We use spectral proper orthogonal decomposition (SPOD) to extract and analyse coherent structures in the turbulent wake of a disk at Reynolds number
$ {\textit {Re}} = 5 \times 10^{4}$
and Froude numbers
$ {\textit {Fr}} = 2$
, 10. We find that the SPOD eigenspectra of both wakes exhibit a low-rank behaviour and the relative contribution of low-rank modes to total fluctuation energy increases with
$x/D$
. The vortex shedding (VS) mechanism, which corresponds to
$ {\textit {St}} \approx 0.11 - 0.13$
in both wakes, is active and dominant throughout the domain in both wakes. The continual downstream decay of the SPOD eigenspectrum peak at the VS mode, which is a prominent feature of the unstratified wake, is inhibited by buoyancy, particularly for
$ {\textit {Fr}} = 2$
. The energy at and near the VS frequency is found to appear in the outer region of the wake when the downstream distance exceeds
$Nt = Nx/U = 6 - 8$
. Visualizations show that unsteady internal gravity waves (IGWs) emerge at the same
$Nt = 6 - 8$
. A causal link between the VS mechanism and the unsteady IGW generation is also established using the SPOD-based reconstruction and analysis of the pressure transport term. These IGWs are also picked up in SPOD analysis as a structural change in the shape of the leading SPOD eigenmode. The
$ {\textit {Fr}} = 2$
wake shows layering in the wake core at
$Nt > 15$
which is captured by the leading SPOD eigenmodes of the VS frequency at downstream locations
$x/D > 30$
. The VS mode of the
$ {\textit {Fr}} = 2$
wake is streamwise coherent, consisting of
$V$
-shaped structures at
$x/D \gtrsim 30$
. Overall, we find that the coherence of wakes, initiated by the VS mode at the body, is prolonged by buoyancy to far downstream. Also, this coherence is spatially modified by buoyancy into horizontal layers and IGWs. Low-order truncations of SPOD modes are shown to efficiently reconstruct important second-order statistics.
The high-Reynolds-number stratified wake of a slender body is studied using a high-resolution hybrid simulation. The wake generator is a 6 : 1 prolate spheroid with a tripped boundary layer, the diameter-based body Reynolds number is
${Re}= U_\infty D/\nu = 10^5$
, and the body Froude numbers are
${Fr}=U_\infty /ND=\{2,10,\infty \}$
. The wake defect velocity decays following three stages with different wake decay rates (Spedding, J. Fluid Mech., vol. 337, 1997, pp. 283–301) as for a bluff body. However, the transition points among stages do not follow the expected
$Nt = Nx/U_\infty$
values. Comparison with the wake of a circular disk in similar conditions (Chongsiripinyo & Sarkar, J. Fluid Mech., vol. 885, 2020) quantifies the influence of the wake generator – bluff versus slender – in stratified flow. The strongly stratified
${Fr}=2$
wake is in a resonant state. The steady lee waves strongly modulate the mean flow, and relative to the disk, the 6 : 1 spheroid (a high-aspect-ratio shape) wake at
${Fr}=2$
shows an earlier transition from the non-equilibrium (NEQ) stage to the quasi-two-dimensional (Q2D) stage. The NEQ–Q2D transition is followed by a sharp increase in the turbulent kinetic energy and horizontal wake meanders. At
${Fr}=10$
, the start of the NEQ stage is delayed for the spheroid. Transfers between kinetic energy and potential energy reservoirs (both mean and turbulence) are analysed, and the flows are compared in phase space (with local Froude and Reynolds numbers as coordinates). Overall, the results of this study point to the difficulty of finding a universal framework for stratified wake evolution, independent of the features of the body, and provide insights into how buoyancy effects depend on the wake generator.
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