Reduced-order representation of stratified wakes by proper orthogonal decomposition utilizing translational symmetry

Abstract

Visualizations of reduced-order representations of stratified wakes of Reynolds number $Re \in \{5,25,100\}\times 10^3$ are presented at a fixed internal Froude number. The reduced-order representations are constructed by applying proper orthogonal decomposition (POD) to numerical datasets that are high-resolution, three-dimensional and time-dependent. Due to the transient nature of the flow, the dynamics to be represented are highly non-stationary, posing a challenge for the effectiveness of POD. The translational symmetry inherent in the computational configuration is utilized for the POD analysis. This technique turns out to be effective in terms of improving the convergence of energy content represented by the POD modes and enhancing the interpretability of the temporal dynamics. Individual POD modes representing distinct dynamics of various scales are visualized. In the turbulent region, visualizations of the reconstructed vertical vorticity fields suggest that the dominant length scale of flow structures decreases with the modal index. For internal wave motions, visualizations of the reconstructed vertical velocity fields show the opposite trend, as the wavelength of internal waves observed in the wake’s ambient increases with the modal index. The temporal coefficients for a given mode are observed to vary minimally between $Re = 2.5\times 10^4$ and $10^5$, suggesting a potential asymptote of the large-scale temporal dynamics in terms of Reynolds number.

Graphical abstract