Flow past a circular cylinder on a β-plane

Abstract

This paper gives analytical and numerical solutions for both westward and eastward flows past obstacles on a β-plane. The flows are considered in the quasi-geostrophic limit where nonlinearity and viscosity allow deviations from purely geostrophic flow. Asymptotic solutions for the layer structure in almost-inviscid flow are given for westward flow past both circular and more elongated cylindrical obstacles. Structures are given for all strengths of nonlinearity from purely linear flow through to strongly nonlinear flows where viscosity is negligible and potential vorticity conserved. These structures are supported by accurate numerical computations. Results on detraining nonlinear western boundary layers and corner regions in Page & Johnson (1991) are used to present the full structure for eastward flow past an obstacle with a Huff rear face, completing previous analysis in Page & Johnson (1990) of eastward flow past obstacles without rear stagnation points. Viscous separation is discussed and analytical structures proposed for separated flows. These lead to predictions for the size of separated regions that reproduce the behaviour observed in experiments and numerical computations on β-plane flows.

Strain Evolution and Instability of an Anticyclonic Eddy From a Laboratory Experiment

“…Previous studies show that the shedding of eddies tends to be inhibited by increasing rotation rate (e.g., Boyer and Davies, 1982;Page, 1985;Heywood et al, 1996). At different background rotation frequencies (i.e., β = 0), the wake can develop a standing Rossby wave structure (McCartney, 1975), and the flow separation and eddy formation are affected by the direction of the incident current with respect to the wave propagation (e.g., Johnson and Page, 1993;Tansley and Marshall, 2001). The proposed mechanisms of eddy decaying include damping by ocean bottom drag (Sen et al, 2008;Arbic et al, 2009) and sea surface wind stresses (Duhaut and Straub, 2006;Hughes and Wilson, 2008), generating lee-waves over small-scale bottom topography (Marshall and Garabato, 2008;Sheen et al, 2014), radiating near-inertial waves through loss of balance (Molemaker et al, 2005;Alford et al, 2013), and instability processes in eddies (Lazar et al, 2013a,b).…”

Wavefields forced by long obstacles on a beta-plane

“…By considering a homogeneous fluid on a β-plane (e.g. Pedlosky 1979), Page & Johnson (1990 and Johnson & Page (1993) (denoted PJ90, PJ91 and JP93 here) attempt to show how a large topographic perturbation could force large-scale perturbations to an eastward flow and thus suggest that some current paths could be determined by standing Rossby waves. The analysis identifies three parameters determining the form of flow patterns in the oceanographically relevant limit of small Rossby and Ekman numbers: α, the ratio of the β-effect to Ekman pumping destruction of vorticity; λ, the ratio of advection to Ekman pumping; and L, the ratio of the along-stream length to cross-stream width of the obstacle.…”

“…A novel technique for the numerical solution of the boundary-layer equation, based on a downstream-upstream iteration procedure, is described. Some modifications of the asymptotic layer structure described in Page & Johnson (1991) and Johnson & Page (1993) for the weakly nonlinear low-friction regime are outlined for the case of a lenticular obstacle.…”