Numerical Simulation of Energy Cascading in Turbulent Flows Using Sabra Shell Model

Abstract

The transfer of energy in turbulent flows occurs as a product of breaking of smaller and smaller eddies, this implies that in a spectral formulation, the transfer occurs from small wavenumbers to large wavenumbers. In order to observe the energy cascading, dissipation scales must be reached, which depend on the Reynolds number, this makes direct simulations of the Navier-Stokes equation impractical. Reduced models were investigated in recent years, such as shell models. Shell models are built by mimicking the spectral model respecting the mechanisms that are preserved, such as energy conservation, scaling and symmetries. In this paper, we will use the Sabra shell model for the study of the energy cascading in turbulent flows and we will show numerically that the energy dissipation is approximately −1/3 which is in agreement with the K41 theory.