Temporal/spatial simulation of the stratified far wake of a sphere

Abstract

Far wakes are generally studied on the basis of a temporal development study, i.e. the flow is assumed periodic in streamwise direction and one focuses on its evolution in time. It is then required to set up an appropriate initial condition to start the calculation. Like in some previous works, we study the far wake of a sphere in a stratified fluid, but rather than starting from an ad hoc initial condition, we first carry out a spatial development simulation in order to define a relevant initialization. The control parameters of the flow are the Prandtl, Reynolds and internal Froude numbers, that we take equal to Pr = 7, Re = 10,000 and F = 25. The numerical method is based on a spectral multi-domain Fourier–Chebyshev approximation, stabilized by using a spectral vanishing viscosity technique, that may be interpreted as a spectral large-eddy simulation closure restricted to the high frequencies. Very realistic results are obtained, especially showing the so-called three-dimensional (3D), non-equilibrium (NEQ) and quasi two-dimensional (Q2D) regimes, with satisfactory comparisons with the experiments.