A variable-coefficient model for decay of isotropic turbulence capturing effects of finite cascade time and Reynolds number
We study isotropic turbulence decay in the context of the k-epsilon model, which solves the dissipation and kinetic energy equations. In modeling the dissipation equation, the coefficient C_epsilon2, suggested by Hanjalic and Launder [Journal of Fluid Mechanics, 1972] [1], is related to the temporal decay power-law by n = 1/(C_epsilon2 -1 )) and is assumed to be a constant value. In this work, we perform high-fidelity numerical simulations to examine the mathematical terms responsible for the decay of isotropic turbulence, considering both scenarios of forced and decaying turbulence. Our data suggest that the instantaneous C_epsilon2 not only depends on the instantaneous Reynolds number but is also sensitive to the history of energy injection in turbulence. We attribute these observations to the finite time required for the cascade from energetic to dissipative scales. Considering data from both decaying and growing forced turbulence, we develop an evolution equation for C_epsilon2 with Reynolds-dependent coefficients. We demonstrate that this model accurately captures the time evolution of dissipation and kinetic energy over a wide range of Reynolds numbers under a wide range of forced and decay scenarios.