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

Abstract

Proper orthogonal decomposition ͑POD͒ 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= ͑UD͒ / =5ϫ 10 3 and Froude number Fr= 2U / ͑ND͒ =4 ͑U and D are characteristic velocity and length scales and N is the stratification frequency͒. At 231 times during the interval 12Ͻ Nt Ͻ 35, the streamwise and spanwise vorticity components are sampled on span-depth ͑yz͒ and stream-depth ͑xz͒ 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.

Analysis of coherence in turbulent stratified wakes using spectral proper orthogonal decomposition

“…Visual inspection shows that the spatial coherence in the wake core, which is a characteristic of dominant SPOD modes, is lost for the high- and high- modes similar to the result in the snapshot POD study of Diamessis et al. (2010). For both and wakes, in the wake core is dominated by small-scale turbulence.…”

“…However, applications of modal decomposition to stratified flows are few in number. Diamessis, Gurka & Liberzon (2010) performed snapshot POD (Sirovich (1987)) on the vorticity field from a temporal simulation at and , noting a link between wake core structures and the angle of emission of IGWs in the outer wake. The layered wake core structure, which is a distinctive feature of stratified turbulent wakes, was found in the POD modes with lower modal index (corresponding to higher energy).…”

Laboratory and numerical experiments on the near wake of a sphere in a stably stratified ambient

“…Then the associated local horizontal length scale, l h = u t loc . The process is similar to that used by Diamessis, Gurka & Liberzon (2010) and Xiang et al (2015), and is repeated for each experimental run and then averaged over all runs. If we retain the local u as a measure of the available kinetic energy in velocity fluctuations, and we keep l h as an indicator of turbulent length scales, then…”

Proper orthogonal decomposition analysis of vortex dynamics of a circular cylinder under synthetic jet control

“…5,7,10,12,17,32,33 Meyer et al 16 showed us a simple way to solve this problem as listed in the following from Eq. The above presents a brief view of the main concept of the POD method and the rigorous presentation of this method can be found elsewhere.…”