The effects of topography on rotating barotropic flows

+152hlm.;24c

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

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

The evolution of a continuously forced shear flow in a closed rectangular domain

\u3cp\u3eA shallow, shear flow produced by a constant Lorentz force in a closed rectangular domain is studied by means of laboratory experiments and numerical simulations. We consider different horizontal aspect ratios of the container and magnitudes of the electromagnetic forcing. The shear flow consists of two parallel opposing jets along the long side of the rectangular tanks. Two characteristic stages were observed. First, the flow evolution is dominated by the imposed forcing, producing a linear increase in time of the velocity of the jets. During the second stage, the shear flow becomes unstable and a vortex pattern is generated, which depends on the aspect ratio of the tank. We show that these coherent structures are able to survive during long periods of time, even in the presence of the continuous forcing. Additionally, quasi-regular variations in time of global quantities (two-dimensional (2D) energy and enstrophy) was found. An analysis of the quasi-two-dimensional (Q2D) energy equation reveals that these oscillations are the result of a competition between the injection of energy by the forcing at a localized area and the global bottom friction over the whole domain. The capacity of the system to gain and dissipate energy is in contrast with an exact balance between these two effects, usually assumed in many situations. Numerical simulations based on a quasi-two-dimensional model reproduced the main experimental results, confirming that the essential dynamics of the flow is approximately bidimensional.\u3c/p\u3

Ekman effects in a rotating flow over bottom topography

This paper presents a general two-dimensional model for rotating barotropic flows over topography. The model incorporates in a vorticity–stream function formulation both inviscid topography effects, associated with stretching and squeezing of fluid columns enforced by their motion over variable topography, and viscous effects, due to the Ekman boundary layer at the solid bottom. From the present formulation, conventional two-dimensional models can be recovered. The model is tested by means of laboratory experiments on homogeneous vortices encountering irregular topographies. The experimental observations are then compared with the corresponding numerical simulations based on the general model. The results suggest that such a formulation incorporates both inviscid and viscous topography effects correctly

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