A novel numerical forcing for homogeneous stratified turbulence in full energy equilibrium

A new numerical method to simulate stationary, homogeneous, and stratified turbulence was developed with an arbitrary energy dissipation rate. Conventional numerical simulations for homogeneous stratified turbulence were accomplished by given mean shears and generated turbulence field either developed or decayed with time. In order to keep stationary turbulence, a linear forcing method for anisotropic turbulence was developed to apply stratified turbulence, where shear was calculated dynamically to satisfy the condition of energy equilibrium. The present method was implemented to direct numerical simulations to realize the generation of small-scale eddy fields, in which the Reynolds number based on the Taylor microscale was about 50. It was confirmed that simulated flow field successfully maintained energy equilibrium with keeping the given dissipation rate. The gradient and flux Richardson numbers determined by the balance of turbulence intensity and stratification were also found to be constant with time. As an application, diffusion of massless dye was numerically simulated in the reproduced turbulent field. The calculated vertical diffusivity was found to be well comparable with that of active heat estimated by a conventional model.