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Journal articles on the topic 'Scalar driven diffusion'
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1
Yeung, P. K. "Multi-scalar triadic interactions in differential diffusion with and without mean scalar gradients." Journal of Fluid Mechanics 321 (August 25, 1996): 235–78. http://dx.doi.org/10.1017/s0022112096007719.
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The spectral mechanisms of the differential diffusion of pairs of passive scalars with different molecular diffusivities are studied in stationary isotropic turbulence, using direct numerical simulation data at Taylor-scale Reynolds number up to 160 on 1283 and 2563 grids. Of greatest interest are the roles of nonlinear triadic interactions between different scale ranges of the velocity and scalar fields in the evolution of spectral coherency between the scalars, and the effects of mean scalar gradients.Analysis of single-scalar spectral transfer (extending the results of a previous study) indicates a robust local forward cascade behaviour at high wavenumbers, which is strengthened by both high diffusivity and mean gradients. This cascade is driven primarily by moderately non-local interactions in which two small-scale scalar modes are coupled via a lower-wavenumber velocity mode near the peak of the energy dissipation spectrum. This forward cascade is coherent, tending to increase the coherency between different scalars at high wavenumbers but to decrease it at lower wavenumbers. However, at early times coherency evolution at high wavenumbers is dominated by de-correlating effects due to a different type of non-local triad consisting of two scalar modes with a moderate scale separation and a relatively high-wavenumber velocity mode. Consequently, although the small-scale motions play little role in spectral transfer, they are responsible for the rapid de-correlation observed at early times. At later times both types of competing triadic interactions become important over a wider wavenumber range, with increased relative strength of the coherent cascade, so that the coherency becomes slow-changing. When uniform mean scalar gradients are present, a stationary state develops in the coherency spectrum as a result of a balance between a coherent mean gradient contribution (felt within about 1 eddy-turnover time) and the net contribution from scale interactions. The latter is made less de-correlating because of a strengthened coherent forward cascade, which is in turn caused by uniform mean gradients acting as a primarily low-wavenumber source of scalar fluctuations with the same spectral content as the velocity field.
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van Sommeren, Daan D. J. A., C. P. Caulfield, and Andrew W. Woods. "Spatially varying mixing of a passive scalar in a buoyancy-driven turbulent flow." Journal of Fluid Mechanics 742 (February 24, 2014): 701–19. http://dx.doi.org/10.1017/jfm.2014.25.
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AbstractWe perform experiments to study the mixing of passive scalar by a buoyancy-induced turbulent flow in a long narrow vertical tank. The turbulent flow is associated with the downward mixing of a small flux of dense aqueous saline solution into a relatively large upward flux of fresh water. In steady state, the mixing region is of finite extent, and the intensity of the buoyancy-driven mixing is described by a spatially varying turbulent diffusion coefficient $\kappa _v(z)$ which decreases linearly with distance $z$ from the top of the tank. We release a pulse of passive scalar into either the fresh water at the base of the tank, or the saline solution at the top of the tank, and we measure the subsequent mixing of the passive scalar by the flow using image analysis. In both cases, the mixing of the passive scalar (the dye) is well-described by an advection–diffusion equation, using the same turbulent diffusion coefficient $\kappa _v(z)$ associated with the buoyancy-driven mixing of the dynamic scalar. Using this advection–diffusion equation with spatially varying turbulent diffusion coefficient $\kappa _v(z)$, we calculate the residence time distribution (RTD) of a unit mass of passive scalar released as a pulse at the bottom of the tank. The variance in this RTD is equivalent to that produced by a uniform eddy diffusion coefficient with value $\kappa _e= 0.88 \langle \kappa _v \rangle $, where $\langle \kappa _v \rangle $ is the vertically averaged eddy diffusivity. The structure of the RTD is also qualitatively different from that produced by a flow with uniform eddy diffusion coefficient. The RTD using $\kappa _v$ has a larger peak value and smaller values at early times, associated with the reduced diffusivity at the bottom of the tank, and manifested mathematically by a skewness $\gamma _1\approx 1.60$ and an excess kurtosis $\gamma _2\approx 4.19 $ compared to the skewness and excess kurtosis of $\gamma _1\approx 1.46$, $\gamma _2 \approx 3.50$ of the RTD produced by a constant eddy diffusion coefficient with the same variance.
3
Carmona, René, and François Delarue. "Singular FBSDEs and scalar conservation laws driven by diffusion processes." Probability Theory and Related Fields 157, no. 1-2 (November 5, 2012): 333–88. http://dx.doi.org/10.1007/s00440-012-0459-7.
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Watanabe, Tsutomu, Marie Takagi, Kou Shimoyama, Masayuki Kawashima, Naoyuki Onodera, and Atsushi Inagaki. "Coherent Eddies Transporting Passive Scalars Through the Plant Canopy Revealed by Large-Eddy Simulations Using the Lattice Boltzmann Method." Boundary-Layer Meteorology 181, no. 1 (July 9, 2021): 39–71. http://dx.doi.org/10.1007/s10546-021-00633-1.
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AbstractA double-distribution-function lattice Boltzmann model for large-eddy simulations of a passive scalar field in a neutrally stratified turbulent flow is described. In simulations of the scalar turbulence within and above a homogeneous plant canopy, the model’s performance is found to be comparable with that of a conventional large-eddy simulation model based on the Navier–Stokes equations and a scalar advection–diffusion equation in terms of the mean turbulence statistics, budgets of the second moments, power spectra, and spatial two-point correlation functions. For a top-down scalar, for which the plant canopy serves as a distributed sink, the variance and flux of the scalar near the canopy top are predominantly determined by sweep motions originating far above the canopy. These sweep motions, which have spatial scales much larger than the canopy height, penetrate deep inside the canopy and cause scalar sweep events near the canopy floor. By contrast, scalar ejection events near the canopy floor are induced by coherent eddies generated near the canopy top. The generation of such eddies is triggered by the downward approach of massive sweep motions to existing wide regions of weak ejective motions from inside to above the canopy. The non-local transport of scalars from above the canopy to the canopy floor, and vice versa, is driven by these eddies of different origins. Such non-local transport has significant implications for the scalar variance and flux budgets within and above the canopy, as well as the transport of scalars emitted from the underlying soils to the atmosphere.
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Song, Na, and Zaiming Liu. "Parameter Estimation for Stochastic Differential Equations Driven by Mixed Fractional Brownian Motion." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/942307.
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We study the asymptotic properties of minimum distance estimator of drift parameter for a class of nonlinear scalar stochastic differential equations driven by mixed fractional Brownian motion. The consistency and limit distribution of this estimator are established as the diffusion coefficient tends to zero under some regularity conditions.
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Coti Zelati, Michele, and Grigorios A. Pavliotis. "Homogenization and hypocoercivity for Fokker–Planck equations driven by weakly compressible shear flows." IMA Journal of Applied Mathematics 85, no. 6 (October 6, 2020): 951–79. http://dx.doi.org/10.1093/imamat/hxaa035.
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Abstract We study the long-time dynamics of 2D linear Fokker–Planck equations driven by a drift that can be decomposed in the sum of a large shear component and the gradient of a regular potential depending on one spatial variable. The problem can be interpreted as that of a passive scalar advected by a slightly compressible shear flow, and undergoing small diffusion. For the corresponding stochastic differential equation, we give explicit homogenization rates in terms of a family of time-scales depending on the parameter measuring the strength of the incompressible perturbation. This is achieved by exploiting an auxiliary Poisson problem, and by computing the related effective diffusion coefficients. Regarding the long-time behavior of the solution of the Fokker–Planck equation, we provide explicit decay rates to the unique invariant measure by employing a quantitative version of the classical hypocoercivity scheme. From a fluid mechanics perspective, this turns out to be equivalent to quantifying the phenomenon of enhanced diffusion for slightly compressible shear flows.
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Jenny, Patrick, Joohwa S. Lee, Daniel W. Meyer, and Hamdi A. Tchelepi. "Scale analysis of miscible density-driven convection in porous media." Journal of Fluid Mechanics 749 (May 16, 2014): 519–41. http://dx.doi.org/10.1017/jfm.2014.229.
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AbstractScale analysis of unstable density-driven miscible convection in porous media is performed. The main conclusions for instabilities in the developed (long time scales) regime are that (i) large-scale structures are responsible for the bulk of the production of concentration variance, (ii) variance dissipation is dominated by the small (diffusive) scales and that (iii) both the production and dissipation rates are independent of the Rayleigh number. These findings provide a strong basis for a new modelling approach, namely, large-mode simulation (LMS), for which closure is achieved by replacing the actual diffusivity with an effective one. For validation, LMS results for vertical flow in a homogeneous rectangular domain are compared with direct numerical simulations (DNS). Some of the analysis is based on the derivation and closure of the concentration mean and variance equations, whereby averaging over the ensemble of all possible initial perturbations is considered. While self-similar solutions are obtained for vertical, statistically one-dimensional fingering, triple correlation of concentration and scalar dissipation rate (rate at which the concentration variance decays due to diffusion) have to be modelled in the general case. For this purpose, an ensemble-averaged Darcy modelling (EADM) approach is proposed.
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Xia, Hua, Nicolas Francois, Horst Punzmann, Kamil Szewc, and Michael Shats. "Extreme concentration fluctuations due to local reversibility of mixing in turbulent flows." Modern Physics Letters B 32, no. 12n13 (May 10, 2018): 1840028. http://dx.doi.org/10.1142/s0217984918400286.
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Mixing of a passive scalar in a fluid (e.g. a radioactive spill in the ocean) is the irreversible process towards homogeneous distribution of a substance. In a moving fluid, due to the chaotic advection [H. Aref, J. Fluid Mech. 143 (1984) 1; J. M. Ottino, The Kinematics of Mixing: Stretching,Chaos and Transport (Cambridge University Press, Cambridge, 1989)] mixing is much faster than if driven by molecular diffusion only. Turbulence is known as the most efficient mixing flow [B. I. Shraiman and E. D. Siggia, Nature 405 (2000) 639]. We show that in contrast to spatially periodic flows, two-dimensional turbulence exhibits local reversibility in mixing, which leads to the generation of unpredictable strong fluctuations in the scalar concentration. These fluctuations can also be detected from the analysis of the fluid particle trajectories of the underlying flow.
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Herlina, H., and J. G. Wissink. "Direct numerical simulation of turbulent scalar transport across a flat surface." Journal of Fluid Mechanics 744 (March 11, 2014): 217–49. http://dx.doi.org/10.1017/jfm.2014.68.
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AbstractTo elucidate the physical mechanisms that play a role in the interfacial transfer of atmospheric gases into water, a series of direct numerical simulations of mass transfer across the air–water interface driven by isotropic turbulence diffusing from below has been carried out for various turbulent Reynolds numbers ($R_T=84,195,507$). To allow a direct (unbiased) comparison of the instantaneous effects of scalar diffusivity, in each of the DNS up to six scalar advection–diffusion equations with different Schmidt numbers were solved simultaneously. As far as the authors are aware this is the first simulation that is capable to accurately resolve the realistic Schmidt number, $\mathit{Sc}=500$, that is typical for the transport of atmospheric gases such as oxygen in water. For the range of turbulent Reynolds numbers and Schmidt numbers considered, the normalized transfer velocity $K_L$ was found to scale with $R_T^{-{1/2}}$ and $\mathit{Sc}^{-{1/2}}$, which indicates that the largest eddies present in the isotropic turbulent flow introduced at the bottom of the computational domain tend to determine the mass transfer. The $K_L$ results were also found to be in good agreement with the surface divergence model of McCready, Vassiliadou & Hanratty (AIChE J., vol. 32, 1986, pp. 1108–1115) when using a constant of proportionality of 0.525. Although close to the surface large eddies are responsible for the bulk of the gas transfer, it was also observed that for higher $R_T$ the influence of smaller eddies becomes more important.
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Antonov, N., M. Hnatich, D. Horváth, and M. Nalimov. "The Anomalous Diffusion of the Self-Interacting Passive Scalar in the Turbulent Environment." International Journal of Modern Physics B 12, no. 19 (July 30, 1998): 1937–62. http://dx.doi.org/10.1142/s0217979298001125.
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Two variants of the statistical model of diffusing self-interacting passive scalar θ(x, t) driven by the incompressible Navier–Stokes turbulence were studied by means of the field-theoretical renormalization group technique and ∊-expansion scheme, where ∊ denotes the parameter of the forcing spectrum. Dual ∫ ddxdt[θ(x, t)]2 and triple ∫ ddxdt[θ(x, t)]3 interaction terms of the action represent two different mechanisms of the self-interaction matching two alternative values of the critical dimension: d c =4 and d c =6. The major part of the calculations was carried out in the one loop order, nevertheless, the inclusion of the specific two loop contributions represents the important step of the analysis of some renormalization group functions. In the basic model variant the effective action is renormalizable for the supercritical dimensions d > d c . This theory exhibits the presence of the asymptotical regime, which is stable for the inertial-conductive range of wave numbers. It was also shown that stability of this regime remains preserved for a variety of the parametric paths connecting domain ∊>0, d>d c with ∊<2, d=3. In the second model variant, the effective action is constructed to be renormalizable at dimensions d≥d c and to justify the realizability of the continuation from ∊>0, d>d c to ∊< 2, d=3. This variant of the model was analyzed using "double expansion" method with the expansion parameters (d-d c )/2 and ∊. The negative correction ζ(ζ≃0.039 for d=3) to the universal Richardson exponent 4/3 is the physical consequence stemming from the calculations.
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SILVA, JOÃO MARIA, and JOSÉ A. S. LIMA. "ON THE STOCHASTIC EVOLUTION OF THE INFLATON FIELD." International Journal of Modern Physics D 13, no. 07 (August 2004): 1315–20. http://dx.doi.org/10.1142/s021827180400547x.
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During the inflationary regime, the expansion of the Universe is driven by a scalar field ϕ(t) which may be in thermal contact with the radiation fluid. In this work, we study the influence of the thermal bath assuming that it is responsible for the stochastic evolution of the inflaton field. Assuming that the fluctuation dynamics is described by a Langevin-type equation of motion, a large set of analytical solutions including white and colored noises are derived. It is found that even in the case of white noise the field experience an anomalous diffusion. Such results may be important for studying thermally induced initial density perturbations in inflationary cosmologies, mainly in the framework of warm inflation.
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Lawrie, Andrew G. W., and Stuart B. Dalziel. "Rayleigh–Taylor mixing in an otherwise stable stratification." Journal of Fluid Mechanics 688 (November 3, 2011): 507–27. http://dx.doi.org/10.1017/jfm.2011.398.
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AbstractWe seek to understand the distribution of irreversible energy conversions (mixing efficiency) between quiescent initial and final states in a miscible Rayleigh–Taylor driven system. The configuration we examine is a Rayleigh–Taylor unstable interface sitting between stably stratified layers with linear density profiles above and below. Our experiments in brine solution measure vertical profiles of density before and after the unstable interface is allowed to relax to a stable state. Our analysis suggests that less than half the initially available energy is irreversibly released as heat due to viscous dissipation, while more than half irreversibly changes the probability density function of the density field by scalar diffusion and therefore remains as potential energy, but in a less useful form. While similar distributions are observed in Rayleigh–Taylor driven mixing flows between homogeneous layers, our new configuration admits energetically consistent end-state density profiles that span all possible mixing efficiencies, ranging from all available energy being expended as dissipation, to none. We present experiments that show that the fluid relaxes to a state with a significantly lower mixing efficiency than the value for ideal mixing in this configuration, and deduce that this mixing efficiency more accurately characterizes Rayleigh–Taylor driven mixing than previous measurements. We argue that the physical mechanisms intrinsic to Rayleigh–Taylor instability are optimal conditions for mixing, and speculate that we have observed an upper bound to fluid mixing in general.
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Wang, Yanxing, James G. Brasseur, Gino G. Banco, Andrew G. Webb, Amit C. Ailiani, and Thomas Neuberger. "A multiscale lattice Boltzmann model of macro- to micro-scale transport, with applications to gut function." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1921 (June 28, 2010): 2863–80. http://dx.doi.org/10.1098/rsta.2010.0090.
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Nutrient absorption in the small intestine cannot occur until molecules are presented to the epithelial cells that line intestinal villi, finger-like protrusions under enteric control. Using a two-dimensional multiscale lattice Boltzmann model of a lid-driven cavity flow with ‘villi’ at the lower surface, we analyse the hypothesis that muscle-induced oscillatory motions of the villi generate a controlled ‘micro-mixing layer’ (MML) that couples with the macro-scale flow to enhance absorption. Nutrient molecules are modelled as passive scalar concentrations at high Schmidt number. Molecular concentration supplied at the cavity lid is advected to the lower surface by a lid-driven macro-scale eddy. We find that micro-scale eddying motions enhance the macro-scale advective flux by creating an MML that couples with the macro-scale flow to increase absorption rate. We show that the MML is modulated by its interactions with the outer flow through a diffusion-dominated layer that separates advection-dominated macro-scale and micro-scale mixed layers. The structure and strength of the MML is sensitive to villus length and oscillation frequency. Our model suggests that the classical explanation for the existence of villi—increased absorptive surface area—is probably incorrect. The model provides support for the potential importance of villus motility in the absorptive function of the small intestine.
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Wissink, J. G., and H. Herlina. "Direct numerical simulation of gas transfer across the air–water interface driven by buoyant convection." Journal of Fluid Mechanics 787 (December 17, 2015): 508–40. http://dx.doi.org/10.1017/jfm.2015.696.
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A series of direct numerical simulations of mass transfer across the air–water interface driven by buoyancy-induced convection have been carried out to elucidate the physical mechanisms that play a role in the transfer of heat and atmospheric gases. The buoyant instability is caused by the presence of a thin layer of cold water situated on top of a body of warm water. In time, heat and atmospheric gases diffuse into the uppermost part of the thermal boundary layer and are subsequently transported down into the bulk by falling sheets and plumes of cold water. Using a specifically designed numerical code for the discretization of scalar convection and diffusion, it was possible to accurately resolve this buoyant-instability-induced transport of atmospheric gases into the bulk at a realistic Prandtl number ($\mathit{Pr}=6$) and Schmidt numbers ranging from$\mathit{Sc}=20$to$\mathit{Sc}=500$. The simulations presented here provided a detailed insight into instantaneous gas transfer processes. The falling plumes with highly gas-saturated fluid in their core were found to penetrate deep inside the bulk. With an initial temperature difference between the water surface and the bulk of slightly above$2$ K, peaks in the instantaneous heat flux in excess of$1600~\text{W}~\text{m}^{-2}$were observed, proving the potential effectiveness of buoyant-convective heat and gas transfer. Furthermore, the validity of the scaling law for the ratio of gas and heat transfer velocities$K_{L}/H_{L}\propto (\mathit{Pr}/\mathit{Sc})^{0.5}$for the entire range of Schmidt numbers considered was confirmed. A good time-accurate approximation of$K_{L}$was found using surface information such as velocity fluctuations and convection cell size or surface divergence. A reasonable time accuracy for the$K_{L}$estimation was obtained using the horizontal integral length scale and the root mean square of the horizontal velocity fluctuations in the upper part of the bulk.
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Garnier, Josselin, and Knut Sølna. "Apparent attenuation of shear waves propagating through a randomly stratified anisotropic medium." Stochastics and Dynamics 16, no. 04 (May 5, 2016): 1650009. http://dx.doi.org/10.1142/s021949371650009x.
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Waves propagating through heterogeneous media experience scattering that can convert a coherent pulse into small incoherent fluctuations. This may appear as attenuation for the transmitted front pulse. The classic O’Doherty–Anstey theory describes such a transformation for scalar waves in finely layered media. Recent observations for seismic waves in the earth suggest that this theory can explain a significant component of seismic attenuation. An important question to answer is then how the O’Doherty–Anstey theory generalizes to seismic waves when several wave modes, possibly with the same velocity, interact. An important aspect of the O’Doherty–Anstey theory is the statistical stability property, which means that the transmitted front pulse is actually deterministic and depends only on the statistics of the medium but not on the particular medium realization when the medium is modeled as a random process. It is shown in this paper that this property generalizes in the case of elastic waves in a nontrivial way: the energy of the transmitted front pulse, but not the pulse shape itself, is statistically stable. This result is based on a separation of scales technique and a diffusion-approximation theorem that characterize the transmitted front pulse as the solution of a stochastic partial differential equation driven by two Brownian motions.
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Alsinan, A., E. Meiburg, and P. Garaud. "A settling-driven instability in two-component, stably stratified fluids." Journal of Fluid Mechanics 816 (March 6, 2017): 243–67. http://dx.doi.org/10.1017/jfm.2017.94.
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We analyse the linear stability of stably stratified fluids whose density depends on two scalar fields where one of the scalar fields is unstably stratified and involves a settling velocity. Such conditions may be found, for example, in flows involving the transport of sediment in addition to heat or salt. A linear stability analysis for constant-gradient base states demonstrates that the settling velocity generates a phase shift between the perturbation fields of the two scalars, which gives rise to a novel, settling-driven instability mode. This instability mechanism favours the growth of waves that are inclined with respect to the horizontal. It is active for all density and diffusivity ratios, including for cases in which the two scalars diffuse at identical rates. If the scalars have unequal diffusivities, it competes with the elevator mode waves of the classical double-diffusive instability. We present detailed linear stability results as a function of the governing dimensionless parameters, including for lateral gradients of the base state density fields that result in predominantly horizontal intrusion instabilities. Highly resolved direct numerical simulation results serve to illustrate the nonlinear competition of the various instabilities for such flows in different parameter regimes.
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Sullivan, Greg D., and E. John List. "On mixing and transport at a sheared density interface." Journal of Fluid Mechanics 273 (August 25, 1994): 213–39. http://dx.doi.org/10.1017/s0022112094001916.
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Mixing and transport of a stratifying scalar are investigated at a density interface imbedded in a turbulent shear flow. Steady-state interfacial shear flows are generated in a laboratory water channel for layer Richardson numbers, Ri, between about 1 and 10. The flow field is made optically homogeneous, enabling the use of laser-induced fluorescence with photodiode array imaging to measure the concentration field at high resolution. False-colour images of the concentration field provide valuable insight into interfacial dynamics: when the local mean shear Richardson number, Ris, is less than about 0.40–0.45, interfacial mixing appears to be dominated by Kelvin–Helmholtz (K–H) instabilities; when Ris is somewhat larger than this, interfacial mixing appears to be dominated by shear-driven wave breaking. In both cases, vertical transport of mixed fluid from the interfacial region into adjacent turbulent layers is accomplished by large-scale turbulent eddies which impinge on the interface and scour fluid from its outer edges.Motivated by the experimental findings, a model for interfacial mixing and entrainment is developed. A local equilibrium is assumed in which the rate of loss of interfacial fluid by eddy scouring is balanced by the rate of production (local mixing) by interfacial instabilities and molecular diffusion. When a single layer is turbulent and entraining, the model results are as follows: in the molecular-diffusion-dominated regime, δ/h ∼ Pe−1/2 and E ∼ Ri−1Pe−1/2; in the wave-breaking-dominated regime, δ/h ∼ Ri−1/2 and E ∼ Ri−3/2; and in the K–H-dominated regime, δ/h ∼ Ri−1 and E ∼ Ri−2, where δ is the interface thickness, h is the boundary-layer thickness, Pe is the Péclet number, and E is the normalized entrainment velocity. In all three regimes, the maximum concentration anomaly, [gcy ]m ∼ Ri−1. When both layers are turbulent and entraining, E and δ depend on combinations of parameters from both layers.
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Sahu, Kirti Chandra. "Double-diffusive instability in core–annular pipe flow." Journal of Fluid Mechanics 789 (January 27, 2016): 830–55. http://dx.doi.org/10.1017/jfm.2015.760.
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The instability in a pressure-driven core–annular flow of two miscible fluids having the same densities, but different viscosities, in the presence of two scalars diffusing at different rates (double-diffusive effect) is investigated via linear stability analysis and axisymmetric direct numerical simulation. It is found that the double-diffusive flow in a cylindrical pipe exhibits strikingly different stability characteristics compared to the double-diffusive flow in a planar channel and the equivalent single-component flow (wherein viscosity stratification is achieved due to the variation of one scalar) in a cylindrical pipe. The flow which is stable in the context of single-component systems now becomes unstable in the presence of two scalars diffusing at different rates. It is shown that increasing the diffusivity ratio enhances the instability. In contrast to the single fluid flow through a pipe (the Hagen–Poiseuille flow), the faster growing axisymmetric eigenmode is found to be more unstable than the corresponding corkscrew mode for the parameter values considered, for which the equivalent single-component flow is stable to both the axisymmetric and corkscrew modes. Unlike single-component flows of two miscible fluids in a cylindrical pipe, it is shown that the diffusivity and the radial location of the mixed layer have non-monotonic influences on the instability characteristics. An attempt is made to understand the underlying mechanism of this instability by conducting the energy budget and inviscid stability analyses. The investigation of linear instability due to the double-diffusive phenomenon is extended to the nonlinear regime via axisymmetric direct numerical simulations. It is found that in the nonlinear regime the flow becomes unstable in the presence of double-diffusive effect, which is consistent with the predictions of linear stability theory. A new type of instability pattern of an elliptical shape is observed in the nonlinear simulations in the presence of double-diffusive effect.
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Yang, Yantao, Roberto Verzicco, and Detlef Lohse. "From convection rolls to finger convection in double-diffusive turbulence." Proceedings of the National Academy of Sciences 113, no. 1 (December 22, 2015): 69–73. http://dx.doi.org/10.1073/pnas.1518040113.
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Double-diffusive convection (DDC), which is the buoyancy-driven flow with fluid density depending on two scalar components, is ubiquitous in many natural and engineering environments. Of great interests are scalars' transfer rate and flow structures. Here we systematically investigate DDC flow between two horizontal plates, driven by an unstable salinity gradient and stabilized by a temperature gradient. Counterintuitively, when increasing the stabilizing temperature gradient, the salinity flux first increases, even though the velocity monotonically decreases, before it finally breaks down to the purely diffusive value. The enhanced salinity transport is traced back to a transition in the overall flow pattern, namely from large-scale convection rolls to well-organized vertically oriented salt fingers. We also show and explain that the unifying theory of thermal convection originally developed by Grossmann and Lohse for Rayleigh–Bénard convection can be directly applied to DDC flow for a wide range of control parameters (Lewis number and density ratio), including those which cover the common values relevant for ocean flows.
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Skene, Calum S., and Peter J. Schmid. "Adjoint-based parametric sensitivity analysis for swirling M-flames." Journal of Fluid Mechanics 859 (November 21, 2018): 516–42. http://dx.doi.org/10.1017/jfm.2018.793.
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A linear numerical study is conducted to quantify the effect of swirl on the response behaviour of premixed lean flames to general harmonic excitation in the inlet, upstream of combustion. This study considers axisymmetric M-flames and is based on the linearised compressible Navier–Stokes equations augmented by a simple one-step irreversible chemical reaction. Optimal frequency response gains for both axisymmetric and non-axisymmetric perturbations are computed via a direct–adjoint methodology and singular value decompositions. The high-dimensional parameter space, containing perturbation and base-flow parameters, is explored by taking advantage of generic sensitivity information gained from the adjoint solutions. This information is then tailored to specific parametric sensitivities by first-order perturbation expansions of the singular triplets about the respective parameters. Valuable flow information, at a negligible computational cost, is gained by simple weighted scalar products between direct and adjoint solutions. We find that for non-swirling flows, a mode with azimuthal wavenumber $m=2$ is the most efficiently driven structure. The structural mechanism underlying the optimal gains is shown to be the Orr mechanism for $m=0$ and a blend of Orr and other mechanisms, such as lift-up, for other azimuthal wavenumbers. Further to this, velocity and pressure perturbations are shown to make up the optimal input and output showing that the thermoacoustic mechanism is crucial in large energy amplifications. For $m=0$ these velocity perturbations are mainly longitudinal, but for higher wavenumbers azimuthal velocity fluctuations become prominent, especially in the non-swirling case. Sensitivity analyses are carried out with respect to the Mach number, Reynolds number and swirl number, and the accuracy of parametric gradients of the frequency response curve is assessed. The sensitivity analysis reveals that increases in Reynolds and Mach numbers yield higher gains, through a decrease in temperature diffusion. A rise in mean-flow swirl is shown to diminish the gain, with increased damping for higher azimuthal wavenumbers. This leads to a reordering of the most effectively amplified mode, with the axisymmetric ($m=0$) mode becoming the dominant structure at moderate swirl numbers.
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Scalo, Carlo, Ugo Piomelli, and Leon Boegman. "Self-similar decay and mixing of a high-Schmidt-number passive scalar in an oscillating boundary layer in the intermittently turbulent regime." Journal of Fluid Mechanics 726 (June 5, 2013): 338–70. http://dx.doi.org/10.1017/jfm.2013.228.
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AbstractWe performed numerical simulations of dissolved oxygen (DO) transfer from a turbulent flow, driven by periodic boundary-layer turbulence in the intermittent regime, to underlying DO-absorbing organic sediment layers. A uniform initial distribution of oxygen is left to decay (with no re-aeration) as the turbulent transport supplies the sediment with oxygen from the outer layers to be absorbed. A very thin diffusive sublayer at the sediment–water interface (SWI), caused by the high Schmidt number of DO in water, limits the overall decay rate. A decomposition of the instantaneous decaying turbulent scalar field is proposed, which results in the development of similarity solutions that collapse the data in time. The decomposition is then tested against the governing equations, leading to a rigorous procedure for the extraction of an ergodic turbulent scalar field. The latter is composed of a statistically periodic and a steady non-decaying field. Temporal averaging is used in lieu of ensemble averaging to evaluate flow statistics, allowing the investigation of turbulent mixing dynamics from a single flow realization. In spite of the highly unsteady state of turbulence, the monotonically decaying component is surprisingly consistent with experimental and numerical correlations valid for steady high-Schmidt-number turbulent mass transfer. Linearly superimposed onto it is the statistically periodic component, which incorporates all the features of the non-equilibrium state of turbulence. It is modulated by the evolution of the turbulent coherent structures driven by the oscillating boundary layer in the intermittent regime, which are responsible for the violent turbulent production mechanisms. These cause, in turn, a rapid increase of the turbulent mass flux at the edge of the diffusive sublayer. This outer-layer forcing mechanism drives a periodic accumulation of high scalar concentration levels in the near-wall region. The resulting modulated scalar flux across the SWI is delayed by a quarter of a cycle with respect to the wall-shear stress, consistently with the non-equilibrium state of the turbulent mixing.
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BISSET, DAVID K., JULIAN C. R. HUNT, and MICHAEL M. ROGERS. "The turbulent/non-turbulent interface bounding a far wake." Journal of Fluid Mechanics 451 (January 25, 2002): 383–410. http://dx.doi.org/10.1017/s0022112001006759.
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The velocity fields of a turbulent wake behind a flat plate obtained from the direct numerical simulations of Moser et al. (1998) are used to study the structure of the flow in the intermittent zone where there are, alternately, regions of fully turbulent flow and non-turbulent velocity fluctuations on either side of a thin randomly moving interface. Comparisons are made with a wake that is ‘forced’ by amplifying initial velocity fluctuations. A temperature field T, with constant values of 1.0 and 0 above and below the wake, is transported across the wake as a passive scalar. The value of the Reynolds number based on the centreplane mean velocity defect and half-width b of the wake is Re ≈ 2000.The thickness of the continuous interface is about 0.07b, whereas the amplitude of fluctuations of the instantaneous interface displacement yI(t) is an order of magnitude larger, being about 0.5b. This explains why the mean statistics of vorticity in the intermittent zone can be calculated in terms of the probability distribution of yI and the instantaneous discontinuity in vorticity across the interface. When plotted as functions of y−yI the conditional mean velocity 〈U〉 and temperature 〈T〉 profiles show sharp jumps at the interface adjacent to a thick zone where 〈U〉 and 〈T〉 vary much more slowly.Statistics for the conditional vorticity and velocity variances, available in such detail only from DNS data, show how streamwise and spanwise components of vorticity are generated by vortex stretching in the bulges of the interface. While mean Reynolds stresses (in the fixed reference frame) decrease gradually in the intermittent zone, conditional stresses are roughly constant and then decrease sharply towards zero at the interface. Flow fields around the interface, analysed in terms of the local streamline pattern, confirm and explain previous results that the advancement of the vortical interface into the irrotational flow is driven by large-scale eddy motion.Terms used in one-point turbulence models are evaluated both conventionally and conditionally in the interface region, and the current practice in statistical models of approximating entrainment by a diffusion process is assessed.
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MUPPIDI, SUMAN, and KRISHNAN MAHESH. "Direct numerical simulation of passive scalar transport in transverse jets." Journal of Fluid Mechanics 598 (February 25, 2008): 335–60. http://dx.doi.org/10.1017/s0022112007000055.
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Direct numerical simulation is used to study passive scalar transport and mixing in a round turbulent jet, in a laminar crossflow. The ratio of the jet velocity to that of the crossflow is 5.7, the Schmidt number of the scalar is 1.49, and the jet-exit Reynolds number is 5000. The scalar field is used to compute entrainment of the crossflow fluid by the jet. It is shown that the bulk of this entrainment occurs on the downstream side of the jet. Also, the transverse jet entrains more fluid than a regular jet even when the jet has not yet bent into the crossflow. The transverse jet's enhanced entrainment is explained in terms of the pressure field around the jet. The acceleration imposed by the crossflow deforms the jet cross-section on the downstream side, which sets up a pressure gradient that drives downstream crossflow fluid toward the jet. The simulation results are used to comment on the applicability of the gradient–diffusion hypothesis to compute passive scalar mixing in this flow field. Computed values of the eddy diffusivity show significant scatter, and a pronounced anisotropy. The near field also exhibits counter gradient diffusion.
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Cartas-Fuentevilla, R., and A. Olvera-Santamaria. "Deforming the theory λϕ4 along the parameters and fields gradient flows." International Journal of Modern Physics A 30, no. 02 (January 20, 2015): 1550008. http://dx.doi.org/10.1142/s0217751x15500086.
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Considering the action for the theory λϕ4 for a massive scalar bosonic field as an entropy functional on the space of coupling constants and on the space of fields, we determine the gradient flows for the scalar field, the mass and the self-interaction parameter. When the flow parameter is identified with the energy scale, we show that there exist phase transitions between unbroken exact symmetry scenarios and spontaneous symmetry breaking scenarios at increasingly high energies. Since a nonlinear heat equation drives the scalar field through a reaction-diffusion process, in general the flows are not reversible, mimicking the renormalization group flows of the c-theorem; the deformation of the field at increasingly high energies can be described as nonlinear traveling waves, or solitons associated to self-similar solutions.
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Buaria, D., P. K. Yeung, and B. L. Sawford. "A Lagrangian study of turbulent mixing: forward and backward dispersion of molecular trajectories in isotropic turbulence." Journal of Fluid Mechanics 799 (June 23, 2016): 352–82. http://dx.doi.org/10.1017/jfm.2016.359.
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Statistics of the trajectories of molecules diffusing via Brownian motion in a turbulent flow are extracted from simulations of stationary isotropic turbulence, using a postprocessing approach applicable in both forward and backward reference frames. Detailed results are obtained for Schmidt numbers ($Sc$) from 0.001 to 1000 at Taylor-scale Reynolds numbers up to 1000. The statistics of displacements of single molecules compare well with the earlier theoretical work of Saffman (J. Fluid Mech. vol. 8, 1960, pp. 273–283) except for the scaling of the integral time scale of the fluid velocity following the molecular trajectories. For molecular pairs we extend Saffman’s theory to include pairs of small but finite initial separation, which is in excellent agreement with numerical results provided that data are collected at sufficiently small times. At intermediate times the separation statistics of molecular pairs exhibit a more robust Richardson scaling behaviour than for the fluid particles. The forward scaling constant is very close to 0.55, whereas the backward constant is approximately 1.53–1.57, with a weak Schmidt number dependence, although no scaling exists if $Sc\ll 1$ at the Reynolds numbers presently accessible. An important innovation in this work is to demonstrate explicitly the practical utility of a Lagrangian description of turbulent mixing, where molecular displacements and separations in the limit of small backward initial separation can be used to calculate the evolution of scalar fluctuations resulting from a known source function in space. Lagrangian calculations of the production and dissipation rates of the scalar fluctuations are shown to agree very well with Eulerian results for the case of passive scalars driven by a uniform mean gradient. Although the Eulerian–Lagrangian comparisons are made only for $Sc\sim O(1)$, the Lagrangian approach is more easily extended to both very low and very high Schmidt numbers. The well-known scalar dissipation anomaly is accordingly also addressed in a Lagrangian context.
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Cattaneo, F., and S. M. Tobias. "On the measurement of turbulent magnetic diffusivities: the three-dimensional case." Journal of Fluid Mechanics 735 (October 24, 2013): 457–72. http://dx.doi.org/10.1017/jfm.2013.506.
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AbstractIt has been shown that it is possible to measure the turbulent diffusivity of a magnetic field by a method involving oscillatory sources. So far the method has only been tried in the special case of two-dimensional fields and flows. Here we extend the method to three dimensions and consider the case where the flow is thermally driven convection in a large-aspect-ratio domain. We demonstrate that if the diffusing field is horizontal the method is successful even if the underlying flow can sustain dynamo action. We show that the resulting turbulent diffusivity is comparable with, although not exactly the same as, that of a passive scalar. We were not able to measure unambiguously the diffusivity if the diffusing field is vertical, but argue that such a measurement is possible if enough resources are utilized on the problem.
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Herlina, H., and J. G. Wissink. "Simulation of air–water interfacial mass transfer driven by high-intensity isotropic turbulence." Journal of Fluid Mechanics 860 (December 7, 2018): 419–40. http://dx.doi.org/10.1017/jfm.2018.884.
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Previous direct numerical simulations (DNS) of mass transfer across the air–water interface have been limited to low-intensity turbulent flow with turbulent Reynolds numbers of $R_{T}\leqslant 500$. This paper presents the first DNS of low-diffusivity interfacial mass transfer across a clean surface driven by high-intensity ($1440\leqslant R_{T}\leqslant 1856$) isotropic turbulent flow diffusing from below. The detailed results, presented here for Schmidt numbers $Sc=20$ and $500$, support the validity of theoretical scaling laws and existing experimental data obtained at high $R_{T}$. In the DNS, to properly resolve the turbulent flow and the scalar transport at $Sc=20$, up to $524\times 10^{6}$ grid points were needed, while $65.5\times 10^{9}$ grid points were required to resolve the scalar transport at $Sc=500$, which is typical for oxygen in water. Compared to the low-$R_{T}$ simulations, where turbulent mass flux is dominated by large eddies, in the present high-$R_{T}$ simulation the contribution of small eddies to the turbulent mass flux was confirmed to increase significantly. Consequently, the normalised mass transfer velocity was found to agree with the $R_{T}^{-1/4}$ scaling, as opposed to the $R_{T}^{-1/2}$ scaling that is typical for low-$R_{T}$ simulations. At constant $R_{T}$, the present results show that the mass transfer velocity $K_{L}$ scales with $Sc^{-1/2}$, which is identical to the scaling found in the large-eddy regime for $R_{T}\leqslant 500$. As previously found for a no-slip interface, also for a shear-free interface the critical $R_{T}$ separating the large- from the small-eddy regime was confirmed to be approximately $R_{T}=500$.
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Yang, Yantao, Roberto Verzicco, and Detlef Lohse. "Scaling laws and flow structures of double diffusive convection in the finger regime." Journal of Fluid Mechanics 802 (August 8, 2016): 667–89. http://dx.doi.org/10.1017/jfm.2016.484.
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Direct numerical simulations are conducted for double diffusive convection (DDC) bounded by two parallel plates. The Prandtl numbers, i.e. the ratios between the viscosity and the molecular diffusivities of scalars, are similar to the values of seawater. The DDC flow is driven by an unstable salinity difference (here across the two plates) and stabilized at the same time by a temperature difference. For these conditions the flow can be in the finger regime. We develop scaling laws for three key response parameters of the system: the non-dimensional salinity flux $\mathit{Nu}_{S}$ mainly depends on the salinity Rayleigh number $\mathit{Ra}_{S}$, which measures the strength of the salinity difference and exhibits a very weak dependence on the density ratio $\unicode[STIX]{x1D6EC}$, which is the ratio of the buoyancy forces induced by two scalar differences. The non-dimensional flow velocity $Re$ and the non-dimensional heat flux $\mathit{Nu}_{T}$ are dependent on both $\mathit{Ra}_{S}$ and $\unicode[STIX]{x1D6EC}$. However, the rescaled Reynolds number $Re\unicode[STIX]{x1D6EC}^{\unicode[STIX]{x1D6FC}_{u}^{eff}}$ and the rescaled convective heat flux $(\mathit{Nu}_{T}-1)\unicode[STIX]{x1D6EC}^{\unicode[STIX]{x1D6FC}_{T}^{eff}}$ depend only on $\mathit{Ra}_{S}$. The two exponents are dependent on the fluid properties and are determined from the numerical results as $\unicode[STIX]{x1D6FC}_{u}^{eff}=0.25\pm 0.02$ and $\unicode[STIX]{x1D6FC}_{T}^{eff}=0.75\pm 0.03$. Moreover, the behaviours of $\mathit{Nu}_{S}$ and $Re\unicode[STIX]{x1D6EC}^{\unicode[STIX]{x1D6FC}_{u}^{eff}}$ agree with the predictions of the Grossmann–Lohse theory which was originally developed for the Rayleigh–Bénard flow. The non-dimensional salt-finger width and the thickness of the velocity boundary layers, after being rescaled by $\unicode[STIX]{x1D6EC}^{\unicode[STIX]{x1D6FC}_{u}^{eff}/2}$, collapse and obey a similar power-law scaling relation with $\mathit{Ra}_{S}$. When $\mathit{Ra}_{S}$ is large enough, salt fingers do not extend from one plate to the other and horizontal zonal flows emerge in the bulk region. We then show that the current scaling strategy can be successfully applied to the experimental results of a heat–copper–ion system (Hage & Tilgner, Phys. Fluids, vol. 22, 2010, 076603). The fluid has different properties and the exponent $\unicode[STIX]{x1D6FC}_{u}^{eff}$ takes a different value $0.54\pm 0.10$.
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Lauritzen, P. H., A. J. Conley, J. F. Lamarque, F. Vitt, and M. A. Taylor. "The terminator "toy" chemistry test: a simple tool to assess errors in transport schemes." Geoscientific Model Development 8, no. 5 (May 4, 2015): 1299–313. http://dx.doi.org/10.5194/gmd-8-1299-2015.
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Abstract. This test extends the evaluation of transport schemes from prescribed advection of inert scalars to reactive species. The test consists of transporting two interacting chemical species in the Nair and Lauritzen 2-D idealized flow field. The sources and sinks for these two species are given by a simple, but non-linear, "toy" chemistry that represents combination (X + X → X2) and dissociation (X2 → X + X). This chemistry mimics photolysis-driven conditions near the solar terminator, where strong gradients in the spatial distribution of the species develop near its edge. Despite the large spatial variations in each species, the weighted sum XT = X + 2X2 should always be preserved at spatial scales at which molecular diffusion is excluded. The terminator test demonstrates how well the advection–transport scheme preserves linear correlations. Chemistry–transport (physics–dynamics) coupling can also be studied with this test. Examples of the consequences of this test are shown for illustration.
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Bandyopadhyay, Abhijit, and Anirban Chatterjee. "Realizing interactions between dark matter and dark energy using k-essence cosmology." Modern Physics Letters A 34, no. 27 (September 6, 2019): 1950219. http://dx.doi.org/10.1142/s0217732319502195.
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In this paper, we exploit dynamics of a [Formula: see text]-essence scalar field to realize interactions between dark components of universe resulting in an evolution consistent with observed features of late-time phase of cosmic evolution. Stress–energy tensor corresponding to a [Formula: see text]-essence Lagrangian [Formula: see text] (where [Formula: see text]) is shown to be equivalent to an ideal fluid with two components having same equation of state. Stress–energy tensor of one of the components may be generated from a constant potential [Formula: see text]-essence Lagrangian of form [Formula: see text] ([Formula: see text] constant) and that of other from another Lagrangian of form [Formula: see text] with [Formula: see text]. We have shown that the unified dynamics of dark matter and dark energy described by a single scalar field [Formula: see text] driven by a [Formula: see text]-essence Lagrangian [Formula: see text] may be viewed in terms of diffusive interactions between the two hypothetical fluid components “1” and “2” with stress–energy tensors equivalent to that of Lagrangians [Formula: see text] and [Formula: see text], respectively. The energy transfer between the fluid components is determined by functions [Formula: see text], [Formula: see text] and their derivatives. Such a realization is shown to be consistent with the Supernova Ia data with certain constraints on the temporal behavior of [Formula: see text]-essence potential [Formula: see text]. We have described a methodology to obtain such constraints.
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Kovács, M., and E. Sikolya. "Stochastic reaction–diffusion equations on networks." Journal of Evolution Equations, June 18, 2021. http://dx.doi.org/10.1007/s00028-021-00719-w.
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AbstractWe consider stochastic reaction–diffusion equations on a finite network represented by a finite graph. On each edge in the graph, a multiplicative cylindrical Gaussian noise-driven reaction–diffusion equation is given supplemented by a dynamic Kirchhoff-type law perturbed by multiplicative scalar Gaussian noise in the vertices. The reaction term on each edge is assumed to be an odd degree polynomial, not necessarily of the same degree on each edge, with possibly stochastic coefficients and negative leading term. We utilize the semigroup approach for stochastic evolution equations in Banach spaces to obtain existence and uniqueness of solutions with sample paths in the space of continuous functions on the graph. In order to do so, we generalize existing results on abstract stochastic reaction–diffusion equations in Banach spaces.
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Fernandez Visentini, Alejandro, Pietro de Anna, Damien Jougnot, Tanguy Le Borgne, Yves Méheust, and Niklas Linde. "Electrical Signatures of Diffusion-Limited Mixing: Insights from a Milli-fluidic Tracer Experiment." Transport in Porous Media, May 24, 2021. http://dx.doi.org/10.1007/s11242-021-01607-0.
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AbstractWe investigate how diffusion-limited mixing of a layered solute concentration distribution within a porous medium impacts bulk electrical conductivity. To do so, we perform a milli-fluidic tracer test by injecting a fluorescent and electrically conductive tracer in a quasi two-dimensional (2D) water-saturated porous medium. High resolution optical- and geoelectrical monitoring of the tracer is achieved by using a fluorimetry technique and equipping the flow cell with a resistivity meter, respectively. We find that optical and geoelectrical outputs can be related by a temporal re-scaling that accounts for the different diffusion rates of the optical and electrical tracers. Mixing-driven perturbations of the electrical equipotential field lines cause apparent electrical conductivity time-series, measured perpendicularly to the layering, to peak at times that are in agreement with the diffusion transport time-scale associated with the layer width. Numerical simulations highlight high sensitivity of such electrical data to the layers’ degree of mixing and their distance to the injection electrodes. Furthermore, the electrical data correlate well with time-series of two commonly used solute mixing descriptors: the concentration variance and the scalar dissipation rate.
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Oliveira, Rafael M., and Eckart Meiburg. "Settling-driven instability in two-component stably stratified Hele-Shaw flows." Journal of Fluid Mechanics 843 (March 22, 2018). http://dx.doi.org/10.1017/jfm.2018.215.
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We investigate the onset of instability in a stably stratified two-component fluid in a vertical Hele-Shaw cell when the unstably stratified scalar has a settling velocity. This linear stability problem is analysed on the basis of Darcy’s law, for constant-gradient base states. The settling velocity is found to trigger a novel instability mode characterized by pairs of inclined waves. For unequal diffusivities, this new settling-driven mode competes with the traditional double-diffusive mode. Below a critical value of the settling velocity, the double-diffusive elevator mode dominates, while, above this threshold, the inclined waves associated with the settling-driven instability exhibit faster growth. The analysis yields neutral stability curves and allows for the discussion of various asymptotic limits.
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Jarrahbashi, Dorrin, Sayop Kim, and Caroline L. Genzale. "Simulation of Combustion Recession After End-of-Injection at Diesel Engine Conditions." Journal of Engineering for Gas Turbines and Power 139, no. 10 (April 25, 2017). http://dx.doi.org/10.1115/1.4036294.
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Recent experimental observations show that lifted diesel flames tend to propagate back toward the injector after the end-of-injection (EOI) under conventional high-temperature conditions. The term “combustion recession” has been adopted to reflect this process dominated by “auto-ignition” reactions. This phenomenon is closely linked to the EOI entrainment wave and its impact on the transient mixture–chemistry evolution upstream of the lift-off length. A few studies have explored the physics of combustion recession with experiments and simplified modeling, but the details of the chemical kinetics and convective–diffusive transport of reactive scalars and the capability of engine computational fluid dynamics (CFD) simulations to accurately capture them are mainly unexplored. In this study, highly resolved numerical simulations have been employed to explore the mixing and combustion of a diesel spray after the EOI and the influence of modeling choices on the prediction of these phenomena. The simulations are centered on a temperature sweep around the engine combustion network (ECN) spray-A conditions, from 800 to 1000 K, where different combustion recession behaviors are observed experimentally. Reacting spray simulations are performed via openfoam, using a Reynolds-averaged Navier–Stokes (RANS) approach with a traditional Lagrangian–Eulerian coupled formulation. Two reduced chemical kinetics models for n-dodecane are used to evaluate the impact of low-temperature chemistry and mechanism formulation on predictions of combustion recession behavior. Observations from the numerical simulations are consistent with recent findings that a two-stage auto-ignition sequence drives the combustion recession process. Simulations with two different chemical mechanisms indicate that low-temperature chemistry reactions drive the likelihood of combustion recession.