Spacetime development of the onset of a shallow-water vortex

Abstract

An impulsively started jet in shallow water gives rise to vortices having a characteristic diameter larger than the water depth. A technique of high-image-density particle image velocimetry allows characterization of the space–time development of the instantaneous flow patterns along planes representing the quasi-two-dimensional and three-dimensional vortex structure. The quasi-two-dimensional patterns exhibit different categories of vortex development and interaction, depending upon the depth of the shallow water layer. Despite these distinctions, the variations of normalized vortex position, diameter, and circulation, as well as peak vorticity within the vortex, are very similar for sufficiently small water depth.These quasi-two-dimensional patterns are, in turn, related to specific forms of three-dimensional flow structure, which is highly ordered. A prevalent feature is a vortex orthogonal to, and just ahead of, the primary, quasi-two-dimensional vortex. Its streamline topology, on a plane parallel to the axis of the quasi-two-dimensional vortex, exhibits a separation bubble with a well-defined separatix at the bottom (bed) surface. Moreover, its vorticity can exceed that of the quasi-two-dimensional pattern by a factor of two. This feature is consistent for all values of water depth. When the depth becomes sufficiently large, however, the three-dimensional vortex pattern involves an array of vorticity concentrations, which extends across the entire depth of the water.On a plane very close to the bottom surface (bed), global instantaneous distributions of velocity and vorticity exhibit large gradients; they are associated with small-scale vorticity concentrations characteristic of rapid transition. The corresponding streamline topology of the averaged flow close to the bed, however, exhibits a stable focus and is a direct indicator of the topology well above the bed.