Rapid distortion theory for compressible homogeneous turbulence under isotropic mean strain

Abstract

Isotropic compressible turbulence subjected to rapid isotropic compression is studied using inviscid rapid distortion theory ͑RDT͒ and direct numerical simulation. An exact solution to the rapid distortion problem is given. Comparisons are made between the simulation results and the RDT solution, as well as previously studied limiting cases of the RDT solution. The comparisons illustrate the range of applicability of the RDT solutions. Implications for the use of RDT results in modeling compressible turbulent flows are briefly discussed.

The effect of compressibility on turbulent shear flow: a rapid-distortion-theory and direct-numerical-simulation study

“…In addition, m 3α = 0, which implies that the equation for the dilatational field is also uninfluenced by the solenoidal velocity, and the right-hand side of (2.18) is zero. A closed-form solution for this case has been found and discussed by Blaisdell, Coleman & Mansour (1996); its form is simplest when γ is equal to 5/3, so that k 2 and a 2 have the same J −2/3 dependence, and simple solutions in terms of exp(ia 0 k(t)t) (where k(t) = J −1/3 (t)K, and a 0 is the initial mean sound speed) can be obtained for the modified dilatation and pressure modes y = ϕ (3) /Jk and z = p/Jρa 2 . The resulting general solution for the transfer matrix g, for the inviscid case, can then be written:…”

“…Because the initial field is in acoustic equilibrium, the RDT solutions, the pressure-released approximation, and a WKB approximation (Durbin & Zeman 1992) yield equivalent statistics; if the acoustic-equilibrium assumption is not made, however, differences occur. These differences, together with the role of M d for rapid spherical compressions, have been investigated in Blaisdell et al (1996).…”

Spectral Modeling and Numerical Simulation of Compressible Homogeneous Sheared Turbulence

“…(Hunt, 1990& Savill, 1987 and references therein). Many papers in literature deal with homogeneous compressible turbulence and RDT solution Coleman & Mansour, 1991;Blaisdell et al, 1993Blaisdell et al, , 1996Durbin & Zeman, 1992;Jacquin et al, 1993;Livescu & Madnia, 2004;Riahi et al, 2007;Riahi, 2008;Riahi & Lili, 2011;Sarkar, 1995;Simone, 1995;Simone et al, 1997). These studies have yielded very valuable physical insight and closure model suggestions.…”

“…The study of compressibility effects on the turbulent homogeneous shear flow behavior made these last years the objective of several researches as mentioned in the works of Blaisdell et al (1993Blaisdell et al ( & 1996 and Sarkar et al (1991Sarkar et al ( & 1992. DNS developed by Sarkar (1995) show that the temporal growth rate of the turbulent kinetic energy is extensively influenced by compressibility.…”

Equilibrium states of homogeneous sheared compressible turbulence

“…Many papers in literature deal with homogeneous compressible turbulence and RDT solution. [5][6][7][8][9][10][11][12][13][14][15][16][17] These studies have yielded very valuable physical insight and closure model suggestions. In all the above works, the fluctuation equations are solved directly to infer turbulence physics.…”