New subgrid-scale models for the large-eddy simulation of compressible turbulent flows are developed and tested based on the Favre-filtered equations of motion for an ideal gas. A compressible generalization of the linear combination of the Smagorinsky model and scale-similarity model, in terms of Favre-filtered fields, is obtained for the subgrid-scale stress tensor. An analogous thermal linear combination model is also developed for the subgrid-scale heat flux vector. The two dimensionless constants associated with these subgrid-scale models are obtained by correlating with the results of direct numerical simulations of compressible isotropic turbulence performed on a 96 (exp 3) grid using Fourier collocation methods. Extensive comparisons between the direct and modeled subgrid-scale fields are provided in order to validate the models. A large-eddy simulation of the decay of compressible isotropic turbulence (conducted on a coarse 32(exp 3) grid) is shown to yield results that are in excellent agreement with the fine-grid direct simulation. Future applications of these compressible subgrid-scale models to the large-eddy simulation of more complex supersonic flows are discussed briefly.

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Toward the large-eddy simulation of compressible turbulent flows

Large-Eddy Simulation of the Shock/Turbulence Interaction

Supersonic random motions are observed in dark clouds and are traditionally interpreted as Alfven waves, but the possibility that these motions are super-Alfvenic has not been ruled out. In this work we report the results of numerical experiments in two opposite regimes: A ~ 1 and A 1, where A is the initial Alfvenic Mach number—the ratio of the rms velocity to the Alfven speed. Our results show that models with A 1 are consistent with the observed properties of molecular clouds that we have tested (statistics of extinction measurements, distribution of integrated antenna temperature, Zeeman-splitting measurements of magnetic field strength, line width versus integrated antenna temperature of molecular emission-line spectra, statistical B-n relation, and scatter in that relation), while models withA ~ 1 have properties that are in conflict with the observations. We find that both the density and the magnetic field in molecular clouds may be very intermittent. The statistical distributions of the magnetic field and gas density are related by a power law, with an index that decreases with time in experiments with decaying turbulence. After about one dynamical time it stabilizes at B ∝ n0.4. Magnetically dominated cores form early in the evolution, while later on the intermittency in the density field wins out, and also cores with a weak field can be generated by mass accretion along magnetic field lines.

A Super-Alfvénic Model of Dark Clouds

In this paper a concept of dilatation dissipation ed for high Reynolds number compressible turbulence is introduced. The concept is predicated on the existence of shocklike structures embedded within energetic turbulent eddies. A parametric expression for ed is found that contains calculable parameters of a turbulent field: turbulence energy and length scale, rms (turbulent) Mach number, and the kurtosis of the fluctuating velocity. The dilatation dissipation is incorporated in a second‐order closure model for compressible mixing layers and model predictions of mean and turbulence quantities are presented and, where possible, compared with experiments. It is shown that the model is capable of predicting the reduction of layer growth rates as a function of the convective Mach number Mc in accordance with Papamoschou–Roshko experiments; the computations are also shown to compare well with available measurements of Reynolds stresses at Mc=0.5–0.86. Finally, the physical implications of the new model and resu...

Dilatation dissipation: The concept and application in modeling compressible mixing layers

Compressibility Effects on Turbulence

Compressible flows with r.m.8. velocities of the order of the speed of sound are studied with direct numerical simulations using a pseudospectral method. We concentrate on turbulent homogeneous flows in the two-dimensional case. The fluid obeys the Navier-Stokes equations for a perfect gas, and viscous terms are included explicitly. No modelling of small scales is used. We show that the behaviour of the flow differs sharply at low compared with high r.m.9. Mach number Ma, with a transition at Mu = 0.3. In the large scales, temporal exchanges between longitudinal and solenoidal modes of energy retain an acoustical character; they lead to a slowing down of the decrease of the Mach number with time, which occurs with interspersed plateaux corresponding to quiescent periods. When the flow is initially supersonic, the small scales are dominated by shocks behind which vortices form. This vortex production is particularly prominent, when two strong shocks collide, with the onset of shear turbulence in the region downstream of the collision. However, at the resolutions reached by our code on a 256 x 256 uniform grid, this mechanism proves insufficient to bring vortices into equipartition with shocks in the small-scale tail of the energy spectrum.

T. Passot

Papers

Numerical simulation of compressible homogeneous flows in the turbulent regime