Rotating hydraulics of flow in a parabolic channel

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Abstract
The investigation of Gill (1977) on the effects of a finite upstream depth upon frictionless flow through a rotating box-like channel has been extended to take into account a parabolic geometry. In addition to being more geophysically realistic, this type of topography with continuously sloping lateral boundaries has the advantage that it yields a unified solution. In contrast to the case of a rectangular channel, no separation of the geostrophically balanced downchannel flow from the sidewalk can take place. The resulting algebraic problem can be resolved either using an iterative technique or by the construction of perturbation series solutions. One of the most important results to emerge from the analysis is that the classical concept of hydraulic control is only applicable for a limited range of the parameters governing the problem. It is finally argued that this behaviour of the solutions is not due to the specific choice of geometry, but rather represents a common feature for all topographies characterized by a continuously sloping cross-stream bottom profile.

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