Line momentum source in shallow inviscid fluid

Abstract

An array of closely spaced, aligned, turbulent, incompressible jets is effectively simulated by a line momentum source. In a shallow inviscid fluid, such a source induces a predominantly two-dimensional non-diffusive flow which is irrotational except along lines of velocity discontinuity downstream of the source. The flow can be generated by a distribution of line vortices of unknown strength along the unknown slipstreamlines. Based upon this vortex model, kinematic and dynamic conditions along the slipstreamlines are formulated, and the two resulting nonlinear singular integral equations are solved numerically using a Newton-Raphson-type iterative collocation method.The flow field shows a marked resemblance to that induced by a nonlinear actuator disk. For the case of no ambient current, experimental results indicate that the slipstreamlines emanate from points which are close to, but not at the ends of, the source. As the ambient current strength increases, a dividing streamline appears in the induced sink flow upstream of the source, and the points from which the slipstreamlines emanate move closer to the ends of the source. Further increases in the current strength result in the smooth blending of this dividing streamline with the slipstreamline.Laboratory experiments performed in a shallow water basin confirm all of the features predicted by the theory.