Flow separation by interfacial upwelling in the coastal ocean
Date
1995
Authors
Jiang, Xiaojun
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Abstract
Coastline curvature is an important factor that causes coastal currents to separate from the boundary. Laboratory experiments have suggested that the separation of a reduced gravity surface current from a corner occurs when p < u/f, where p is the local radius of curvature, u is the characteristic flow speed, and f is the Coriolis parameter. An inviscid , reduced gravity model, in which the current is insulated from the interior by a density front, is used to explore the hypothesis that the centrifugal upwelling of the density interface is one mechanism of flow separation, and separation criteria are derived for various coastal currents under the assumption that the length scale of the alongstream variations is long compared to the width of the current. Uniform potential vorticity 𝛿 is used for simplicity.
Two cases have been studied, one with a vertical sidewall (Klinger 1994), the other a sloping one. Model results for the vertical case agree with Klinger's (1994) computations and also agree reasonably well with laboratory results. Cases with
different slopes are compared, with h0, the upstream depth at the interface intersection point y*, and W0, the distance from yx to the offshore edge, being the same as for the vertical case. The results are almost identical to the corresponding vertical ones when the slopes (multipled by R/h0 ) is greater than 2, where R is the internal Rossby radius based on h0. As s decreases, Pc decreases. Also, the current at the separation point speeds up more. When the velocity decrease near the bottom due to friction is taken into consideration, cross-stream flow will result. The flow switches from offshore to inshore when in non-dimensional form, ū > (p + y)/2.
The consistency of the neglect of longshore derivatives is checked just upstream of the separation point. The ratios between the neglected terms and the maximum of the retained terms are 0(1) for the vertical case, indicating that the approximation is not valid there; the ratios in the sloping case decrease with decreasing s and are less than 0.5 when s < 2.