The characteristics of the meandering effect in a stratified wake

Abstract

The gradual suppression of the vertical motions and the emergence of large-scale horizontal structures are characteristics of a stratified wake flow. We isolate the resulting wake meandering from the stationary velocity, i.e., the velocity without meandering, by utilizing direct numerical simulations covering Reynolds numbers $Re_B=UD/\nu$ between $[10 000, 50 000]$ and Froude number $Fr_B=U_B/ND$ between $[2, 50]$ ($U_B$ is the freestream velocity, $D$ is the characteristic length scale, and $N$ is the buoyancy frequency). The meandering range is growing in the horizontal direction as the wake width, but decreases in the vertical direction, opposite to the wake height. The meandering, especially in the horizontal direction, leads to the dispersion of the instantaneous velocity and layered flow structures. Thus, the mean velocity profile deviates from the assumption of two-dimensional self-similarity in the late wake. Due to the distortion of the mean velocity profile, the superposition of the meandering to the stationary velocity is non-trivial. The scaling of the width and the height transitions at different points, and the scaling of the velocity deficit is further more complicated. Through theoretical analysis, we obtain and verify the momentum flux equation. We can accurately measure the impact of the meandering on the scaling of the lengths, and also the scaling of the velocity deficit.