Summary: We present some preliminary results from using large eddy simulation to compute the late wake of a sphere towed at constant speed through a non-stratified and a uniformly stratified fluid. The wake is computed in each case for two values of the Reynolds number: \(Re=10^4\), which is comparable to that used in laboratory experiments, and \(Re=10^5\). An important aspect of the simulation is the use of an iterative procedure to relax the initial turbulence field, so that normal and shear turbulent stresses are properly correlated and the turbulent production and dissipation are in equilibrium. For the lower Reynolds number our results compare well with existing experimental results. For the higher Reynolds number we find that even though the turbulence is more developed and the wake contains finer structure, most of the similarity properties of the wake are unchanged compared with those observed at the lower Reynolds number.