Flow Separation on the β-plane

• Main Author: Steinmoeller, Derek
• Format: Master Thesis
• Language: English
• Published: University of Waterloo 2009
• Subjects: beta-plane; fluid dynamics; barotropic; vorticity; flow; geophysical fluid; ocean; current; boundary; layer; separation; geostrophy; quasi-geostrophy; cylinder; cape hatteras; gulf stream; western boundary current; viscous; rotating; rotation; GFD; CFD; Chebyshev; Fourier; spectral; numerics; influence matrix; earth; eddy; Rossby; vortex; wave; vortices; eddies; cylindrical; obstacle; Applied Mathematics; Antarctic; The Antarctic; Antarc*
• Online Access: http://hdl.handle.net/10012/4417

In non-rotating fluids, boundary-layer separation occurs when the nearly inviscid flow just outside a viscous boundary-layer experiences an appreciable deceleration due to a region of adverse pressure gradient. The fluid ceases to flow along the boundary due to a flow recirculation region close to the boundary. The flow is then said to be "detached." In recent decades, attention has shifted to the study of boundary-layer separation in a rotating reference frame due to its significance in Geophysical Fluid Dynamics (GFD). Since the Earth is a rotating sphere, the so-called β-plane approximation f = f0 + βy is often used to account for the inherent meridional variation of the Coriolis parameter, f, while still solving the governing equations on a plane. Numerical simulations of currents on the β-plane have been useful in understanding ocean currents such as the Gulf Stream, the Brazil Current, and the Antarctic Circumpolar Current to name a few. In this thesis, we first consider the problem of prograde flow past a cylindrical obstacle on the β-plane. The problem is governed by the barotropic vorticity equation and is solved using a numerical method that is a combination of a finite difference method and a spectral method. A modified form of the β-plane approximation is proposed to avoid computational difficulties. Results are given and discussed for flow past a circular cylinder at selected Reynolds numbers (Re) and non-dimensional β-parameters (β^). Results are then given and discussed for flow past an elliptic cylinder of a fixed aspect ratio (r = 0.2) and at two angles of inclination (90°, 15°) at selected Re and β^. In general, it is found that the β-effect acts to suppress boundary-layer separation and to allow Rossby waves to form in the exterior flow field. In the asymmetrical case of an inclined elliptic cylinder, the β-effect was found to constrain the region of vortex shedding to a small region near the trailing edge of the cylinder. The shed vortices were found to propagate around the trailing edge ...