The Modified Zero-Fourth Cumulant Approximation for Burgers Turbulence

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  • Modified Zero Fourth Cumulant Approxima

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Abstract

Burgers turbulence is investigated using the modified zero-fourth cumulant approximation which was employed by Tatsumi et al. (J. Fluid Mech. 85 (1978) 97) for incompressible isotropic turbulence. The dynamical equation for the energy spectrum due to this approximation is solved numerically for two typical initial conditions. The energy spectrum is shown to satisfy each similarity law in the energy-containing and the energy-dissipation ranges respectively. The spectrum assumes the k−2 form, k being the wavenumber, at wavenumbers just beyond the energy-containing range and the exp (−σk) form, σ being a constant, in the far-dissipation range. Statistical quantities such as the energy, the skewness of the velocity derivative, the microscale and the microscale Reynolds number are derived from the data of the energy spectrum. Comparative discussions are made with the results due to shock dynamics and numerical experiments.

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