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Jesse Legaspi | Applied Mathematics, University of Waterloo
Exploration of the full nonlinear wave/potential-vortex mode decomposition of stratified turbulence DNS
Fluid motion in stratified turbulence is comprised of internal gravity waves and quasi-horizontal vortices. To fundamentally understand the dynamics of stratified turbulence, the two modes can be studied for their individual behaviour and the nature of their interactions. This necessitates some means of separating stratified turbulence into their wave mode and vortex mode. The wave/potential-vortex decomposition in Staquet and Riley (1989) (hereafter, SR89) is one such method developed for purely stratified flows with finite Froude number.
In the proposed project, the SR89 decomposition is implemented and includes a filtering method that preconditions the field variables, which removes problematic small-scale fluctuations. The method is examined for its convergence and the filter is analyzed for its effect on the kinetic energy spectra for both wave and potential-vortex modes. The examined simulations are configured so that kinetic energy spectra of both modes can be decently analyzed as the buoyancy Reynolds number and the stratification strength are varied. Next, as an important characterizing property, the potential vorticity will be studied by means of a spectral budget equation obtained for the potential enstrophy, a related quantity. Through the SR89 decomposition method, the potential-vortex mode is easily accessible and facilitates this analysis. Lastly, we make an excursion to very small length scales to study intermittency in stratified turbulence. Small-scale turbulence that the SR89 decomposition filters out can be retained and analyzed, primarily by examining distribution plots and computing statistical moments.