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Rotating flows around sharp corners and in channel mouths Cherniawsky, Josef Yuri
Abstract
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 reentrant (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 fplane. 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 reentrant corner, the upwelling is important only if the radius of curvature is much smaller than the lateral scale X. liorever, for reentrant 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.
Item Metadata
Title 
Rotating flows around sharp corners and in channel mouths

Creator  
Publisher 
University of British Columbia

Date Issued 
1985

Description 
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 reentrant (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 fplane. 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 reentrant corner, the upwelling is important only if the radius of curvature is much smaller than the lateral scale X. liorever, for reentrant 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.

Genre  
Type  
Language 
eng

Date Available 
20100611

Provider 
Vancouver : University of British Columbia Library

Rights 
For noncommercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.

DOI 
10.14288/1.0053214

URI  
Degree  
Program  
Affiliation  
Degree Grantor 
University of British Columbia

Campus  
Scholarly Level 
Graduate

Aggregated Source Repository 
DSpace

Item Media
Item Citations and Data
Rights
For noncommercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.