Geostrophic Adjustment Problems in a Polar Basin

• Published in: Atmosphere-ocean 2012-06, Vol.50 (2), p.134-155
• Main Authors: Luneva, Maria V., Willmott, Andrew J., Maqueda, Miguel Angel Morales
• Format: Article
• Language: English
• Subjects: Banks (topography); Barotropic mode; Bottom friction; Circulation; Dissipation; Energy; Equivalence; Evolution; Excitation; Friction; geostrophic adjustment; Group velocity; Kelvin waves; Latitude; Ocean circulation; Ocean currents; Ocean models; Physiographic features; Planetary evolution; Planetary waves; polar circulation; Rossby waves; Rotation; Slope; Steady state; Structures; Time; Topography; Topography (geology); Vortices; vorticity waves; Water circulation; Wave propagation
• ISSN: 0705-5900; 1480-9214
• DOI: 10.1080/07055900.2012.659719

The geostrophic adjustment of a homogeneous fluid in a circular basin with idealized topography is addressed using a numerical ocean circulation model and analytical process models. When the basin is rotating uniformly, the adjustment takes place via excitation of boundary propagating waves and when topography is present, via topographic Rossby waves. In the numerically derived solution, the waves are damped because of bottom friction, and a quasi-steady geostrophically balanced state emerges that subsequently spins-down on a long time scale. On the f-plane, numerical quasi-steady state solutions are attained well before the system's mechanical energy is entirely dissipated by friction. It is demonstrated that the adjusted states emerging in a circular basin with a step escarpment or a top hat ridge, centred on a line of symmetry, are equivalent to that in a uniform depth semicircular basin, for a given initial condition. These quasi-steady solutions agree well with linear analytical solutions for the latter case in the inviscid limit. On the polar plane, the high latitude equivalent to the β-plane, no quasi-steady adjusted state emerges from the adjustment process. At intermediate time scales, after the fast Poincaré and Kelvin waves are damped by friction, the solutions take the form of steady-state adjusted solutions on the f-plane. At longer time scales, planetary waves control the flow evolution. An interesting property of planetary waves on a polar plane is a nearly zero eastward group velocity for the waves with a radial mode higher than two and the resulting formation of eddy-like small-scale barotropic structures that remain trapped near the western side of topographic features. RÉSUMÉ Traduit par la rédaction] Nous étudions l'ajustement géostrophique d'un fluide homogène dans un bassin circulaire ayant une topographie idéalisée à l'aide d'un modèle numérique de circulation océanique et de modèles analytiques de processus. Quand le bassin est en rotation uniforme, l'ajustement se fait par l'excitation d'ondes de propagation aux limites, et en présence de topographie, par des ondes de Rossby topographiques. Dans la solution numériquement dérivée, les ondes sont amorties à cause frottement contre le fond, et un état quasi-stable géostrophiquement équilibré s'établit pour ensuite décélérer sur une longue période de temps. Sur le plan f, les solutions numériques d'états quasi-stables sont atteintes bien avant que l'énergie du système mécanique soit en