The effects of topography on rotating barotropic flows

+152hlm.;24c

Collision of anticyclonic, lens-like eddies with a meridonial western boundary

The collision of anticyclonic, lens-like eddies with a meridional western boundary is investigated as a function of two independent, nondimensional numbers: ß = ß0 R/f o and e = ¿/f o, where f 0 and ß0 are the Coriolis parameter and its rate of change with latitude, respectively, both evaluated at the reference latitude. R is the eddy's radius, and ¿ is its angular frequency. The numerical experiments show that in all cases there is a southward expulsion of mass proportional to both ß and e. which is estimated during the eddy-boundary interaction. The eddies are invariably deformed with the initial collision, but afterward, they reacquire a new circular shape. There is a meridional translation of the eddy along the boundary which depends exclusively on the initial ratio r = e/ß. If r > 1, the eddy goes southward, but if r <1, the eddy goes northward first and then southward. As the eddy loses mass and reacquires a new circular shape, there is a readjustment of ß and e such that ß decreases because its radius becomes smaller and e increases by energy conservation. This implies that the eddies ultimately migrate southward. A formula, derived for the meridional speed of the center of mass of the eddy is consistent with the numerical results. A physical interpretation shows that after collision a zonal force is exerted on the eddy by the wall which is balanced by a meridional migration. Nonlinearities induce a southward motion, while high ß values could produce northward motion, depending on the mass distribution along the wall

Collision of anticyclonic, lens-like eddies with a meridonial western boundary

The collision of anticyclonic, lens-like eddies with a meridional western boundary is investigated as a function of two independent, nondimensional numbers: ß = ß0 R/f o and e = ¿/f o, where f 0 and ß0 are the Coriolis parameter and its rate of change with latitude, respectively, both evaluated at the reference latitude. R is the eddy's radius, and ¿ is its angular frequency. The numerical experiments show that in all cases there is a southward expulsion of mass proportional to both ß and e. which is estimated during the eddy-boundary interaction. The eddies are invariably deformed with the initial collision, but afterward, they reacquire a new circular shape. There is a meridional translation of the eddy along the boundary which depends exclusively on the initial ratio r = e/ß. If r > 1, the eddy goes southward, but if r <1, the eddy goes northward first and then southward. As the eddy loses mass and reacquires a new circular shape, there is a readjustment of ß and e such that ß decreases because its radius becomes smaller and e increases by energy conservation. This implies that the eddies ultimately migrate southward. A formula, derived for the meridional speed of the center of mass of the eddy is consistent with the numerical results. A physical interpretation shows that after collision a zonal force is exerted on the eddy by the wall which is balanced by a meridional migration. Nonlinearities induce a southward motion, while high ß values could produce northward motion, depending on the mass distribution along the wall

Ekman decay of a dipolar vortex in a rotating fluid

The evolution of quasi-two-dimensional (2D) dipolar vortices over a flat bottom in a rotating fluid system is studied numerically, and the main results are experimentally verified. Our aim is to examine the dipole decay due to bottom friction effects. The numerical simulations are based on the 2D physical model derived by Zavala Sansón and van Heijst [J. Fluid Mech. 412, 75 (2000)], which contains nonlinear Ekman terms, associated with bottom friction, in the vorticity equation. In contrast, the conventional 2D model with bottom friction only retains a linear stretching term in the same equation. It is shown that the dipole trajectory is deflected towards the right (i.e., in the anticyclonic direction) when nonlinear Ekman terms are included. This effect is not observed in simulations based on the conventional model, where the dipole trajectory is a straight line. The basic reason for this behavior is the slower decay of the anticyclonic part of the dipole, with respect to the cyclonic one, due to nonlinear Ekman effects. Another important result is the exchange of fluid between the cyclonic part and the ambient, leaving a tail behind the dipole. By means of laboratory experiments in a rotating tank, these results are qualitatively verified

Preferential states of rotating turbulent flows in a square container with a step topography

The self-organization of confined, quasi-two-dimensional turbulent flows in a rotating square container with a step-like topography is investigated by means of laboratory experiments and numerical simulations based on a rigid lid, shallow-water formulation. The domain is divided by a bottom discontinuity into two rectangular regions, one being shallow and the other deep. The existence of a preferential vorticity distribution in the long-term evolution of the decaying flow is discussed. Initially, the turbulent flow organizes into larger structures. After a few rotation periods, a continuous jet-like flow is consistently observed along the step, with the shallow region at its right. This flow is associated with the adjustment of the fluid to equilibrium over a bottom discontinuity in an anti-clockwise rotating system. At the end of the step, two persistent structures are formed due to the collision of this jet with the vertical wall: a cyclonic circulation cell in the deep region, while an anticyclonic cell occurs in the shallow part of the domain. The laboratory experiments are well-reproduced by the simulations. Due to bottom friction effects, the fluid motion is halted before a complete organization of the flow is accomplished. In order to study the full process, additional numerical simulations were performed with zero Ekman friction. Same principal features are observed as in the experiments, but now a complete organization of the flow into four vortices is obtained: in the deep part of the flow domain, a cyclone-anticyclone pair is observed that fills up the entire region, and the mirrored double cell structure occurs on the shallow side. Such a disposition of the vortices is directly associated with the interaction of the flow along the step and the downstream wall at which it collides, as observed in the experiments. It is shown that this arrangement is systematically obtained in simulations with very different initial conditions. The existence of a preferential vorticity distribution induced by a topographic step is further discussed in terms of the aspect ratio of the domain

Experiments on barotropic vortex-wall interaction on a topographic β plane

The problem of a barotropic cyclonic vortex, moving on a ß plane and interacting with a meridional vertical wall, is studied by means of laboratory experiments and a finite difference numerical model. In the laboratory, the vortex is produced in a rectangular rotating tank with a weakly sloping bottom. This socalled topographic ß plane simulates the latitudinal variations of the Coriolis parameter (ß effect). On this ß plane, the cyclonic vortex moves to the northwest and eventually interacts with the western wall. Two different results are found, depending on the initial strength and zonal position of the vortex. (1) For strong vortices, opposite-sign vorticity is created at the wall owing to the no-slip boundary condition, which leads, together with the cyclone, to the formation of a dipole structure that subsequently moves away from the wall in the northeastward direction. New wall interactions may occur when the original vortex recovers its northwestward motion. (2) In the case of weak vortices, the cyclone remains approximately at the same latitude for some time and later drifts slowly southward until it is dissipated by viscous effects. It is proposed that this behavior is a consequence of the vortex dispersion due to the ß effect