UBC Theses and Dissertations
Rotating flows around sharp corners and in channel mouths Cherniawsky, Josef Yuri
This thesis examines buoyancy driven steady flows in mouths of sea straits and around coastal protrusions. At high latitudes, the Coriolis force keeps these currents banked against the coast even around relatively sharp re-entrant (convex) corners with radii of curvature that are comparable to the width of the current. On the other hand, if the radius of curvature of the corner is much smaller than the width of the current, the current may leave the coast at the apex of the corner. A central part of the thesis is the solution of the nonlinear problem of a steady inviscid reduced gravity flow in a wedge, 0<θ<π/a (with a>l/2), around a sharp corner on an f-plane. An exponential upper layer upstream depth profile, h=Hexp(-x/X) (where x and X are the offshore distance and the current width scale, respectively), is combined with conservation of potential vorticity, Bernoulli and transport equations. The resulting nonlinear equations are expanded in a Rossby number ∈=V/fX (where f is the Coriolis parameter and V is the upstream boundary value of velocity). The 0(1) and 0(∈) equations are solved. First, they are simplified via transformations of the transport streamfunction variables: ⍦₀=p⁴ʹ³ and ⍦₁=2p¹ʹ³q. By modifying the results of Bromwich's (1915) and Whipple's (1916) diffraction theory, the 0(1) solution is expressed in a compact integral form, [formula omitted] The 0(∈) contribution q is calculated using an approximate Green's function method. The wedge of an angle 3π/2 (a=2/3) is used as an example to show details of the solution. The results exhibit the relative importance of the centrifugal, Coriolis and pressure gradient forces. Centrifugal upwelling (surfacing) of the interface occurs very close to the apex. For a rounded re-entrant corner, the upwelling is important only if the radius of curvature is much smaller than the lateral scale X. liorever, for re-entrant corners, the flow is supercritical within an arc, whose size depends upon the Rossby number and the angle of the wedge. Using two or more corner solutions, plausible flow streamlines can be generated in more complicated domains, as long as no two corners are closer than the Rossby radius of deformation. This procedure is illustrated with two examples: (a) circulation in a channel mouth and (b) flow around a square bump in a coastline. Finally, baroclinic circulation is modeled for boundaries that approximate coastlines near the mouth of Hudson Strait.
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