arXiv subjects

Susan Kurien

Publications and source records attributed to Susan Kurien.

18 recordsLinked to original sources

arXiv2021

Local Wave Number Model for Inhomogeneous Two-Fluid Mixing

We present a study of a two-point spectral turbulence model (Local Wave-Number model or LWN model) for the Rayleigh-Taylor (RT) instability. The model outcomes are compared with statistical quantities extracted from three-dimensional simulation of the RT problem. These simulations are initialized with high wavenumber perturbations at the interface of a heavy fluid placed on top of a light fluid so that the density gradient is in the direction opposite to acceleration due to gravity. We consider flows of low to medium density contrast and compare the LWN model against simulation data using the mix-width evolution as the primary metric. The original model specified physically reasonable but largely \emph{ad hoc} terms to account for the inhomogeneous mechanisms involved in growing the mixing layer. We systematically assess the role of each of the terms in the LWN model equations by comparison with simulation. Two of these, the kinematic source term, introduced to maintain a finite covariance between density and specific volume, and a spectral distortion term, introduced as spectral modifications of the density-specific-volume covariance, both result in severely over-predicting the mix layer growth. A simplified model eliminating those two terms is shown to improve the capture of both mix-width evolution as well as the turbulent mass flux velocity profiles across the mix layer at different times. However, this simplification reveals that fidelity to other metrics such as the density-specific-volume covariance, and the turbulent kinetic energy are somewhat compromised. The implications of this outcome are discussed with respect to the physics of the RT problem, and we provide this study as a guide for the practical use of such a model.

physics.flu-dyn↗

arXiv2018

Two-point spectral model for variable-density homogeneous turbulence

We present a study of buoyancy-driven variable-density homogeneous turbulence, using a two-point spectral closure model. We compute the time-evolution of the spectral distribution in wavenumber $k$ of the correlation of density and specific-volume $b(k)$, the mass flux $\bm{a}(k)$, and the turbulent kinetic energy $E(k)$, using a set of coupled equations. Under the modeling assumptions, each dynamical variable has two coefficients governing spectral transfer among modes. In addition, the mass flux $\bm{a}(k)$ has two coefficients governing the drag between the two fluids. Using a prescribed initial condition for $b(k)$ and starting from a quiescent flow, we first evaluate the relative importance of the different coefficients used to model this system, and their impact on the statistical quantities. We next assess the accuracy of the model, relative to Direct Numerical simulation of the complete hydrodynamical equations, using $b$, ${\bm a}$ and $E$ as metrics. We show that the model is able to capture the spectral distribution and global means of all three statistical quantities at both low and high Atwood number for a set of optimized coefficients. The optimization procedure also permits us to discern a minimal set of four coefficients which are sufficient to yield reasonable results while pointing to the mechanisms that dominate the mixing process in this problem.

physics.flu-dyn↗

arXiv2015

Spectral Model of Non-Stationary, Inhomogeneous Turbulence

We compare results from a spectral model for non-stationary, inhomogeneous turbulence (Besnard et al., Theor. Comp. Fluid. Dyn., vol. 8, pp 1-35, 1996) with Direct Numerical Simulation (DNS) data of a shear-free mixing layer (SFML) (Tordella et al., Phys. Rev. E, vol. 77, 016309, 2008). The SFML is used as a test case in which the efficacy of the model closure for the physical-space transport of the fluid velocity field can be tested in a flow with inhomogeneity, without the additional complexity of mean-flow coupling. The model is able to capture certain features of the SFML quite well for intermediate to long-times, including the evolution of the mixing-layer width and turbulent kinetic energy. At short-times, and for more sensitive statistics such as the generation of the velocity field anisotropy, the model is less accurate. We present arguments, supported by the DNS data, that a significant cause of the discrepancies is the local approximation to the intrinsically non-local pressure-transport in physical-space that was made in the model, the effects of which would be particularly strong at short-times when the inhomogeneity of the SFML is strongest.

physics.flu-dyn↗

arXiv2011

Joint downscale fluxes of energy and potential enstrophy in rotating stratified Boussinesq flows

We employ a coarse-graining approach to analyze nonlinear cascades in Boussinesq flows using high-resolution simulation data. We derive budgets which resolve the evolution of energy and potential enstrophy simultaneously in space and in scale. We then use numerical simulations of Boussinesq flows, with forcing in the large-scales, and fixed rotation and stable stratification along the vertical axis, to study the inter-scale flux of energy and potential enstrophy in three different regimes of stratification and rotation: (i) strong rotation and moderate stratification, (ii) moderate rotation and strong stratification, and (iii) equally strong stratification and rotation. In all three cases, we observe constant fluxes of both global invariants, the mean energy and mean potential enstrophy, from large to small scales. The existence of constant potential enstrophy flux ranges provides the first direct empirical evidence in support of the notion of a cascade of potential enstrophy. The persistent forward cascade of the two invariants reflects a marked departure of these flows from two-dimensional turbulence.

physics.flu-dyn↗

arXiv2010

Scaling of high-wavenumber energy spectra in the unit aspect-ratio rotating Boussinesq system

Phenomenological and numerical studies of the small scale spectra of energy are presented for high Reynolds number rotating Boussinesq flows in unit aspect-ratio domains. We introduce a non-dimensional parameter Gamma such that when the potential vorticity is nearly linear in the dynamical variables, we deduce that for Gamma much less than 1, the potential enstrophy suppresses the transfer of horizontal kinetic energy into wavemodes with large horizontal component k_h while forcing it to become independent of vertical wavevector component k_z, scaling as k_h^{-5}. When Gamma much greater than 1, the potential enstrophy suppresses the transfer of potential energy into the wavemodes with large vertical component k_z while forcing it to become independent of k_h, scaling as k_z^{-5) power. Spectra computed from high-resolution simulations of the Boussinesq equations with isotropic low-wavenumber forcing are used to explore such anisotropic constraints on the energy and provide a posteriori justification for the joint flux ansatz used to obtain the (-5) scaling exponent. In all cases the empirical evidence points to both energy and potential enstrophy being jointly transferred downscale with the spectral scaling of the the former constrained by the latter.

nlin.CD↗

arXiv2008

Hyperviscosity, Galerkin truncation and bottlenecks in turbulence

It is shown that the use of a high power $α$ of the Laplacian in the dissipative term of hydrodynamical equations leads asymptotically to truncated inviscid \textit{conservative} dynamics with a finite range of spatial Fourier modes. Those at large wavenumbers thermalize, whereas modes at small wavenumbers obey ordinary viscous dynamics [C. Cichowlas et al. Phys. Rev. Lett. 95, 264502 (2005)]. The energy bottleneck observed for finite $α$ may be interpreted as incomplete thermalization. Artifacts arising from models with $α> 1$ are discussed.

nlin.CD↗

arXiv2007

Spectral scaling of the Leray-$α$ model for two-dimensional turbulence

We present data from high-resolution numerical simulations of the Navier-Stokes-$α$ and the Leray-$α$ models for two-dimensional turbulence. It was shown previously (Lunasin et al., J. Turbulence, 8, (2007), 751-778), that for wavenumbers $k$ such that $kα\gg 1$, the energy spectrum of the smoothed velocity field for the two-dimensional Navier-Stokes-$α$ (NS-$α$) model scales as $k^{-7}$. This result is in agreement with the scaling deduced by dimensional analysis of the flux of the conserved enstrophy using its characteristic time scale. We therefore hypothesize that the spectral scaling of any $α$-model in the sub-$α$ spatial scales must depend only on the characteristic time scale and dynamics of the dominant cascading quantity in that regime of scales. The data presented here, from simulations of the two-dimensional Leray-$α$ model, confirm our hypothesis. We show that for $kα\gg 1$, the energy spectrum for the two-dimensional Leray-$α$ scales as $k^{-5}$, as expected by the characteristic time scale for the flux of the conserved enstrophy of the Leray-$α$ model. These results lead to our conclusion that the dominant directly cascading quantity of the model equations must determine the scaling of the energy spectrum.

physics.flu-dyn↗

arXiv2007

Anisotropic small-scale constraints on energy in rotating stratified turbulence

Rapidly rotating, stably stratified three-dimensional inviscid flows conserve both energy and potential enstrophy. We show that in such flows, the forward cascade of potential enstrophy imposes anisotropic constraints on the wavenumber distribution of kinetic and potential energy. The horizontal kinetic energy is suppressed in the large, nearly horizontal wave modes, and should decay with the horizontal wavenumber as $k_h^{-3}$. The potential energy is suppressed in the large, nearly vertical wave modes, and should decay with the vertical wavenumber as $k_z^{-3}$. These results augment the only other exact prediction for the scaling of energy spectra due to constraints by potential enstrophy obtained by Charney (J. Atmos. Sci. 28, 1087 (1971)), who showed that in the quasi-geostrophic approximation for rotating stratified flows, the energy spectra must scale isotropically with total wavenumber as $k^{-3}$. We test our predicted scaling estimates using resolved numerical simulations of the Boussinesq equations in the relevant parameter regimes, and find reasonable agreement.

nlin.CD↗

arXiv2006

On the Two-point Correlation of Potential Vorticity in Rotating and Stratified Turbulence

A framework is developed to describe the two-point statistics of potential vorticity in rotating and stratified turbulence as described by the Boussinesq equations. The Karman-Howarth equation for the dynamics of the two-point correlation function of potential vorticity reveals the possibility of inertial-range dynamics in certain regimes in the Rossby, Froude, Prandtl and Reynolds number parameters. For the case of large Rossby and Froude numbers, and for the case of quasi-geostrophic dynamics, a linear scaling law with 2/3 prefactor is derived for the third-order mixed correlation between potential vorticity and velocity, a result that is analogous to the Kolmogorov 4/5-law for the third-order velocity structure function in turbulence theory.

nlin.CD↗

arXiv2004

Isotropic third-order statistics in turbulence with helicity: the 2/15-law

The so-called 2/15-law for two-point, third-order velocity statistics in isotropic turbulence with helicity is computed for the first time from a direct numerical simulation of the Navier-Stokes equations in a 512^3 periodic domain. This law is a statement of helicity conservation in the inertial range, analogous to the benchmark Kolmogorov 4/5-law for energy conservation in high-Reynolds number turbulence. The appropriately normalized parity-breaking statistics, when measured in an arbitrary direction in the flow, disagree with the theoretical value of 2/15 predicted for isotropic turbulence. They are highly anisotropic and variable and remain so over a long times. We employ a recently developed technique to average over many directions and so recover the statistically isotropic component of the flow. The angle-averaged statistics achieve the 2/15 factor to within about 7% instantaneously and about 5% on average over time. The inertial- and viscous-range behavior of the helicity-dependent statistics and consequently the helicity flux, which appear in the 2/15-law, are shown to be more anisotropic and intermittent than the cor- responding energy-dependent reflection-symmetric structure functions, and the energy flux, which appear in the 4/5-law. This suggests that the Kolmogorov assumption of local isotropy at high Reynolds numbers needs to be modified for the helicity-dependent statistics investigated here.

nlin.CD↗

arXiv2004

Cascade time-scales for energy and helicity in homogeneous isotropic turbulence

We extend the Kolmogorov phenomenology for the scaling of energy spectra in high-Reynolds number turbulence, to explicitly include the effect of helicity. There exists a time-scale $τ_H$ for helicity transfer in homogeneous, isotropic turbulence with helicity. We arrive at this timescale using the phenomenological arguments used by Kraichnan to derive the timescale $τ_E$ for energy transfer (J. Fluid Mech. {\bf 47}, 525--535 (1971)). We show that in general $τ_H$ may not be neglected compared to $τ_E$, even for rather low relative helicity. We then deduce an inertial range joint cascade of energy and helicity in which the dynamics are dominated by $τ_E$ in the low wavenumbers with both energy and helicity spectra scaling as $k^{-5/3}$; and by $τ_H$ at larger wavenumbers with spectra scaling as $k^{-4/3}$. We demonstrate how, within this phenomenology, the commonly observed ``bottleneck'' in the energy spectrum might be explained. We derive a wavenumber $k_h$ which is less than the Kolmogorov dissipation wavenumber, at which both energy and helicity cascades terminate due to dissipation effects. Data from direct numerical simulations are used to check our predictions.

nlin.CD↗

arXiv2004

Sign-symmetry of temperature structure functions

New scalar structure functions with different sign-symmetry properties are defined. These structure functions possess different scaling exponents even when their order is the same. Their scaling properties are investigated for second and third orders, using data from high-Reynolds-number atmospheric boundary layer. It is only when structure functions with disparate sign-symmetry properties are compared can the extended self-similarity detect two different scaling ranges that may exist, as in the example of convective turbulence.

nlin.CD↗

arXiv2003

Recovering Isotropic Statistics in Turbulence Simulations: The Kolmogorov 4/5th-Law

One of the main benchmarks in direct numerical simulations of three-dimensional turbulence is the Kolmogorov 1941 prediction for third-order structure functions with homogeneous and isotropic statistics in the infinite-Reynolds number limit. Previous DNS techniques to obtain isotropic statistics have relied on time-averaging structure functions in a few directions over many eddy turnover times, using forcing schemes carefully constructed to generate isotropic data. Motivated by recent theoretical work which removes isotropy requirements by spherically averaging structure functions over all directions, we will present results which supplement long-time averaging by angle-averaging over up to 73 directions from a single flow snapshot. The directions are among those natural to a square computational grid, and are weighted to approximate the spherical average. The averaging process is cheap, and for the Kolmogorov 1941 4/5ths law, reasonable results can be obtained from a single snapshot of data. This procedure may be used to investigate the isotropic statistics of any quantity of interest.

nlin.CD↗

arXiv2002

The reflection-antisymmetric counterpart of the Kármán-Howarth dynamical equation

We study the isotropic, helical component in homogeneous turbulence using statistical objects which have the correct symmetry and parity properties. Using these objects we derive an analogue of the Kármán-Howarth equation, that arises due to parity violation in isotropic flows. The main equation we obtain is consistent with the results of O. Chkhetiani [JETP, 63, 768, (1996)] and V.S. L'vov et al. [chao-dyn/9705016, (1997)] but is derived using only velocity correlations, with no direct consideration of the vorticity or helicity. This alternative formulation offers an advantage to both experimental and numerical measurements. We also postulate, under the assumption of self-similarity, the existence of a hierarchy of scaling exponents for helical velocity correlation functions of arbitrary order, analogous to the Kolmogorov 1941 prediction for the scaling exponents of velocity structure function.

nlin.CD↗

arXiv2001

Dynamical equations for high-order structure functions, and a comparison of a mean field theory with experiments in three-dimensional turbulence

Two recent publications [V. Yakhot, Phys. Rev. E {\bf 63}, 026307, (2001) and R.J. Hill, J. Fluid Mech. {\bf 434}, 379, (2001)] derive, through two different approaches that have the Navier-Stokes equations as the common starting point, a set of steady-state dynamic equations for structure functions of arbitrary order in hydrodynamic turbulence. These equations are not closed. Yakhot proposed a "mean field theory" to close the equations for locally isotropic turbulence, and obtained scaling exponents of structure functions and an expression for the tails of the probability density function of transverse velocity increments. At high Reynolds numbers, we present some relevant experimental data on pressure and dissipation terms that are needed to provide closure, as well as on aspects predicted by the theory. Comparison between the theory and the data shows varying levels of agreement, and reveals gaps inherent to the implementation of the theory.

nlin.CD↗

arXiv2000

Measures of Anisotropy and the Universal Properties of Turbulence

Local isotropy, or the statistical isotropy of small scales, is one of the basic assumptions underlying Kolmogorov's theory of universality of small-scale turbulent motion. While, until the mid-seventies or so, local isotropy was accepted as a plausible approximation at high enough Reynolds numbers, various empirical observations that have accumulated since then suggest that local isotropy may not obtain at any Reynolds number. These notes examine in some detail the isotropic and anisotropic contributions to structure functions by considering their SO(3) decomposition. Viewed in terms of the relative importance of the isotropic part to the anisotropic parts of structure functions, the basic conclusion is that the isotropic part dominates the small scales at least up to order 6. This follows from the fact that, at least up to that order, there exists a hierarchy of increasingly larger power-law exponents, corresponding to increasingly higher-order anisotropic sectors of the SO(3) decomposition. The numerical values of the exponents deduced from experiment suggest that the anisotropic parts in each order roll off less sharply than previously thought by dimensional considerations, but they do so nevertheless.

nlin.CD↗

arXiv1999

The Scaling Structure of the Velocity Statistics in Atmospheric Boundary Layer

The statistical objects characterizing turbulence in real turbulent flows differ from those of the ideal homogeneous isotropic model.They containcontributions from various 2d and 3d aspects, and from the superposition ofinhomogeneous and anisotropic contributions. We employ the recently introduceddecomposition of statistical tensor objects into irreducible representations of theSO(3) symmetry group (characterized by $j$ and $m$ indices), to disentangle someof these contributions, separating the universal and the asymptotic from the specific aspects of the flow. The different $j$ contributions transform differently under rotations and so form a complete basis in which to represent the tensor objects under study. The experimental data arerecorded with hot-wire probes placed at various heights in the atmospheric surfacelayer. Time series data from single probes and from pairs of probes are analyzed to compute the amplitudes and exponents of different contributions to the second order statistical objects characterized by $j=0$, $j=1$ and $j=2$. The analysis shows the need to make a careful distinction between long-lived quasi 2d turbulent motions (close to the ground) and relatively short-lived 3d motions. We demonstrate that the leading scaling exponents in the three leading sectors ($j = 0, 1, 2$) appear to be different butuniversal, independent of the positions of the probe, and the large scaleproperties. The measured values of the exponent are $ζ^{(j=0)}_2=0.68 \pm 0.01$, $ζ^{(j=1)}_2=1.0\pm 0.15$ and $ζ^{(j=2)}_2=1.38 \pm 0.10$. We present theoretical arguments for the values of these exponents usingthe Clebsch representation of the Euler equations; neglecting anomalous corrections, the values obtained are 2/3, 1 and 4/3 respectively.

chao-dyn↗

arXiv1998

The Extraction of Anisotropic Contributions in Turbulent Flows

We analyze turbulent velocity signals measured by two probes in the atmosphere, both at the height of 35 meters but displaced by 40 cm nominally orthogonal to the mean wind. Choosing a suitable coordinate system with respect to that of the mean wind, we derive theoretical forms for second order structure functions, and fit them to experimental data. We show that the effect of flow anisotropy is small on the longitudinal component but significant on the transverse component. The data provide an estimate of a universal exponent from among a hierarchy that governs the decay of flow anisotropy with the scale-size.

chao-dyn↗