Disk wakes in nonlinear stratification

Abstract

Nonlinearity of density stratification modulates buoyancy effects. We report results from a body-inclusive large eddy simulation of a wake in nonlinear stratification, specifically for a circular disk at diameter-based Reynolds number ( ${\it Re} $ ) of $5000$ . Five density profiles are considered; the benchmark has linear stratification and the other four have hyperbolic tangent profiles of the same thickness to model a pycnocline. The disk moves inside the central core of the pycnocline in two of those four cases and, in the other two cases with a shifted density profile, the disk moves partially/completely outside the pycnocline. The maximum buoyancy frequency ( $N_{max}$ ) for all the profiles is the same. The first part of the study investigates the centred cases. Non-uniform stratification results in increasing wake turbulence relative to the benchmark owing to reduced suppression of turbulence production as well as wave trapping in the pycnocline. Steady lee waves are also quantified to understand the limitations of linear theory. The second part pays attention to the effect of a relative shift between the pycnocline and the disk. The wake defect velocity decays substantially faster in the cases with a shift and the wake has higher turbulence level. The effect of disk location on the Kelvin wake waves (a family of steady waves within the pycnocline) and its modal form is obtained and explained by solving the Taylor–Goldstein equation. The family of unsteady internal gravity waves that are generated by the wake is also studied and the effect of disk shift is quantified.