Relevant bibliographies by topics / Turbulence Eigenfunctions

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Academic literature on the topic 'Turbulence Eigenfunctions'

Author: Grafiati
Published: 4 June 2021
Last updated: 18 February 2022

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Journal articles on the topic "Turbulence Eigenfunctions"

1

Wai, OWH, and KW Bedford. "Empirical orthogonal functional analysis of sediment concentration profiles subjected to waves and currents." Marine and Freshwater Research 46, no. 1 (1995): 373. http://dx.doi.org/10.1071/mf9950373.

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Spatial and temporal eigenfunctions for profiles of suspended-sediment concentrations collected during three distinct flow conditions (current-dominated, wave-dominated, and wave- current-dominated) were used to study the non-linear sediment dynamics in the water column. The eigenfunctions were obtained by the method of Empirical Orthogonal Function (EOF) analysis. The variance distribution of the first spatial eigenfunction associated with the largest eigenvalue reflects the characteristic structure of the original profiles, and the second largest spatial eigenfunction indicates the location of possible structural or boundary layer changes in the profiles. The first temporal eigenfunctions for the current- and wave-driven profiles correlate with the turbulence-wave kinetic energy. Because of the complexity of the wave-current flow field, the first two temporal eigenfunctions for the wave-current-driven profiles have a weak relation with the major driving forces. Orthogonal functions can be used to reconstruct sediment concentration profiles efficiently and accurately. To reconstruct 97% of the variation of 10-min averaged profiles in a 2-h data record, only two eigenvalues, and their corresponding orthogonal functions are required, even in the complex wave-current flow field.
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MANDAL, A. C., L. VENKATAKRISHNAN, and J. DEY. "A study on boundary-layer transition induced by free-stream turbulence." Journal of Fluid Mechanics 660 (July 15, 2010): 114–46. http://dx.doi.org/10.1017/s0022112010002600.

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Boundary-layer transition at different free-stream turbulence levels has been investigated using the particle-image velocimetry technique. The measurements show organized positive and negative fluctuations of the streamwise fluctuating velocity component, which resemble the forward and backward jet-like structures reported in the direct numerical simulation of bypass transition. These fluctuations are associated with unsteady streaky structures. Large inclined high shear-layer regions are also observed and the organized negative fluctuations are found to appear consistently with these inclined shear layers, along with highly inflectional instantaneous streamwise velocity profiles. These inflectional velocity profiles are similar to those in the ribbon-induced boundary-layer transition. An oscillating-inclined shear layer appears to be the turbulent spot-precursor. The measurements also enabled to compare the actual turbulent spot in bypass transition with the simulated one. A proper orthogonal decomposition analysis of the fluctuating velocity field is carried out. The dominant flow structures of the organized positive and negative fluctuations are captured by the first few eigenfunction modes carrying most of the fluctuating energy. The similarity in the dominant eigenfunctions at different Reynolds numbers suggests that the flow prevails its structural identity even in intermittent flows. This analysis also indicates the possibility of the existence of a spatio-temporal symmetry associated with a travelling wave in the flow.
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Böberg, L., and U. Brosa. "Onset of Turbulence in a Pipe." Zeitschrift für Naturforschung A 43, no. 8-9 (September 1, 1988): 697–726. http://dx.doi.org/10.1515/zna-1988-8-901.

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AbstractTurbulence in a pipe is derived directly from the Navier-Stokes equation. Analysis of numerical simulations revealed that small disturbances called 'mothers' induce other much stronger disturbances called 'daughters'. Daughters determine the look of turbulence, while mothers control the transfer of energy from the basic flow to the turbulent motion. From a practical point of view, ruling mothers means ruling turbulence. For theory, the mother-daughter process represents a mechanism permitting chaotic motion in a linearly stable system. The mechanism relies on a property of the linearized problem according to which the eigenfunctions become more and more collinear as the Reynolds number increases. The mathematical methods are described, comparisons with experiments are made, mothers and daughters are analyzed, also graphically, with full particulars, and the systematic construction of small systems of differential equations to mimic the non-linear process by means as simple as possible is explained. We suggest that more then 20 but less than 180 essential degrees of freedom take part in the onset of turbulence.
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Lienhard, J. H., and I. Catton. "Heat Transfer Across a Two-Fluid-Layer Region." Journal of Heat Transfer 108, no. 1 (February 1, 1986): 198–205. http://dx.doi.org/10.1115/1.3246887.

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Heat transfer across a two-fluid-layer region is calculated for Rayleigh numbers in excess of the critical value. The method of solution is based on Landau’s comments regarding the onset of turbulence, following Malkus and others. The linear stability problem is solved for its eigenvalues and eigenfunctions, and the eigenfunctions are used to calculate the contribution of secondary motion to heat transfer. Results are obtained in terms of an overall Nusselt number as a function of Rayleigh number, midlayer thickness, and midlayer thermal conductivity.
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Esler, J. G., and T. L. Ashbee. "Universal statistics of point vortex turbulence." Journal of Fluid Mechanics 779 (August 14, 2015): 275–308. http://dx.doi.org/10.1017/jfm.2015.410.

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A new methodology, based on the central limit theorem, is applied to describe the statistical mechanics of two-dimensional point vortex motion in a bounded container $\mathscr{D}$, as the number of vortices $N$ tends to infinity. The key to the approach is the identification of the normal modes of the system with the eigenfunction solutions of the so-called hydrodynamic eigenvalue problem of the Laplacian in $\mathscr{D}$. The statistics of the projection of the vorticity distribution onto these eigenfunctions (‘vorticity projections’) are then investigated. The statistics are used first to obtain the density-of-states function and caloric curve for the system, generalising previous results to arbitrary (neutral) distributions of vortex circulations. Explicit expressions are then obtained for the microcanonical (i.e. fixed energy) probability density functions of the vorticity projections in a form that can be compared directly with direct numerical simulations of the dynamics. The energy spectra of the resulting flows are predicted analytically. Ensembles of simulations with $N=100$, in several conformal domains, are used to make a comprehensive validation of the theory, with good agreement found across a broad range of energies. The probability density function of the leading vorticity projection is of particular interest because it has a unimodal distribution at low energy and a bimodal distribution at high energy. This behaviour is indicative of a phase transition, known as Onsager–Kraichnan condensation in the literature, between low-energy states with no mean flow in the domain and high-energy states with a coherent mean flow. The critical temperature for the phase transition, which depends on the shape but not the size of $\mathscr{D}$, and the associated critical energy are found. Finally the accuracy and the extent of the validity of the theory, at finite $N$, are explored using a Markov chain phase-space sampling method.
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Nizamova, A. D., V. N. Kireev, and S. F. Urmancheev. "Research of eigenfuctions perturbation of the transverse component velocity thermoviscous liquids flow." Multiphase Systems 14, no. 2 (2019): 132–37. http://dx.doi.org/10.21662/mfs2019.2.018.

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The viscous model fluid flow in a plane channel with a linear temperature profile is considered. The problem of the thermoviscous fluid flow stability is solved on the basis of the previously obtained generalized Orr–Sommerfeld equation by the spectral method of decomposition into Chebyshev polynomials. We study the effect of taking into account the linear and exponential dependences of the viscosity of a liquid on temperature on the eigenfunctions of the hydrodynamic stability equation and on perturbations of the transverse velocity of an incompressible fluid in a plane channel when various wall temperatures are specified. Eigenfunctions are found numerically for two eigenvalues of the linear and exponential dependence of viscosity on temperature. Presented pictures of their own functions. The eigenfunctions demonstrate the behavior of the transverse velocity perturbations, their possible growth or attenuation over time. For the given eigenfunctions, perturbations of the transverse flow velocity of a thermoviscous fluid are obtained. It is shown that taking the temperature dependence of viscosity into account affects the eigenfunctions of the equations of hydrodynamic stability and perturbations of the transverse flow velocity. Perturbations of the transverse velocity significantly affect the hydrodynamic instability of the fluid flow. The results show that when considering the unstable eigenvalue over time, the velocity perturbations begin to grow, which leads to turbulence of the flow. The maximum values of the eigenfunctions and perturbations of the transverse velocities are shifted to the hot wall. It is seen that for an unstable eigenvalue, the perturbations of the transverse flow velocity increase over time, and for a stable one, they decay.
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GIBSON, J. F., J. HALCROW, and P. CVITANOVIĆ. "Visualizing the geometry of state space in plane Couette flow." Journal of Fluid Mechanics 611 (September 25, 2008): 107–30. http://dx.doi.org/10.1017/s002211200800267x.

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Motivated by recent experimental and numerical studies of coherent structures in wall-bounded shear flows, we initiate a systematic exploration of the hierarchy of unstable invariant solutions of the Navier–Stokes equations. We construct a dynamical 105-dimensional state-space representation of plane Couette flow at Reynolds number Re = 400 in a small periodic cell and offer a new method of visualizing invariant manifolds embedded in such high dimensions. We compute a new equilibrium solution of plane Couette flow and the leading eigenvalues and eigenfunctions of known equilibria at this Re and cell size. What emerges from global continuations of their unstable manifolds is a surprisingly elegant dynamical-systems visualization of moderate-Re turbulence. The invariant manifolds partially tessellate the region of state space explored by transiently turbulent dynamics with a rigid web of symmetry-induced heteroclinic connections.
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Pirozzoli, Sergio, Davide Modesti, Paolo Orlandi, and Francesco Grasso. "Turbulence and secondary motions in square duct flow." Journal of Fluid Mechanics 840 (February 14, 2018): 631–55. http://dx.doi.org/10.1017/jfm.2018.66.

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We study turbulent flows in pressure-driven ducts with square cross-section through direct numerical simulation in a wide enough range of Reynolds number to reach flow conditions which are representative of fully developed turbulence ($Re_{\unicode[STIX]{x1D70F}}\approx 1000$). Numerical simulations are carried out over very long integration times to get adequate convergence of the flow statistics, and specifically to achieve high-fidelity representation of the secondary motions which arise. The intensity of the latter is found to be on the order of 1 %–2 % of the bulk velocity, and approximately unaffected by Reynolds number variation, at least in the range under scrutiny. The smallness of the mean convection terms in the streamwise vorticity equation points to a simple characterization of the secondary flows, which in the asymptotic high-$Re$ regime are approximated with good accuracy by eigenfunctions of the Laplace operator, in the core part of the duct. Despite their effect of redistributing the wall shear stress along the duct perimeter, we find that secondary motions do not have a large influence on the bulk flow properties, and the streamwise velocity field can be characterized with good accuracy as resulting from the superposition of four flat walls in isolation. As a consequence, we find that parametrizations based on the hydraulic diameter concept, and modifications thereof, are successful in predicting the duct friction coefficient.
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Knorr, George. "Symmetries in hydrodynamic turbulence and MHD dynamo theory." Journal of Plasma Physics 56, no. 3 (December 1996): 391–406. http://dx.doi.org/10.1017/s002237780001936x.

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The three-dimensional equations of ideal hydrodynamics and ideal MHD are expanded in eigenfunctions of the curl, and the resulting basic interactions of these nonlinear systems are analysed. As the equations are invariant under time and amplitude reversal, a criterion defining the arrow of time is introduced. A new parameter, the center of energy, serves to characterize a basic interaction. In the 3D Euler equations we find four different interactions and their mirror images, two of which can transport energy to smaller wavenumbers. This can lead to the appearance of structures in turbulent flow, and throws doubt on a derivation of Kolmogorov's law based on a cascading of energy to higher wavenumbers.In energy the corresponding two-dimensional equations, which are isomorphic to the guiding centre model in plasma physics, only one interaction exists, with a strong inverse cascade, which can lead to accumulation of energy in the spatially largest accessible modes. In MHD theory it is possible to separate magnetic from kinetic interactions. The former give again four basic interactions, two being regular and two being inverse cascades. One of these is quite strong, and can lead to the MHD dynamo effect. Kinetic energy can be transferred into magnetic energy. The dynamo effect is is accompanied by alignment of velocity and magnetic fields. We show that stationary velocity fields may lead to exponentially growing magnetic fields and we give an explicit criterion for this instability.
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Gohardehi, Siavash, Saeed Arablu, Hossein Afshin, and Bijan Farhanieh. "Investigation of the effect of turbulence intensity and nozzle exit boundary layer thickness on stability pattern of subsonic jet." Mechanics & Industry 20, no. 1 (2019): 103. http://dx.doi.org/10.1051/meca/2018041.

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In this study, factors affecting the noise generation by instability waves in a subsonic jet with acoustic Mach number of 0.5 are investigated using linear stability analysis. The base flow required for instability analysis is obtained by modeling the jet stream based on the k-ε turbulence model and using the empirical coefficients suggested by Thies and Tam [1]. The resulting base flow profiles are used to solve the linear instability equation, which governs the pressure perturbation for obtaining the eigenvalues and eigenfunctions. The results of linear instability analysis for phase and amplitude of pressure fluctuations are compared against the existing experimental data, which demonstrated the validity of the conducted instability analysis. The effects of turbulence intensity and thickness of the boundary layer at the jet nozzle exit on the results of the linear instability analysis are investigated. The results show that as the turbulence intensity at nozzle exit increases, the frequency range for which the spatial growth rates are positive grows smaller, and except for very low frequencies, this leads to decreased growth rates in both axisymmetric and first azimuthal modes. Also, in both of these modes, an increase in the thickness of the boundary layer at nozzle exit leads to a decrease in perturbation's growth rates in the surveyed frequency ranges.
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Dissertations / Theses on the topic "Turbulence Eigenfunctions"

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Oxberry, Geoffrey M. "Elucidation of the time scales of coherent structures in Newtonian turbulent channel flows through Karhunen-Loeve analysis." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 87 p, 2006. http://proquest.umi.com/pqdweb?did=1203585611&sid=2&Fmt=2&clientId=8331&RQT=309&VName=PQD.

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SAKAI, Yasuhiko, Nobuhiko TANAKA, and Takehiro KUSHIDA. "On the Development of Coherent Structure in a Plane Jet (Part1, Characteristics of Two-Point Velocity Correlation and Analysis of Eigenmodes by the KL Expansion)." The Japan Society of Mechanical Engineers, 2006. http://hdl.handle.net/2237/9011.

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Book chapters on the topic "Turbulence Eigenfunctions"

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Sirovich, Lawrence. "Empirical Eigenfunctions and Low Dimensional Systems." In New Perspectives in Turbulence, 139–63. New York, NY: Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4612-3156-1_5.

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Rempfer, D. "On dynamical systems obtained via Galerkin projections onto low-dimensional bases of eigenfunctions." In Fundamental Problematic Issues in Turbulence, 233–45. Basel: Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8689-5_24.

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Henningson, Dan S. "An Eigenfunction Expansion of Localized Disturbances." In Advances in Turbulence 3, 162–69. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-84399-0_18.

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Sirovich, L., M. Maxey, and H. Tarman. "An Eigenfunction Analysis of Turbulent Thermal Convection." In Turbulent Shear Flows 6, 68–77. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-73948-4_7.

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Rajaee, Mojtaba, Sture K. F. Karlsson, and Lawrence Sirovich. "Free shear flow coherent structures in a low-dimensional eigenfunction space." In Eddy Structure Identification in Free Turbulent Shear Flows, 261–67. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-2098-2_23.

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Conference papers on the topic "Turbulence Eigenfunctions"

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Wang, Yue, Wei-Hua Cai, Tong-Zhou Wei, Lu Wang, and Feng-Chen Li. "Experimental Study on Two-Oscillating Grid Turbulence With Polymer Additives." In ASME/JSME/KSME 2015 Joint Fluids Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/ajkfluids2015-7904.

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In order to investigate the polymer effect on grid turbulence, the experiments study on grid turbulence has been built based on Particle Image Velocimetry. The Newtonian fluid flow and 200ppm polymer solution flow in grid turbulence were carried out at different grid oscillating frequency, such as 5Hz, 7.5Hz, 10Hz and 12.5Hz. The experimental results show that the viscous dissipation rate and vortex vector ωz is smaller and more regular in space distribution in polymer solution case at grid oscillating frequency with 5Hz. It indicates that the existence of polymer additives inhibits enormously the viscous dissipation rate and vortex vector, but this phenomenon can be attenuated with the increase of grid oscillating frequency. From this result, it shows that there exists a critical Reynolds number for the inhibition of polymer effect, which is the same as that in turbulent channel flows with polymers. Then, proper orthogonal decomposition (POD) has been used to extract coherent structures in grid turbulence. It is found that it needs 24 and 4 POD eigenfunctions to examine coherent structure in the Newtonian fluid and the polymer solution cases respectively at grid oscillating frequency with 10Hz. It suggests that the coherent structures can be inhibited due to the existence of polymers so as to the flow field to be more regular. But, with the increase of grid oscillating frequency, the number of POD eigenfunctions for the Newtonian fluid case and the polymer solution case respectively are approaching the same. Through this analysis, it can be also seen that the inhibition effect of polymers is close relation with the grid oscillating frequency.
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WINTER, M., T. BARBER, R. EVERSON, and L. SIROVICH. "Eigenfunction analysis of turbulent mixing phenomena." In 29th Aerospace Sciences Meeting. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1991. http://dx.doi.org/10.2514/6.1991-520.

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de Barros, Felipe P. J., and Renato M. Cotta. "Integral Transforms for Three-Dimensional Steady Turbulent Dispersion in Rivers and Channels." In ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. ASMEDC, 2005. http://dx.doi.org/10.1115/ht2005-72863.

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A three-dimensional steady-state mathematical model is considered for predicting the fate of dissolved contaminants in rivers and channels under turbulent flows. The model allows for variable velocity fields and non-uniform turbulent diffusivities. Making use of the Generalized Integral Transform Technique (GITT), a hybrid numerical-analytical solution is then obtained. The solution convergence behavior is investigated and the criterion for reordering the terms in the infinite series is discussed, with the aim of reducing the computational effort associated with the double eigenfunction expansion. A test case is presented to illustrate the proposed approach.
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Hosseinali, Mahdi, Stephen Wilkins, Lhendup Namgyal, and Joseph Hall. "A Comparison of Classic and Snapshot Proper Orthogonal Decomposition on the Three Dimensional Wall Jet Flow Field." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-38602.

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In this paper, classic Proper Orthogonal Decomposition (POD) on a polar coordinate and snapshot POD on a Cartesian grid will be applied separately in the near field of a turbulent wall jet. Three-component stereoscopic PIV measurements are performed in the transverse plane of a wall jet formed using a round contoured nozzle with a Reynolds number of 250,000. Eigenfunctions and energy distributions of the two methods are compared. Reconstructions using same number of modes and same content of energy have been compared. The effect of grid resolution on the energy content of the classic method has also been studied.
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Mann, Richa, Lawrence S. Ukeiley, and John M. Seiner. "Velocity and Pressure Measurements of a Mach 0.85 Axisymmetric Jet." In ASME/JSME 2007 5th Joint Fluids Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/fedsm2007-37164.

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The turbulent properties of a heated and unheated Mach 0.85 axisymmetric jet have been studied. The velocity field of the jet at static temperature ratios of 0.87 and 2.34, was measured in the streamwise radial plane using Particle Image Velocimetry. The velocity measurements were acquired between streamwise locations of 3D and 8D downstream from the nozzle exit. Proper Orthogonal Decomposition (POD) was applied to the velocity field using snapshot POD. The POD analysis showed that the eigenvalues of the heated jet had higher fraction of energy. The POD eigenfunctions or modes of the streamwise velocity of both jets were similar, while the POD modes of the radial velocity of both jets were very different. The POD modes of radial velocity of the unheated jet were symmetrical about the jet centerline, and the modes of the heated jet seemed to merge at the centerline. The near field pressure measurements were acquired just outside the shearlayer. A linear array of five pressure transducers was placed at 7° to the nozzle lipline, so that it would be parallel to the shear layer. The transducers in the array were spaced one diameter apart. Pressure measurements were acquired at streamwise locations between 4.25D and 10.25D from the nozzle exit. Based on the slope of the pressure spectra, the propagating events in the two jets were identified. The POD was also applied to the pressure data, and the POD modes of the two jets were compared. The peak in the amplitude of the POD mode of the heated jet was at a higher frequency. With increasing mode numbers, the peak in the POD mode of both jets shifted to a downstream location.
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