Motions of Vortices and Circulating Cylinder in Shear Flow with Friction

Abstract

On including a frictional drag proportional and opposite to the velocity of a rotating cylinder or vortex placed in a shearing current, it is found that the combined influence of the drag and the rotor force resulting from the net pressure acting on the cylinder (vortex) is to make the cylinder or vortex move in a mean direction at an angle to the mean flow, toward the right if the circulation& Γ around the cylinder is positive, and toward the left if Γ is negative. In addition, the center of the cylinder also undergoes an oscillatory motion about its mean path, and the period of this oscillation and the shape of the path depend both on Γ and on the mean current. The analysis also shows that when the absolute vorticity of the basic flow is not uniform, another force in the direction of the vorticity gradient acts on the vortex, which tends to drive cyclonic vortices toward higher vorticity regions and anticyclonic vortices toward lower vorticity regions.