Spatial characterization of vortical structures and internal waves in a stratified turbulent wake using proper orthogonal decomposition

Abstract

Proper orthogonal decomposition (POD) has been applied to two-dimensional transects of vorticity obtained from numerical simulations of the stratified turbulent wake of a towed sphere at a Reynolds number Re=(UD)/ν=5×103 and Froude number Fr=2U/(ND)=4 (U and D are characteristic velocity and length scales and N is the stratification frequency). At 231 times during the interval 12<Nt<35, the streamwise and spanwise vorticity components are sampled on span-depth (yz) and stream-depth (xz) planes, respectively, at select streamwise and spanwise locations. POD appears to provide a natural decomposition of the vorticity field inside the wake core in terms of the relative influence of buoyancy on flow dynamics. The geometry of the individual eigenmodes shows a vorticity structure that is buoyancy-controlled at the lowest modes and is increasingly more actively turbulent as modal index is increased. In the wake ambient, i.e., the initially quiescent region outside the turbulent wake, the geometry of the POD modes consists of distinct internal wave rays whose angle to the horizontal is strongly dependent on modal index. Reconstruction of vorticity fields from subranges of POD modes indicates that, both inside the wake core but also in the wave-dominated ambient, each modal subrange is not only associated with a particular flow structure but also a characteristic timescale of motion. These preliminary findings suggest that POD may be a highly suitable alternative to globally defined basis functions in analyzing spatially localized internal wave fields emitted from a turbulent source that are also localized in space. In particular, it may serve as a platform toward an improved understanding of two fundamental questions associated with the nonequilibrium regime of stratified wake evolution: the structural transitions of the vorticity field within the wake core and the radiation of internal waves by the wake.