Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session R23: Turbulence Theory: Rotating/Stratified/Compressible |
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Chair: Georgios Matheou, Jet Propulsion Laboratory Room: 30D |
Tuesday, November 20, 2012 1:00PM - 1:13PM |
R23.00001: Anisotropy statistics in homogeneous stratified sheared turbulence Georgios Matheou, Daniel Chung Stably stratified flows are prominent in many engineering and geophysical applications. Stratified turbulence is characterized by anisotropic large scales but for a high Reynolds number flow smaller scales are expected to become progressively more isotropic. We investigate the anisotropy characteristics of stationary homogeneous stratified sheared turbulence at various stratifications and Reynolds numbers. Three sets of direct numerical simulations are utilized with $Re_\lambda = 220$--800. For each Taylor Reynolds number, four simulations were carried out that range from neutral to very stably stratified conditions. Elementary anisotropy statistics are discussed and compared to estimates for the onset of local isotropy. [Preview Abstract] |
Tuesday, November 20, 2012 1:13PM - 1:26PM |
R23.00002: Small-scale turbulence in stably stratified flows Saba Almalkie, Steve de Bruyn Kops We study statistical characteristics of small-scale turbulence under the stabilizing effect of stratification using direct numerical simulations of horizontally homogeneous, vertically stratified turbulence. The simulations use up to $4096\times4096\times2048$ grid points to resolve the dissipation scales over a range of Froude and buoyancy Reynolds numbers. The focus is on the effects of large-scale anisotropy associated with different levels of stratification on the dynamics and isotropy of small scales. The isotropy of small scales is addressed in terms of full statistical analysis of the velocity gradient tensor up to the fourth order. Our results reveal the two dominant dynamics of stratified turbulence as three-dimensional turbulence and background stratified flow. These two competing dynamics affect each component of the velocity gradient tensor differently. As a result, statistical characteristics of kinetic energy dissipation rate depend on the stratification level. The probability density function of local energy dissipation rate reflects these two dominant dynamics by exhibiting a bimodal distribution. The results shed light on the definition of proper surrogates for energy dissipation rate in flows dominated by stratified turbulence. [Preview Abstract] |
Tuesday, November 20, 2012 1:26PM - 1:39PM |
R23.00003: Acceleration Statistics in Rotating and Sheared Turbulence Frank Jacobitz, Kai Schneider, Wouter Bos, Marie Farge Acceleration statistics are of fundamental interest in turbulence ranging from theoretical questions to modeling of dispersion processes. Direct numerical simulations of sheared and rotating homogeneous turbulence are performed with different ratios of Coriolis parameter to shear rate. The statistics of Lagrangian and Eulerian acceleration are studied with a particular focus on the influence of the rotation ratio and also on the scale dependence of the statistics. The probability density functions (pdfs) of both Lagrangian and Eulerian acceleration show a strong and similar influence on the rotation ratio. The flatness further quantifies its influence and yields values close to three for strong rotation. For moderate and vanishing rotation, the flatness of the Eulerian acceleration is larger than that of the Lagrangian acceleration, contrary to previous results for isotropic turbulence. A wavelet-based scale-dependent analysis shows that the flatness of both Eulerian and Lagrangian acceleration increases as scale decreases. For strong rotation, the Eulerian acceleration is more intermittent than the Lagrangian acceleration, while the opposite result is obtained for moderate rotation. [Preview Abstract] |
Tuesday, November 20, 2012 1:39PM - 1:52PM |
R23.00004: Scale locality and the inertial range in compressible turbulence Hussein Aluie We use a coarse-graining approach to prove that inter-scale transfer of kinetic energy in compressible turbulence is dominated by local interactions. Locality here means that interactions between disparate scales decay at least as fast as a power-law function of the scale-disparity ratio. In particular, our results preclude transfer of kinetic energy from large-scales directly to dissipation scales, such as into shocks, in the limit of high Reynolds number turbulence as is commonly believed. The assumptions we make in our proofs on the scaling of velocity, pressure, and density structure functions are weak and enjoy compelling empirical support. Under a stronger assumption on pressure dilatation co-spectrum, we show that \emph{mean} kinetic and internal energy budgets statistically decouple beyond a transitional ``conversion'' range. Our analysis demonstrates the existence of an ensuing inertial scale-range over which mean SGS kinetic energy flux becomes constant, independent of scale. Over this inertial range, mean kinetic energy cascades locally and in a conservative fashion, despite not being an invariant. We provide numerical support to our results on locality through an investigation of the cascade in the presence of shocks in Burger's flow. [Preview Abstract] |
Tuesday, November 20, 2012 1:52PM - 2:05PM |
R23.00005: The role of helicity in stratified turbulence Cecilia Rorai, Duane Rosenberg, Annick Pouquet, Pablo D. Mininni In magnetohydrodynamics (MHD) helicity plays an important role in the generation of large-scale magnetic fields; in atmospheric sciences, it has been claimed to be responsible for the stability of supercell thunderstorms, while in homogeneous and isotropic turbulence it is known to delay the energy decay but leave the statistical properties of the flow unaltered, thus being considered marginally relevant. However, recent numerical calculations have demonstrated that when rotation is introduced in the system, helicity plays an essential role. We report preliminary results on a numerical study of freely decaying strongly stratified turbulence, as occurs in the atmosphere and oceans, in the presence of helicity. The Boussinesq equations are integrated in a periodic domain with different initial conditions: a non-helical Taylor-Green flow, a fully helical Beltrami flow, and random flows with a tunable helicity. Different values of the Reynolds and Froude numbers are selected. The question we address is how these different initial velocity fields and helicity values affect the evolution of turbulence in terms of excitation of internal waves, energy decay and isotropic and anisotropic energy spectra. [Preview Abstract] |
Tuesday, November 20, 2012 2:05PM - 2:18PM |
R23.00006: Modeling various effects of compressibility on the pressure Hessian tensor Sawan Suman, Sharath Girimaji Modeling the role of the pressure Hessian tensor in the evolution of turbulent velocity gradients is critical for developing closed Lagrangian equations of velocity gradients. In incompressible flows, substantial success has been achieved in this regard (Chevillard et al. Phys. Fluids, 2008). However, these incompressible models strongly hinge on Poisson equation of pressure, and thus - despite their success in incompressible flows - are not useful for compressible flows, wherein pressure behaves as a bona-fide thermodynamic variable evolving via the state and energy equations. Some initial attempts at modeling the pressure Hessian tensor inclusive of essential compressible physics have recently been made (Suman {\&} Girimaji, J. Fluid Mech. 2009, 2011). However several further improvements are still desirable. With this motivation, we present a novel strategy of including further compressibility physics in these models by directly parameterizing a local state of the pressure Hessian tensor in terms of (i) local dilatation and (ii) rate of change of local dilatation. The rationale behind this modeling strategy and an evaluation of the model performance will be presented. [Preview Abstract] |
Tuesday, November 20, 2012 2:18PM - 2:31PM |
R23.00007: Small-scale intermittency and shocks in high Reynolds number compressible turbulence Diego Donzis In many flows of interest turbulence interacts with shock waves. A canonical configuration is isotropic turbulence convected through a normal shock. Even without this shock, compressible flows develop so-called shocklets, which may affect the overall dynamics. It is also well-known that due to intermittency scales smaller than the mean Kolmogorov scale (associated with very large gradients) develop at high Reynolds numbers. It is, therefore, of interest to assess whether and under what conditions intermittent gradients can be comparable to those of shocks. Information about the most intense turbulence gradients is obtained from scaling exponents of structure functions. It is shown that in turbulence obeying Kolmogorov scaling, turbulence gradients become weak compared to shock gradients as Reynolds number increases. However, for turbulence with anomalous scaling, gradients are comparable to that of shocks. This provides a plausible mechanism for so-called broken regimes in shock-turbulence interactions where flow properties undergo smooth changes instead of a quasi-discontinuous jump across the shock. Furthermore, our DNS database is used to show that large gradients and velocities are correlated, an effect that increases the effectiveness of turbulence to disrupt shocks. [Preview Abstract] |
Tuesday, November 20, 2012 2:31PM - 2:44PM |
R23.00008: A simple model for space-time correlation in compressible isotropic turbulence Dong Li, Li Guo, Xing Zhang, Guowei He Space-time correlation is fundamental to describe turbulent fluctuations in both space and time. Kraichnan proposes the sweeping model for space-time correlations in incompressible isotropic turbulence. Taylor's model for turbulent shear flows is broadly used although it is limited to the frozen-flow assumption. The extension of Taylor's model to non-frozen flows can be achieved by including the eddy distortion with experimental validation. However, these models don't apply to compressible turbulent flows. Lee et al (1992) develop a model for the compressible components of compressible flows. In this study, we will develop a model for space-time correlations of velocity fluctuations which contain both compressible and incompressible components. The model reveals two dynamic processes of turbulent fluctuations in compressible turbulence: (1) the compressible component propagates at the sound speed relative to local flow; (2) the local flow is convected by energy-contained eddies. The model is supported by direct numerical simulation of compressible isotropic turbulence in the sense of that all curves of the normalized time correlations for different wavenumbers collapse into a single one and their envelope is governed by the attenuation term in the present model. [Preview Abstract] |
Tuesday, November 20, 2012 2:44PM - 2:57PM |
R23.00009: Statistics for One-dimensional Compressible Turbulence with Large-scale Forcing Qionglin Ni, Shiyi Chen A numerical study was performed to explore the difference between the one-dimensional hydrodynamic compressible turbulence and Burgers turbulence. The compressible flows were simulated at three different turbulent Mach numbers ($M_{t}$): 0.1, 1.0 and 3.2 using a large-scale random forcing scheme. We observed that the isentropic condition was approximately valid in the $M_{t}$ = 1.0 case, and its statistical scalings were close to those in the Burgers equation. We then used the subensemble method to decompose the velocity field of the flow into two subensembles, according to the local energy fluxes in the positive and negative directions, respectively, and found that the subensemble probabilities were scale invariant in the inertial range. Further investigation revealed that the corresponding transition process between two subensembles in the compressible turbulence, unlike its Markovian counterpart in the Burgers turbulence, was not in accordance with a Markov process. [Preview Abstract] |
Tuesday, November 20, 2012 2:57PM - 3:10PM |
R23.00010: On the cascade of kinetic energy in three-dimensional compressible turbulence Jianchun Wang, Yantao Yang, Yipeng Shi, Zuoli Xiao, Xiantu He, Shiyi Chen A high resolution numerical simulation of three-dimensional compressible turbulence with large scale forcing is performed to study the kinetic energy transfer. In particular, the forcing scheme is designed to control the ratio of energy input from the solenoidal and compressive velocity components. Numerical simulation reveals that the compressive component of the density-weighted velocity has major contribution to the kinetic energy flux, due to the presence of large-scale shocks. Using a ``coarse-graining'' approach, we further show that the kinetic energy flux from both solenoidal and compressive components are nearly constant over the inertial range. However, the cascade rate of compressive mode is much faster than that of solenoidal mode, leading to the dominant of solenoidal kinetic energy over its compressive counterpart at high wavenumbers. We argue that this difference between the energy transfer rates is the major physical reason why the energy spectrum in the compressible turbulence always displays the Kolmogorov's -5/3 scaling in the inertial range, a phenomenon of incompressible turbulence. [Preview Abstract] |
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