Towards Simulation of Stratified Turbulent Wakes at Very High Reynolds numbers

Analyzing the dynamics of stratified turbulent wakes through numerical simulation poses large computational and numerical challenges. We will present a high-order flow solver using a Fourier spectral method in the horizontal and a modal spectral element method (SEM) discretization in the wall-normal direction. The use of a modal SEM retains the flexibility of localized flow resolution of the wake core and, in combination with static condensation, results in a large number of small tridiagonal systems that allows us to have an algorithm that is as inexpensive as second-order finite difference schemes. Particular attention has been paid to aspects of the code design/implementation aimed to obtain simulations of wakes at a body-based Reynolds number $Re \sim O(10^6)$. We will discuss code performance, and present results from implicit Large Eddy Simulations of stratified sphere wakes at internal Froude number, $Fr=4$. The preliminary analysis will focus on studying turbulent fine structures during the intermediate-late stage of the wake evolution when the flow is considered to be under strongly stratified conditions. The duration of potentially different regimes at high $Re$ would then be quantified on appropriate regime diagrams.