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 in the late wake are commonly seen in a stratified wake flow. These long-lived coherent patterns are referred to as meandering and their impacts on the statistics are still not well studied. This paper aims to examine the kinematic impacts of the meandering effect in stratified wakes and how it affects the statistics of the velocity profiles, wake width, and wake height. To do this, we isolate wake meandering from the stationary velocity, i.e., the velocity without meandering, by utilizing direct numerical simulations (DNS) covering bulk Reynolds numbers Re_𝐵=𝑈_𝐵⁢𝐷/𝜈 in the range [10000,50000] and bulk Froude number Fr_𝐵=𝑈_𝐵/𝑁⁢𝐷 in the range [2,50] (𝑈_𝐵 is the free-stream velocity, 𝐷 is the characteristic length scale, and 𝑁 is the buoyancy frequency). The results show that the range of meandering increases in both the horizontal and vertical directions as the flow evolves. This complies with the wake width growth in the horizontal direction, but is opposed to the wake height in the vertical direction. The traditional scalings of the velocity, width, and height rely on the assumption of self-similarity and simultaneous transitions for all three scalings. However, the meandering, especially in the horizontal direction, leads to the distortion of the instantaneous velocity and layered flow structures. Thus, the mean velocity profile deviates from two-dimensional self-similarity in the late wake. Apart from the distortion of the velocity profile, the meandering of the wake also imposes anisotropy on the scaling of the statistics. The scaling of the width and the height transitions at different points, and they are related to the scaling of the velocity deficit through the momentum flux equation. Through theoretical analysis, we obtain the superposition of the meandering to the stationary velocity. We can accurately measure how the meandering distorts the self-similar velocity profile and impacts the scaling of the width and height, and thus how the meandering changes the scaling of the velocity deficit.

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