On reduced-gravity flow through sills |
| |
| Authors: | Peter D Killworth |
| |
| Institution: | 1. NERC Oceanography Unit, c/o Dept of Atmospheric Physics , Clarendon Laboratory , Parks Road, Oxford , OXI 3PU;2. Institute of Oceanographic Sciences, Deacon Laboratory , Wormley , Godalming , Surrey |
| |
| Abstract: | Abstract The hydraulic flow of a reduced-gravity fluid of non-negative potential vorticity through a sill is considered. It is shown that for any flow with a reversal of current, another, physically realisable, flow exists which is unidirectional and/or resting, and carries more flux than the original flow. Thus only non-negative flows need be considered when examining maximal hydraulic fluxes. Then, for a simple sill (one which slopes downward on the left and upward on the right, looking downstream), it is shown that zero potential vorticity flow, possibly modified by having a region of motionless fluid at its right, carries the maximum flux possible for that sill shape. This makes the calculation of maximal fluxes for a given sill considerably simpler, and examples of parabolic and V-shaped sills are computed. |
| |
| Keywords: | Hydraulics bounds potential vorticity maximal flux |
|
|
