Numerical simulation of the wake of a towed sphere in a weakly stratified fluid

Abstract

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 = 104, which is comparable to that used in laboratory experiments, and Re = 105. An important aspect of the simulation is the use of an iterative procedure to relax the initial turbulence field so that the 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 laboratory 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.

Self-preservation in stratified momentum wakes

“…On the other hand, high Re, high resolution, numerical simulations of a simple stratified flow geometry [15] have indicated that as Re increases, more small-scale instabilities of the vertical shear layers develop, becoming a continuous source of small-scale turbulence, and raising the idea that at sufficiently high Re, the large-scale coherent structures seen in laboratory experiment may never develop, or survive. However in the range of Re l ∈ [800, 6400], where l is a numerically-imposed initial length scale of the Taylor-Green vortices, the large-scales were only weakly dependent on Re l , a finding that is consistent with the increased fine structure of the higher Re wake simulations of Dommermuth et al [11], but which still produced large-scale structures in the late wake.…”

“…All contributions from internal wave motions which lead to significant peaks in experimental measurements of u w as late as N t = 15 [17] are omitted, as are any production terms where energy is drawn to the mean flow from the turbulent motions. Anisotropy of the dissipation rate tensor and of the velocity and vorticity energy balance has been noted and discussed in simulations of stratified turbulence [22,23] and specifically for DNS of stratified wakes [10,11]. The analysis that follows must be considered one where such intermediate dynamics are ignored, valid at the latter stages of the wake evolution only when w ≈ 0 and u w << u v .…”

“…A momentum Froude number of 8.89, and a momentum Reynolds number of 2250 correspond to F = 4 and Re = 5000 for the canonical towed-sphere example, allowing comparisons with experimental results from three different facilities [12,4,8] and with numerical simulations that used three different methods [10,11,27].…”

“…The basic phenomenology of the NEQ and Q2D regimes has been replicated also in numerical simulations [10,11], but agreement on vertical length scales has been more elusive.…”

“…Numerical simulations appeared to share similar features [10,11], but the setting of the initial vertical length scales according to F was never resolved as the simulations would typically be run for only one finite value of F . This vertical growth of the wake is not yet well understood and precise measurements have been difficult to obtain, both experimentally and numerically.…”