Reynolds stresses and budgets in temporally-evolving stratified wakes*

We present detailed analyses of the Reynolds stresses and their budgets in temporally evolving stratified wakes using direct numerical simulation. Ensemble averaging is employed to mitigate statistical errors in the data, and the results are presented as functions of both the transverse and vertical coordinates---at multiple time instants across the near-wake, non-equilibrium, and quasi-two-dimensional regimes for wakes in weakly and strongly stratified environments. We first study the spatial structures of the Reynolds stresses as well as their budget terms. Key findings include the identification of dominant terms in the Reynolds stress transport equations, the generation and destruction processes of the Reynolds stresses, the role of spatial and inter-component redistribution of the Reynolds stresses, and the energy transfer between the Reynolds stress and the mean flow. The study also examines the effects of the Reynolds number and the Froude number. Additionally, we assess the validity of the eddy-viscosity-type models and some existing closures for the Reynolds stress model, highlighting the limitations of isotropy and return-to-isotropy hypotheses in stratified flows.