Grid-point and time-step requirements for large-eddy simulation and Reynolds-averaged Navier-Stokes of stratified wakes

Estimates of grid-point and time-step requirements exist for many canonical flows but not for stratified wakes. The purpose of this work is to fill in this gap. We apply the basic meshing principles and estimate the grid-point and time-step requirements for Reynolds-averaged Navier-Stokes (RANS) and large-eddy simulation (LES) of stratified wake flows at high Reynolds numbers, as arise in many geophysical, aircraft, and undersea vehicle systems. Scales representative of a submarine operating in a stably stratified ocean environment are considered, and the quantitative conclusions reached here can be adapted accordingly for particular applications. For a submarine, typical wake conditions are R e 0 = 10 8 and F r 0 = 10 2, and wakes extend to Nt = 1000, where Re0 and Fr0 are the initial Reynolds number and the internal Froude number of the wake, respectively, and N is the buoyancy frequency. We consider both spatially developing and temporally evolving wakes. We show that the grid points required for LES and RANS do not depend on the Reynolds number. The ratio of the grid points needed for LES and RANS is proportional to (N t 2, LW) 2 / 3, where t 2, LW marks the end of the late wake and the end of a computational fluid dynamics calculation. According to the present conservative estimates, 0.36 × 10 12 and 0.7 × 10 9 grid points are needed for LES and RANS of a spatially developing wake. The numbers are 8 × 10 9 and 3 × 10 6 for LES and RANS of a temporally evolving wake.