We analyze a large-eddy simulation data set of wakes of a towed sphere of diameter $D$ at speed $U$ in a uniformly stratified Boussinesq fluid with buoyancy frequency $N$ and kinematic viscosity $\nu$. These temporally evolving wakes are simulated using a spectral multidomain penalty-method-based incompressible Navier-Stokes solver for $\text{Fr}\equiv 2U/ND\in \{4,16,64\}$ and $\text{Re}\equiv UD/\nu \in \{5\times {10}^3,{10}^5,4\times {10}^5\}$, enabling a systematic examination of stratified wakes at three different values of $\text{Re}$ sufficiently separated in magnitude. As such, particular attention is paid to the effects of varying $\text{Re}$ on the evolution of large-scale characteristics of stratified wake turbulence. We examine the evolution of horizontal and vertical integral length scales (${\ell }_h$ and ${\ell }_v$), horizontal and vertical fluctuation velocities ($\mathcal{U}$ and $\mathcal{W}$), local vertical shear, as well as the resulting dimensionless parameters based on the above quantities. In particular, the vertical turbulent Froude number ${\text{Fr}}_v^{★}\equiv 2\pi \mathcal{U}/N{\ell }_v$ is found to be of order unity, a signature of the dynamics in the strongly stratified regime where shear instabilities develop between anisotropic flow layers. The horizontal turbulent Reynolds number ${\text{Re}}_h\equiv \mathcal{U}{\ell }_h/\nu$ stays approximately constant in time and the horizontal turbulent Froude number ${\text{Fr}}_h\equiv \mathcal{U}/N{\ell }_h$ decays in time as ${\left(Nt\right)}^{-1}$, consistent with scaling analysis of freely decaying turbulence. We characterize the transitions between distinct stratified flow regimes and examine the effects of body-based parameters $\text{Re}$ and $\text{Fr}$ on these transitions. The transition from the weakly to the strongly stratified regime, which is marked by ${\text{Fr}}_v^{★}$ decaying to unity, occurs when ${\text{Fr}}_h\simeq O\left(0.01\right)$. We further show that the initial value of ${\text{Re}}_h$ at which the flow completes the above transition scales as $\text{Re}{\text{Fr}}^{-2/3}$, which provides a way to predict the possibility of accessing the strongly stratified regime for a wake of given $\text{Re}$ and $\text{Fr}$. The analysis reported here constitutes an attempt to obtain the predictive capability of stratified wake turbulence in terms of Reynolds number $\text{Re}$, applying select elements of strongly stratified turbulence theory, so far typically utilized for homogeneous turbulence, to a canonical inhomogeneous turbulent free-shear flow.

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• Stratified geophysical flows
• Wakes & jets