Permanence of large eddies in variable-density homogeneous turbulence with small Mach numbers

Abstract

In this work, we study the large-scale structure of homogeneous flows displaying high density contrasts and small turbulent Mach numbers. Following Batchelor & Proudman (PTRSA 258, 1956), we draw an analogy between this configuration and that of a single isolated eddy displaying density non-uniformities. By doing so, we are able to highlight the crucial role played by the solenoidal component of the momentum in the preservation of initial conditions. In particular, we show that the large-scale initial conditions of the spectrum of the solenoidal momentum are preserved provided its infrared exponent is smaller than $4$. This condition is reminiscent of the one usually derived in constant density flow, except that it does not apply to the velocity spectrum. The latter is actually shown to be impermanent for infrared exponents larger or equal to $2$. The consequences of these properties on the self-similar decay of the flow are discussed. Finally, these predictions are verified by performing large eddy simulations of homogeneous isotropic turbulence.

References in corpus (4)

• Low Mach Number Modeling of Type Ia Supernovae
• Free Decay of Turbulence and Breakdown of Self-Similarity
• Atwood and Reynolds numbers effects on the evolution of buoyancy-driven homogeneous variable-density turbulence
• Variable-density buoyancy-driven turbulence with asymmetric initial density distribution

Cited by in corpus (2)

• Local Wave Number Model for Inhomogeneous Two-Fluid Mixing
• Cascade of circulicity in compressible turbulence