Hydraulic adjustment to an obstacle in a rotating channel

In order to gain insight into the hydraulics of rotating-channel flow, a se t of initial-value problems analogous to Long's towing experiments is consi dered. Specifically, we calculate the adjustment caused by the introduction of a stationary obstacle into a steady, single-layer flow in a rotating ch annel of infinite length. Using the semigeostrophic approximation and the a ssumption of uniform potential vorticity, we predict the critical obstacle height above which upstream influence occurs. This height is a function of the initial Froude number, the ratio of the channel width to an appropriate ly defined Rossby radius of deformation, and a third parameter governing ho w the initial volume flux in sidewall boundary layers is partitioned. (In a ll cases, the latter is held to a fixed value specifying zero flow in the r ight-hand (facing downstream) boundary layer.) The temporal development of the flow according to the full, two-dimensional shallow water equations is calculated numerically, revealing numerous interesting features such as ups tream-propagating shocks and separated rarefying intrusions, downstream hyd raulic jumps in both depth and stream width, flow separation, and two types of recirculations. The semigeostrophic prediction of the critical obstacle height proves accurate for relatively narrow channels and moderately accur ate for wide channels. Significantly, we find that contact with the left-ha nd wall (facing downstream) is crucial to most of the interesting and impor tant features. For example, no instances are found of hydraulic control of flow that is separated from the left-hand wall at the sill, despite the fac t that such states have been predicted by previous semigeostrophic theories . The calculations result in a series of regime diagrams that should be ver y helpful for investigators who wish to gain insight into rotating, hydraul ically driven flow.