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The concept of flows driven by sources and sinks of mass was used to develop a theory of flow due to an isolated point sink of mass in a continuously stratified fluid considered in the f- and beta-plane. The theory provided an analytical solution to the far field flows due to an isolated point sink of mass in a continuously stratified fluid. This was discussed in terms of its application to understanding rotating stratified flow over topography.

The time-dependent interaction of a point vortex with a vorticity jump separating regions of opposite signed and constant vorticities on the surface of a non-rotating sphere is examined. First, small amplitude interfacial waves are considered where linear theory is applicable. A point vortex in a region of same-signed vorticity will initially move away from the interface and a point vortex in a region of opposite-signed vorticity will move towards it. Weak vortices sufficiently far from the interface then undergo meridional oscillation while precessing about the sphere. The sense of azimuthal precession is determined by the sign of the vorticity jump at the interface. It is demonstrated by both linear and nonlinear theories that a vortex at a pole in a region of same-signed vorticity is a stable equilibrium whereas a vortex at a pole in a region of opposite-signed vorticity is an unstable equilibrium. Numerical computations using contour dynamics confirm these results and the dynamics of more nonlinear cases are examined. [ABSTRACT FROM AUTHOR]

A family of translating vortex equilibria for the two-dimensional Euler equations is investigated both analytically and numerically. The equilibria are comprised of a nonlinear wave propagating along an infinitely long vortical interface together with a comoving point vortex and dipole. The vortical interface separates the flow of uniform vorticity from a nontrivial irrotational flow. The analytical construction, though not an exact solution for the equilibria, is a relatively simple model having good quantitative agreement with the numerical solution well into the nonlinear regime. In the limit of small wave amplitude the analytical and numerical solutions approach those obtained using linear theory. [ABSTRACT FROM AUTHOR]

Baroclinic geostrophic adjustment in a rotating circular basin is investigated in a laboratory study. The adjustment process consists of a linear phase before advective and dissipative effects dominate the response for longer time. This work describes in detail the hydrodynamics and energetics of the linear phase of the adjustment process of a two-layer fluid from an initial step height discontinuity in the density interface $\uDelta H$ to a final response consisting of both geostrophic and fluctuating components. For a forcing lengthscale $r_f$ equal to the basin radius $R_0$, the geostrophic component takes the form of a basin-scale double gyre while the fluctuating component is composed of baroclinic Kelvin and Poincaré waves. The Burger number $S\,{=}\,R/r_f$ ($R$ is the baroclinic Rossby radius of deformation) and the dimensionless forcing amplitude $\epsilon\,{=}\,\uDelta H/H_1$ ($H_1$ is the upper-layer depth) characterize the response of the adjustment process. In particular, comparisons between analytical solutions and laboratory measurements indicate that for time $\tau$: $1 \,{<}\, \tau \,{<}\, S^{-1}$ ($\tau$ is time scaled by the inertial period $2 \pi/f$), the basin-scale double gyre is established, followed by a period where the double gyre is sustained, given by $S^{-1} \,{<}\, \tau \,{<}\, 2\epsilon^{-1}$ for a moderate forcing and $S^{-1}\,{<}\, \tau\,{<}\,\tau_D$ for a weak forcing ($\tau_D$ is the dimensionless dissipation timescale due to Ekman damping). The analytical solution is used to calculate the energetics of the baroclinic geostrophic adjustment. The results are found to compare well with previous studies with partitioning of energy between the geostrophic and fluctuating components exhibiting a strong dependence on $S$. Finally, the outcomes of this study are considered in terms of their application to lakes influenced by the rotation of the Earth. [ABSTRACT FROM AUTHOR]

The offshore spreading of coastal river outflows over shelf-like topography is inhibited by the demands of potential vorticity conservation. As a result, outflows tend to remain coastally trapped and flow parallel to the coast. Alongshore currents may also form when the outflow fluid has vorticity relative to the surrounding fluid, in which case the ‘image’ vorticity drives the outflow parallel to the coast. In the present work, the combined effects of topography and anomalous vorticity of the outflow in forming coastal currents are studied. Shelf-like topography is considered in the form of a sudden step change in depth, running parallel to a straight coast, some distance offshore. A simple model incorporating these effects is formulated using quasigeostrophic dynamics for a barotropic fluid with a rigid lid. The role of topographic wave radiation in establishing coastal currents is studied using the linearised barotropic potential vorticity equation for the case of a weak outflow of fluid with zero anomalous vorticity. The outflow is shown to be confined to the shelf and flows to the right of the source region. For stronger outflows, with relative vorticity, the method of contour dynamics is used to study the nonlinear evolution of the outflow plume and, in particular, its interaction with topography. The effects of outflow strength, magnitude and sign of the relative vorticity of the outflow fluid are considered in detail. In particular, the offshore penetration distance and rate of alongshore spreading of the outflow plume are studied. When the outflow comprises of fluid with positive (cyclonic) vorticity, the topographic and vorticity-driven image effects reinforce each other and increase the spreading rate of the outflow plume to the right of the source. For negative (anticyclonic) vorticity outflows the effects oppose each other leading to enhanced offshore spreading of the outflow. The numerical results demonstrate that the offshore transport is achieved by an efficient dipolar vortex mechanism. [Copyright &y& Elsevier]

A new nonlinear translating V-state of the barotropic quasigeostrophic equations with topography in the form of an infinitely long escarpment (or step) is computed numerically. Before the numerical computation, with the assumption of small excursions by fluid columns across the step, the linear equations of motion are solved analytically, demonstrating the possibility of constructing a translating V-state. The linear V-state has zero total circulation and self-propagates parallel to the step. It consists of two line vortices with positive circulation located on the deep side of the step and a finite-area patch of constant negative vorticity on the shallow side comprising of fluid which has crossed the step from the deep side. The linear solution motivates the numerical search for a nonlinear translating V-state comprising of two line vortices and a finite-area patch of constant vorticity. An algorithm based on contour dynamics and Newton''s method is used to find such a V-state. Time-dependent contour dynamics is used to compute the evolution of the V-state and it is found to be unstable. However, the growth rate of disturbances is sufficiently small for the V-state to survive several turn-over times. [Copyright &y& Elsevier]