Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session A29: Turbulence: CompressibilityCompressible Turbulence

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Chair: Sharath Girimaji, Texas A&M University Room: 205 
Sunday, November 19, 2017 8:00AM  8:13AM 
A29.00001: Exact Theory of Compressible Fluid Turbulence Theodore Drivas, Gregory Eyink We obtain exact results for compressible turbulence with any equation of state, using coarsegraining/filtering. We find two mechanisms of turbulent kinetic energy dissipation: scalelocal energy cascade and ``pressurework defect'', or pressurework at viscous scales exceeding that in the inertialrange. Planar shocks in an ideal gas dissipate all kinetic energy by pressurework defect, but the effect is omitted by standard LES modeling of pressuredilatation. We also obtain a novel inverse cascade of thermodynamic entropy, injected by microscopic entropy production, cascaded upscale, and removed by largescale cooling. This nonlinear process is missed by the Kovasznay linear mode decomposition, treating entropy as a passive scalar. For small Mach number we recover the incompressible ``negentropy cascade'' predicted by Obukhov. We derive exact Kolmogorov 4/5thtype laws for energy and entropy cascades, constraining scaling exponents of velocity, density, and internal energy to subKolmogorov values. Although precise exponents and detailed physics are Machdependent, our exact results hold at all Mach numbers. Flow realizations at infinite Reynolds are ``dissipative weak solutions'' of compressible Euler equations, similarly as Onsager proposed for incompressible turbulence. [Preview Abstract] 
Sunday, November 19, 2017 8:13AM  8:26AM 
A29.00002: The influence of compressibility on nonlinear spectral energy transfer – Part 1: Fundamental mechanisms Divya Sri Praturi, Sharath Girimaji Nonlinear spectral energy transfer by triadic interactions is one of the foundational processes in fluid turbulence. Much of our current knowledge of this process is contingent upon pressure being a Lagrange multiplier with the only function of reorienting the velocity wave vector. In this study, we examine how the nonlinear spectral transfer is affected in compressible turbulence when pressure is a true thermodynamic variable with a wave character. We perform direct numerical simulations of multimode evolution at different turbulent Mach numbers of $M_t = 0.03, 0.6$. Simulations are performed with initial modes that are fully solenoidal, fully dilatational and mixed solenoidaldilatational. It is shown that solenoidalsolenoidal interactions behave in canonical manner at all Mach numbers. However, dilatational and mixed mode interactions are profoundly different. This is due to the fact that wavepressure leads to kineticinternal energy exchange via the pressuredilatation mechanism. An important consequence of this exchange is that the triple correlation term, responsible for spectral transfer, experiences nonmonotonic behavior resulting in inefficient energy transfer to other modes. [Preview Abstract] 
Sunday, November 19, 2017 8:26AM  8:39AM 
A29.00003: The influence of compressibility on nonlinear spectral energy transfer  Part 2: Effect on hypersonic boundary layer transition Ankita Mittal, Sharath Girimaji We examine the effect of compressible spectral energy transfer in the nonlinear regime of transition to turbulence of hypersonic boundary layers. The nature of spectral energy transfer between perturbation modes is profoundly influenced by two compressibility mechanisms. First and foremost, the emergence of nonlinear pressuredilatation mechanism leads to kineticinternal energy exchange within the perturbation field. Such interchange is absent in incompressible flow as pressure merely reorients the perturbation amplitude vector while conserving kinetic energy. Secondly, the nature of triadic interactions also changes due to variability in density. In this work, we demonstrate that the efficiency of nonlinear spectral energy transfer is diminished in compressible boundary layers. Emergence of new perturbation modes or `broadbanding' of the perturbation field is significantly delayed in comparison to incompressible boundary layer undergoing transition. A significant amount of perturbation energy is transformed to internal energy and thus unavailable for `tripping' the flow into turbulent state. These factors profoundly change the nature of the nonlinear stage of transition in compressible boundary layer leading to delayed onset of fullfledged turbulence. [Preview Abstract] 
Sunday, November 19, 2017 8:39AM  8:52AM 
A29.00004: Velocityvorticity correlation structures (VVCS) in spatially developing compressible turbulent boundary layer ShiYao Li, ZhenSu She, Jun Chen A velocityvorticity correlation structure (VVCS) analysis is applied to the direct numerical simulation (DNS) of compressible turbulent boundary layer (CTBL) at Mach numbers, $Ma=2.25$, $4.50$ and $6.0$. It is shown that the VVCS analysis captures the geometry variation in the streamwise direction during the transition and in the wallnormal direction in the fully developed regime. Specifically, before transition, the VVCS captures the instability wave number, while in the transition region it displays a distinct scaling change of the dimensions. The fully developed turbulence regime is characterized by a nearly constant spatial extension of the VVCS. Particularly, after turbulence is well developed, a multilayer structure in the wall normal direction is observed in the maximum correlation coefficient and in the length scales of the VVCS, as expected from a recent symmetrybased theory, the ensemble structure dynamics (SED). The most interesting outcome is an observed linear dependence of the length scale of the VVCS from $y^+\approx50$ to $200$, which is a direct support to Townsend’s attachededdy theory. In conclusion, the VVCS analysis quantifies the geometrical characteristics of the coherent structures in turbulent compressible shear flows throughout the whole domain. [Preview Abstract] 
Sunday, November 19, 2017 8:52AM  9:05AM 
A29.00005: Selfconsistent viscous heating of rapidly compressed turbulence Alejandro Campos, Brandon Morgan Given turbulence subjected to infinitely rapid deformations, linear terms representing interactions between the mean flow and the turbulence dictate the evolution of the flow, whereas nonlinear terms corresponding to turbulenceturbulence interactions are safely ignored. For rapidly deformed flows where the turbulence Reynolds number is not sufficiently large, viscous effects can't be neglected and tend to play a prominent role, as shown in the study of Davidovits \& Fisch (2016). For such a case, the rapid increase of viscosity in a plasmaas compared to the weaker scaling of viscosity in a fluidleads to the sudden viscous dissipation of turbulent kinetic energy. As shown in Davidovits \& Fisch, increases in temperature caused by the direct compression of the plasma drive sufficiently large values of viscosity. We report on numerical simulations of turbulence where the increase in temperature is the result of both the direct compression (an inviscid mechanism) and the selfconsistent viscous transfer of energy from the turbulent scales towards the thermal energy. A comparison between implicit largeeddy simulations against wellresolved direct numerical simulations is included to asses the effect of the numerical and subgridscale dissipation on the selfconsistent viscous [Preview Abstract] 
Sunday, November 19, 2017 9:05AM  9:18AM 
A29.00006: Simulation of Compressible Flows and Shock Turbulence Interaction Using Observable Euler and NavierStokes Equations Majid Allahyari, Kamran Mohseni We present the results of numerical simulation of several canonical problems involving shock and turbulence based on an inviscid regularization technique, termed the observable method. This technique applies the observable divergence theorem to the conservation laws to obtain the observable version of Euler and NavierStokes equations. The method is completely inviscid, does not introduce artificial dissipation, and eliminates the need for complex numerical schemes. Simulations of shockvorticity/entropy wave interaction and decaying threedimensional homogeneous isotropic turbulence demonstrate the good performance of the observable method. Moreover, the presented method shows consistent results compared to the DNS results for a canonical shockturbulence interaction problem. [Preview Abstract] 
Sunday, November 19, 2017 9:18AM  9:31AM 
A29.00007: Shock jumps in shockturbulence interactions in the presence of very strong turbulence fluctuations ChangHsin Chen, Diego Donzis Shockturbulence interactions are ubiquitous in nature and engineering and have, thus, been studied extensively with simulations and experiments. With the continuous increase of computational power available, investigations have considered an increasingly wide range of conditions in terms of the strength of turbulence and shock waves. One consistent observation in the literature is the departure from RankineHugoniot relations due to turbulent fluctuations upstream of the shock. Based on the socalled quasiequilibrium assumption, analytical solutions for thermodynamic jumps that take into account the observed "holes" in the shock are presented and compared to new DNS data using shockresolving simulations. By considering the effect of subsonic regions upstream of the shock, the good agreement obtained in previous work is extended to the broken regime at $M_t/\Delta M > 2$. Based on these results we also present refined analytical solutions on the dilatation at the shock. This is discussed in the context of shock structure and the conditions for shock destruction by turbulence. An extended study of how changes experienced by turbulence can be characterized by the flow and thermodynamic conditions will also be discussed. [Preview Abstract] 
Sunday, November 19, 2017 9:31AM  9:44AM 
A29.00008: New insights on compressible turbulent mixing in spectral space John Panickacheril John, Diego Donzis, Katepalli Sreenivasan Previous studies have shown that dilatational forcing has an effect in the dynamics of the velocity field in compressible turbulence. However, there has virtually been no studies of these effects on scalar mixing, the specific mechanisms responsible for compressibility effects and the scaling with governing parameters. Using a large DNS database, generated with different ratios of solenoidal to dilatational forcing, we find that the commonly used turbulent Mach number $(M_{t})$ fails to parametrize mixing efficiency. Instead, the dilatational Mach number $(M_{td}$) is a better scaling parameter to observe nonmonotonic trends. We observe an accumulation of energy at large scales when compressibility is high; this has an effect on the energy and scalar cascade. We analyze both budgets to assess changes in global and interscale statistics for each mode and their interactions. For moderate compressibility levels, the normalized spectra of both modes do not collapse even when their own dissipation rates are used. Furthermore, a dilatational cascade is formed at high compressibilty levels with advection terms scaling with $\chi$, the ratio of dilatational to total kinetic energy. Results on scalar dissipation and their relation to thermodynamic variables are also presented. [Preview Abstract] 
Sunday, November 19, 2017 9:44AM  9:57AM 
A29.00009: Theory of Relativistic Fluid Turbulence Gregory Eyink, Theodore Drivas Relativistic turbulence is expected in highenergy astrophysical flows, e.g. AGN outflow jets. We obtain exact theory by spacetime coarsegraining the fluid stressenergy tensor, giving the analogue of Reynolds stress. Kinetic energy cascade is not natural in relativity, but cascade of internal energy is found with scaletransfer due to contraction of the Reynolds stressenergy tensor with the 4gradient of the coarsegrained 4velocity. Unlike nonrelativistic turbulence, where energy flux is Galileiinvariant, Lorentz invariance of relativistic cascade is broken at finite Reynolds number but restored in the infiniteReynolds limit. Otherwise, our results closely parallel those on nonrelativistic compressible turbulence, with (i) a new mechanism of turbulent energy dissipation due to ``pressuredilatation defect'' exemplified by relativistic shocks and (ii) an inverse cascade of entropy with microscopic entropy production as source and largescale cooling as sink. We obtain Kolmogorov 4/5thtype laws that give estimates on turbulent scaling exponents. When speed of light goes to infinity, our theory recovers nonrelativistic results. The analysis provides the framework for relativistic LES modeling and extends Onsager's ``dissipative Euler'' theory to relativistic turbulence. [Preview Abstract] 
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