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 June 2011
Eastern oceanic boundary currents are subject to hydrodynamic instability, generate
small scale features that are visible in satellite images and may radiate westward into
the interior, where they can be modified by the large-scale circulations. This thesis
studies the stability of an eastern boundary current with and without the large-scale
flow influence in an idealized framework represented by barotropic quasi-geostrophic
The linear stability analysis of a meridional current with a continuous velocity
profile shows that meridional eastern and western boundary currents support a limited
number of radiating modes with long meridional and zonal wavelengths and
small growth rates. However, the linearly stable, long radiating modes of an eastern
boundary current can become nonlinearly unstable by resonating with short trapped
unstable modes. This phenomenon is clearly demonstrated in the weakly nonlinear
simulations. Results suggest that linearly stable longwave modes deserve more attention
when the radiating instability of a meridional boundary current is considered.
A large-scale flow affects the short trapped unstable mode and long radiating
mode through different mechanisms. The large-scale flow modifies the structure of
the boundary current to stabilize or destabilize the unstable modes, leading to a
meridionally localized maximum in the perturbation kinetic energy field. The shortwave
mode is accelerated or decelerated by the meridional velocity adjustment of the
large-scale flow to have an elongated or a squeezed meridional structure, which is confirmed both in a linear WKB analysis and in nonlinear simulations. The squeezed or
elongated unstable mode detunes the nonlinear resonance with the longwave modes,
which then become less energetic. These two modes show different meridional structures
in kinetic energy field because of the different mechanisms.
In spite of the model simplicity, these results can potentially explain the formation
of the zonal jets observed in altimeter data, and indicate the influence of the large-scale wind-driven circulation on eastern boundary upwelling systems in the real ocean.
Studies with more realistic configurations remain future challenges.
Meridional overturning circulation
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