Dynamic mode decomposition of stratified sphere wakes

Dynamic mode decomposition (DMD) has been applied to data from simulations of stably stratified flow past a sphere. The simulation data is obtained using direct numerical simulation (DNS) at Reynolds number, Re = 500, and large-eddy simulation (LES) at a higher Re =10, 000. At Re = 500, the wake changes qualitatively from being three-dimensional and unsteady (although not turbulent) with shedding of three-dimensional vortices in the unstratified case at Fr = ∞ to being unsteady (not turbulent) with shedding of quasi two-dimensional vortices at Fr = 0.125. Stratification also leads to the formation of body-generated steady lee waves which progressively dominate the wake as the strength of stratification increases in the Fr = O(1) regime. The Re = 10, 000 case has fully-developed turbulence in the examined cases of Fr = ∞, 3, 1 with significant differences between Fr = 3 and 1. The objective of the present work is to assess the ability of DMD to capture the varied effects of buoyancy on a bluff body wake. The sparsity-promoting variant of DMD that is employed here helps identify the dynamically important modes once the conventional DMD spectra are obtained. Investigation shows that DMD successfully captures vortex shedding, lee waves, and other large-scale features of stratified flow with a few modes. With increasing number of modes, the reconstruction error decreases systematically in the case of Re = 500 while at Re = 10, 000, the error tends to plateau. Thus, although large-scale flow features and their variation with buoyancy can be captured using a relatively smaller number of modes, it may be necessary to supplement DMD with other reconstruction tools for representation of the turbulent wake at high Re.