The sensitivity and predictability of mesoscale eddies in an idealized model ocean
Haidvogel, Dale B.
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LocationWestern Boundary Current
Two numerical applications of two-level quasigeostrophic theory are used to investigate the interrelationships of the mean and mesoscale eddy fields in a closed-basin ocean model. The resulting techniques provide a more accurate description of the local dynamics, origins, and parametric dependences of the eddies than that available in previous modelling studies. First, we propose a novel and highly efficient quasigeostrophic closed-domain model which has among its advantages a heightened resolution in the boundary layer regions. The pseudospectral method, employing an orthogonal expansion in Fourier and Chebyshev functions, relies upon a discrete Green's function technique capable of satisfying to spectral accuracy rather arbitrary boundary conditions on the eastern and western (continental) walls. Using this formulation, a series of four primary numerical experiments tests the sensitivity of wind-driven single and double-gyred eddying circulations to a transition from free-slip to no-slip boundary conditions. These comparisons indicate that, in the absence of topography, no-slip boundaries act primarily to diffuse vorticity more efficiently. The interior transport fields are thus reduced by as much as 50%, but left qualitatively unchanged. In effect, once having separated from the western wall, the internal jet has no know1edge, apart from its characteristic flow speed, of the details of the boundary layer structure. Next, we develop a linearized stability theory to analyze the local dynamic processes responsible for the eddy fields observed in these idealized models. Given two-dimensional (x, z) velocity profiles of arbitrary horizontal orientation, the resulting eigenfunction problems are solved to predict a variety of eddy properties: growth rate, length and time scales, spatial distribution, and energy fluxes. This simple methodology accurately reproduces many of the eddy statistics of the fully nonlinear fields; for instance, growth rates of 10-100 days predicted for the growing waves by the stability analysis are consistent with observed model behavior and have been confirmed independently by a perturbation growth test. Local energetic considerations indicate that the eddy motions arise in distinct and recognizable regions of barotropic and baroclinic activity. The baroclinic instabilities deîend sensitively on the vertical shear which must exceed 0(5 cm sec-1) across the thermocline to induce eddy growth. As little as a 10% reduction in |uz|, however, severely suppresses the cascade of mean potential energy to the eddy field. In comparison, the barotropic energy conversion process scales with the horizontal velocity shear, |uy|, whose threshold values for instability, a (2 x 10-6 sec-1), is undoubtedly geophysically realizable. A simple scatter diagram of |uy| versus |uz| for all the unstable modes studied shows a clear separation between the regions of barotropic and baroclinic instability. While the existence of baroclinic modes can be deduced from either time mean or instantaneous flow profiles, barotropic modes cannot be predicted from mean circulation profiles (in which the averaging process reduces the effective horizontal shears). Finally, we conduct a separate set of stability experiments on analytically generated jet profiles. The resulting unstable modes align with the upper level velocity maxima and, although highly sensitive to local shear amplitude, depend much less strongly on jet separation and width. Thus, the spatial and temporal variability of the mesoscale statistics monitored in the nonlinear eddy simulations can be attributed almost entirely to time-dependent variations in local shear strength. While these results have been obtained in the absence of topography and in an idealized system, they yet have strong implications for the importance of the mid-ocean and boundary layer regions as possible eddy generation sites.
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution April, 1976
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