Vortex Systems in Shallow Water

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Abstract Proposal Number: CTS-9803734 Principal Investigator: Rockwell The objectives of this investigation are to gain a basic understanding of the vortex development, interaction and decay in shallow water. Large-scale vortical motions in jets, wakes, and mixing-layers occur in shallow free-surface configurations are diverse such as an open channel with flood plains, an embankment along a river, a sudden expansion of a surface waterway, a reservoir or lake inlet, the confluence of channels or rivers, a coastal shelf zone, a bridge abutment, and an isolated blunt obstacle such as a pier, island or cluster of vegetation. The development of these vortices has important consequences for thermal mixing, mixing of scalars, resonant oscillations of channels and harbors (seiches), overall performance characteristics of channel and river confluences, and the averaged discharge capacity of complex channels for flood routing. Furthermore, in all of these configurations, the underlying bed may be subject to scour or erosion due to the unsteady and time-averaged bed loading induced by vortex motions. In contrast to vortex development and interaction in shear layers of large spanwise extent, very little is known of the vortex structure in shallow water bounded by a free-surface and a bed (solid) surface. The first global, instantaneous representations of the two- and three-dimensional vortex structure will be attainable using recently developed techniques of high-image-density particle image velocimetry (HID-PIV). This approach will yield the space-time patterns of instantaneous vorticity and related topological features central to understanding the vortex development, vortex-vortex interactions, and vortex decay. Such an approach provides a physical basis for determining the classical turbulence statistics and mixing efficiency. A better understanding of the connection between vortex structure and bed scour and erosion can lead to new types of control techniques. In the near-field o f vortex development, small perturbations will substantially alter the initially-formed vortices and the rapidly developing three-dimensional vortex structure. In the far field, where the large-scale, quasi-two-dimensional vortical structures are expected to develop, control will take the form of spatial and temporal alterations of the bed friction and normal velocity at the bed; and localized generation of secondary concentrations of vorticity that may constructively or destructively interfere with the incident vortical structures. 2 1