Modulation of the wake of a horizontal cylinder by pycnocline thickness in stratified flow

Abstract

This study investigates the modulating effect of the pycnocline thickness in two-dimensional stratified flow on a cylinder. It encompasses three typical flow regimes identified by Boyer in experiments conducted within the Reynolds number range of Re = 260–2000. Quantitative control of the modulation effect of internal interface waves on the cylinder wake is achieved by varying the thickness of the pycnocline. Under appropriate thickness of the pycnocline, a multiple-centerline-structure can transition to isolated-mixed-structure flow regimes and Double-Eddy-Wavy-Wake flow regimes. Similar modulation patterns are also observed in isolated-mixed flow regimes. Normalized pressure distribution and velocity fields indicate that in low Reynolds number flow regimes (Re < 600), downstream isolated mixed regions generate dynamic pressure that periodically cascades upstream. This periodic reverse energy transfer provides favorable adverse pressure gradients, cyclically reducing the drag force on the cylinder. The cyclic period is, for the first time, classified into four stages: dynamic pressure storage stage, dynamic pressure transfer stage, dynamic pressure consumption stage, and dynamic pressure exhaustion stage. Despite the highly nonlinear modulation effect of internal interface waves in low Reynolds number conditions, the linear predictive theory of lee waves based on streamline equations remains instructive in predicting the trend of lee waves wavelength variation with pycnocline thickness. Drawing upon the modulation study results concerning the pycnocline thickness on lee waves, a regime map is constructed, illustrating the directional evolution of lee waves flow patterns based on variations in pycnocline thickness.