of the turbulent fluctuations: the analysis of the scale invariant structure function exponent ζ(q) and the Double Trace Moment technique. At small scales, we do not detect any significant difference between the universal multifiractal behavior of temperature and fluorescence in an Eulerian framework. This supports the hypothesis that the latter is passively advected with the flow as the former. On the one hand, we show that large scale measurements are Lagrangian and indeed we obtain for temperature fluctuations a ω2 power spectrum corresponding to the theoretical scaling of a Lagrangian passive scalar. Furthermore, we show that Lagrangian temperature fluctuations are multiscaling and intermittent. On the other hand, the flatter slope at large scales of the fluorescence power spectrum points out that the plankton is at these scales a "biologically active" scalar.
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YANG, YUE, and D. I. PULLIN. "Geometric study of Lagrangian and Eulerian structures in turbulent channel flow." Journal of Fluid Mechanics 674 (March 2, 2011): 67–92. http://dx.doi.org/10.1017/s0022112010006427.
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We report the detailed multi-scale and multi-directional geometric study of both evolving Lagrangian and instantaneous Eulerian structures in turbulent channel flow at low and moderate Reynolds numbers. The Lagrangian structures (material surfaces) are obtained by tracking the Lagrangian scalar field, and Eulerian structures are extracted from the swirling strength field at a time instant. The multi-scale and multi-directional geometric analysis, based on the mirror-extended curvelet transform, is developed to quantify the geometry, including the averaged inclination and sweep angles, of both structures at up to eight scales ranging from the half-height δ of the channel to several viscous length scales δν. Here, the inclination angle is on the plane of the streamwise and wall-normal directions, and the sweep angle is on the plane of streamwise and spanwise directions. The results show that coherent quasi-streamwise structures in the near-wall region are composed of inclined objects with averaged inclination angle 35°–45°, averaged sweep angle 30°–40° and characteristic scale 20δν, and ‘curved legs’ with averaged inclination angle 20°–30°, averaged sweep angle 15°–30° and length scale 5δν–10δν. The temporal evolution of Lagrangian structures shows increasing inclination and sweep angles with time, which may correspond to the lifting process of near-wall quasi-streamwise vortices. The large-scale structures that appear to be composed of a number of individual small-scale objects are detected using cross-correlations between Eulerian structures with large and small scales. These packets are located at the near-wall region with the typical height 0.25δ and may extend over 10δ in the streamwise direction in moderate-Reynolds-number, long channel flows. In addition, the effects of the Reynolds number and comparisons between Lagrangian and Eulerian structures are discussed.
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Good, P., C. Giannakopoulos, F. M. O’Connor, S. R. Arnold, M. de Reus, and H. Schlager. "Constraining tropospheric mixing timescales using airborne observations and numerical models." Atmospheric Chemistry and Physics 3, no. 4 (July 16, 2003): 1023–35. http://dx.doi.org/10.5194/acp-3-1023-2003.
Full textAbstract:
Abstract. A technique is demonstrated for estimating atmospheric mixing time-scales from in-situ data, using a Lagrangian model initialised from an Eulerian chemical transport model (CTM). This method is applied to airborne tropospheric CO observations taken during seven flights of the Mediterranean Intensive Oxidant Study (MINOS) campaign, of August 2001. The time-scales derived, correspond to mixing applied at the spatial scale of the CTM grid. They are relevant to the family of hybrid Lagrangian-Eulerian models, which impose Eulerian grid mixing to an underlying Lagrangian model. The method uses the fact that in Lagrangian tracer transport modelling, the mixing spatial and temporal scales are decoupled: the spatial scale is determined by the resolution of the initial tracer field, and the time scale by the trajectory length. The chaotic nature of lower-atmospheric advection results in the continuous generation of smaller spatial scales, a process terminated in the real atmosphere by mixing. Thus, a mix-down lifetime can be estimated by varying trajectory length so that the model reproduces the observed amount of small-scale tracer structure. Selecting a trajectory length is equivalent to choosing a mixing timescale. For the cases studied, the results are very insensitive to CO photochemical change calculated along the trajectories. That is, it was found that if CO was treated as a passive tracer, this did not affect the mix-down timescales derived, since the slow CO photochemistry does not have much influence at small spatial scales. The results presented correspond to full photochemical calculations. The method is most appropriate for relatively homogeneous regions, i.e. it is not too important to account for changes in aircraft altitude or the positioning of stratospheric intrusions, so that small scale structure is easily distinguished. The chosen flights showed a range of mix-down time upper limits: a very short timescale of 1 day for 8 August, due possibly to recent convection or model error, 3 days for 3 August, probably due to recent convective and boundary layer mixing, and 6-9 days for 16, 17, 22a, 22c and 24 August. These numbers refer to a mixing spatial scale of 2.8°, defined here by the resolution of the Eulerian grid from which tracer fields were interpolated to initialise the Lagrangian model. For the flight of 3 August, the observed concentrations result from a complex set of transport histories, and the models are used to interpret the observed structure, while illustrating where more caution is required with this method of estimating mix-down lifetimes.