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arXiv · 2004.02726

On cascade of kinetic energy in compressible hydrodynamic turbulence

Petr Hellinger·Andrea Verdini·Simone Landi·Luca Franci·Emanuele Papini·Lorenzo Matteini
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Abstract

Properties of the turbulent cascade of kinetic energy are studied using direct numerical simulations of three-dimensional hydrodynamic decaying turbulence with a moderate Reynolds number and the initial Mach number $M=1$. Compressible and incompressible versions of the Karman-Howarth-Monin (KHM) and low-pass filtering/coarse-graining approaches are compared. In the simulation the total energy is well conserved; the scale dependent KHM and coarse-grained energy equations are also well conserved; the two approaches show similar results, the system does not have an inertial range for the cascade of kinetic energy, the region where this cascade dominates also have a non-negligible contribution of the kinetic-energy decay, dissipation, and pressure-dilatation effects. While the two approaches give semi-quantitatively similar results for the kinetic energy cascade, dissipation and pressure-dilatation rates, they differ in the increment separation and filtering scales; these scales are not simply related. The two approaches may be used to find the inertial range and to determine the cascade/dissipation rate of the kinetic energy.

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Petr Hellinger, Andrea Verdini, Simone Landi, Luca Franci, Emanuele Papini, Lorenzo Matteini. 2020-04-06. On cascade of kinetic energy in compressible hydrodynamic turbulence. https://arxiv.org/abs/2004.02726

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