On the theory of thin rotating jets: A quasi‐geostrophic time dependent model

The time‐dependent meandering in a thin baroclinic jet over bottom topography is discussed in the quasi‐geostrophic approximation. The motion of the axis of the jet is taken to be vertically coherent and the axis itself is defined as inextensible. The motion is examined from a frame of reference moving with the axis but fixed at an arbitrary longitude in terms of an open ocean spatial initial value problem. The velocities of the axis and of the jet are quasi‐geostrophic, and vorticity conservation for the first non‐geostrophic components constrains the evolution of the axis and gives a path equation. The spatial linearized stability problem is studied and the jet is found to be baroclinically unstable to path disturbances of sufficiently high frequency which amplify downstream. An exact solution is obtained to the nonlinear path equation over a flat bottom with no ß‐effect. The evolution of the path of these unstable meanders is such that the path closes itself and forms rings (at which point the analysis breaks down). It is proposed that the baroclinic jet processes studied here are fundamental to the dynamics of Gulf Stream meandering and isolated eddy production.     

Jupiter’s Great Red Spot: compactness condition and stability

Linear Rossby wave dispersion relationships suggest that Jupiter’s Great Red Spot (GRS) is a baroclinic structure embedded in a barotropic shearing zonal flow. Quasi-geostrophic (QG) two-layer simulations support the theory, as long as an infinitely deep zonal flow is assumed. However, once a finite depth of the lower layer is assumed, a self-interaction of the baroclinic eddy component produces a barotropic radiating field, so that the GRS-like eddy can no longer remain compact. Compactness is recovered by explicitly introducing a deep dynamics of the interior for the lower layer, instead of the shallow QG formulation. An implication of the result is a strong coupling of the GRS to a convectively active interior.Paper presented to the NP Symposia of the 1991 Wiesbaden EGS Assembly on “Nonlinear processes in Geophysics”     

Numerical studies of barotropic modons

Numerical solutions of barotropic modons are examined to assess the accuracy with which they can be calculated, their behavior under the influence of dissipation, and their resistance to perturbations.     

Simple applications of McWilliams' “A note on a consistent quasigeostrophic model in a multiply connected domain”

We have solved several linear quasigeostrophic problems in singly and multiply connected domains to illustrate the use and effects of correct boundary conditions which balance circulation changes with forcing along each boundary. The results with these boundary conditions differ markedly from those obtained by setting the streamfunction to zero on the walls either when the fluid is forced by a time-dependent wind stress curl or when the fluid oscillates in a free basin mode in a domain which contains interior islands.     

Particle trajectories and simple models of transport in coherent vortices

The particle trajectories and transport effects of coherent vortices are computed and a number of advection and diffusion experiments using a time-dependent dynamical ring model are analyzed. Several features of the tracer distributions in the numerical solutions are similar to features noted in sea surface temperature images of Gulf Stream rings and are discussed from the point of view of the model. Comparisons between tracer distributions computed using the dynamic ring model and several purely kinematic ring representations demonstrate that most of the important features of ring transport are not altered by slow dynamical evolution. Loss rates from the ring trapped zone are also estimated, which permits calculation of cross-Gulf Stream chemical and biological fluxes due to ring formation. We demonstrate that the salinoty flux to the Slope Water caused by rings is comparable to that caused by the atmosphere.The transport of passive scalars produced by a series of rings moving through a channel (modeling the Slope Water region between the Shelf and the Gulf Stream) is computed. It is found that transport in the along-channel direction is enhanced by the presence of rings and is characterized by Nusselt numbers of 0(30–40). Cross-channel fluxes, while enhanced, are somewhat less affected by rings, and are generally characterized by Nusselt numbers < 0(10). The combined effect of rings on the Slope is seen to make it an anisotropic medium, with along-channel transport one to two orders of magnitude more efficient than cross-channel transport. The implications with respect to the Slope are discussed.     

Can the Intermediate Western Boundary Current recirculation trigger the Vitória Eddy formation?

Ocean Dynamics - South of the Vitória-Trindade Ridge, a seamount chain off East Brazil, the Brazil Current (BC) meanders cyclonically within Tubarão Bight, occasionally forming the...     

Modeled interactions of mesoscale eddies with the East Pacific Rise: Implications for larval dispersal

Larval transport from distant populations is essential for maintenance and renewal of populations in patchy and disturbed ecosystems such as deep-sea hydrothermal vents. We use quasi-geostrophic modeling to consider the potential for long-distance dispersal of hydrothermal vent larvae in mesoscale eddies interacting with the northern East Pacific Rise. Modeled eddy dynamics were similar to the observed propagation dynamics of Tehuantepec eddies, including their ability to cross the ridge. Simulated surface anticyclones were associated with coherent cyclones in the deep layer with relatively strong current velocities that could significantly increase the dispersal potential of passive particles. Eddy interactions with ridge topography further enhanced tracer dispersal along the ridge axis through shearing and elongation of the eddy core. Simulations suggest that the passage of an eddy would result in local loss from the vent field and aggregate transport with potential enhancement of dispersal between vent fields separated by up to 270 km. Based on the latitude at which most Tehuantepec eddies cross the ridge, eddy-induced flows would enhance connectivity between the 13°N, 11°N, and 9°N vent fields along the East Pacific Rise asymmetrically with higher transport from northern vent fields to southern vent fields.     

Thin jet and contour dynamics models of Gulf Stream meandering

This paper reexamines the theory of the meandering of the Gulf Stream and other inertial jets. We develop a hybrid model (with piecewise constant potential vorticity in the upper layer and a deep layer initially at rest) which allows us to clarify the relationships among thin jet, contour dynamics, and instability models. Approximating the hybrid model leads to a simple two-contour model which can be analyzed easily and can be integrated numerically for large amplitude disturbances. The jet evolution predicted by the approximate model is quite similar to the meander development under the full dynamics, except that the time scales are shorter. The model shows that baroclinic processes clearly play a significant role in the growth of meanders, while upper-layer interactions drive the final pinch-off of eddies. In addition to such process studies, the approximate model provides a simple dynamical system for further investigations.