The effect of a uniform cross-flow on the circulation of vortex rings

Abstract

This paper describes observations and measurements of the effects of a uniform cross flow on the vorticity field and circulation of a laminar vortex ring ejected from an elevated pipe. From particle-image velocimetry (PIV) in the plane defined by the axis of the vortex ring and the direction of the cross flow, we observe the growth and decay of the vortex-ring and its interaction with the shear layer which is produced by the cross flow over the surface of the elevated pipe. As the vortex ring is generated it passes through and disrupts this shear layer. Some rotational fluid from the shear layer is carried with the vortex ring as it moves away from the elevated pipe. From the PIV data, we calculate a positive-core circulation on the upstream side of the vortex ring and a negative circulation on the other side. The growth rate of positive-core circulation is reduced by cancellation with the cross-flow shear-layer vorticity which is of opposite sign. The initial negative circulation is equal to the circulation of the cross-flow shear layer, but the cross flow and the cross-flow shear layer have no effect of the growth rate of the negative circulation.