A variable-coefficient model for decay of isotropic turbulence capturing effects of turbulence age and Reynolds number

We study isotropic turbulence decay in the context of k- model which solves the dissipation and kinetic energy equations. In the dissipation equation, the coefficient C, which is related to the temporal decay power-law by n =1/(C-1), 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 suggests that the instantaneous C not only depends on the instantaneous Reynolds number but it is also sensitive to the history of energy injection in turbulence, which we refer to as the age effect. We attribute these observations to the finite time of cascade from the energetic scales to the dissipative scales. Considering data from both decaying and growing forced turbulence, we develop an evolution equation for C 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.