Direct numerical simulation of decaying compressible turbulence and shocklet statistics

We present results from 1283 and 2563 direct numerical simulations (DNS) of decaying compressible, isotropic turbulence at fluctuation Mach numbers of Mt∼0.1–0.5 and at Taylor Reynolds numbers Reλ=O(50–100). The presence or absence of fluctuations of thermodynamic quantities as well as velocity divergence in the initial conditions are found to have a negligible effect on the decay of turbulent kinetic energy. The decay of the turbulent kinetic energy shows no significant effect of Mt and power laws fitted to the timewise decay exhibit exponents n=1.3–1.7 that are similar to those found for decaying incompressible turbulence. The main new phenomenon produced by compressibility is the appearance of random shocklets which form during the main part of the decay. An algorithm is developed to extract and quantify the shocklet statistics from the DNS fields. A model for the probability density function (PDF) of the shocklet strength Mn−1 (Mn is the normal shock Mach number) is derived based on combining weak-sho...

[1]  Gordon Erlebacher,et al.  The analysis and simulation of compressible turbulence , 1990, Theoretical and Computational Fluid Dynamics.

[2]  V. M. Edelstein.  Band-spin-orbit-energy effects in conductivity of two-dimensional weakly disordered semiconductor systems , 1995 .

[3]  S. Lele.  Compact finite difference schemes with spectral-like resolution , 1992 .

[4]  J. R. Gurd,et al.  Interactive computer graphics , 1975 .

[5]  J. Peinke,et al.  Turbulence at helium temperature - velocity-measurements , 1994 .

[6]  Parviz Moin,et al.  EDDY SHOCKLETS IN DECAYING COMPRESSIBLE TURBULENCE , 1991 .

[7]  Geoffrey Ingram Taylor,et al.  The Statistical Theory of Isotropic Turbulence , 1937 .

[8]  T. A. Zang,et al.  Toward the large-eddy simulation of compressible turbulent flows , 1990, Journal of Fluid Mechanics.

[9]  Anthony Leonard,et al.  Power-law decay of homogeneous turbulence at low Reynolds numbers , 1994 .

[10]  T. A. Zang,et al.  Direct and large-eddy simulations of three-dimensional compressible Navier-Stokes turbulence , 1992 .

[11]  T. Kármán,et al.  On the Statistical Theory of Isotropic Turbulence , 1938 .

[12]  Sanjiva K. Lele,et al.  Compressibility Effects on Turbulence , 1994 .

[13]  T. Passot,et al.  Numerical simulation of compressible homogeneous flows in the turbulent regime , 1987, Journal of Fluid Mechanics.

[14]  A. Vincent,et al.  The spatial structure and statistical properties of homogeneous turbulence , 1991, Journal of Fluid Mechanics.

[15]  S. Orszag,et al.  Enstrophy budget in decaying compressible turbulence , 1990 .

[16]  Probability density distribution of velocity differences at very high Reynolds numbers. , 1994, Physical review letters.

[17]  S. Orszag,et al.  Energy and spectral dynamics in decaying compressible turbulence , 1992 .

[18]  P. A. Thompson,et al.  Compressible Fluid Dynamics , 1972 .

[19]  J. R. Ristorcelli,et al.  CONSISTENT INITIAL CONDITIONS FOR THE DNS OF COMPRESSIBLE TURBULENCE , 1996 .

[20]  Nagi N. Mansour,et al.  Compressibility effects on the growth and structure of homogeneous turbulent shear flow , 1993, Journal of Fluid Mechanics.

[21]  J. E. Moyal.  The spectra of turbulence in a compressible fluid; eddy turbulence and random noise , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[22]  Gordon Erlebacher,et al.  The analysis and modelling of dilatational terms in compressible turbulence , 1989, Journal of Fluid Mechanics.

[23]  P. Saffman.  The large-scale structure of homogeneous turbulence , 1967, Journal of Fluid Mechanics.

[24]  N. S. Barnett,et al.  Private communication , 1969 .

[25]  Steven A. Orszag,et al.  Energy and spectral dynamics in forced compressible turbulence , 1990 .