Flow patterns induced by a moving disturbance in rotational flows within the forced Korteweg-de Vries equation

TL;DR

This paper investigates flow patterns beneath a moving disturbance in a sheared, rotational fluid using the forced Korteweg-de Vries equation, revealing how vorticity and disturbance speed influence flow structures.

Contribution

It provides the first exact solutions for steady flow structures under a moving disturbance in a rotational, weakly nonlinear regime, including the conditions for stagnation points.

Findings

Stagnation points exist only in one solution branch.

Flow bifurcates based on vorticity and disturbance speed.

Stagnation points can occur at low vorticity with high disturbance speed.

Abstract

Flow structures beneath a moving disturbance along a water free surface in the weakly nonlinear weakly dispersive regime in a sheared channel with finite depth and constant vorticity are investigated. We compute the exact two branches of steady solutions in the disturbance moving frame. The velocity field in the bulk fluid is approximated which allows us to compute the flow structures beneath the free surface including stagnation points and Kelvin cat-eyes structures. We show that stagnation points exist only in one branch of solutions. The bifurcation of the flow is analyzed according to the intensity of the vorticity and the speed of the moving disturbance. Differently from the unforced problem, stagnation points can arise for small values of the vorticity as long as the moving disturbance travels sufficiently fast.