Multiple equilibria and lowfrequency variability of winddriven ocean models
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http://hdl.handle.net/1912/4783DOI
10.1575/1912/4783Abstract
The steady states of two models of the doublegyre winddriven ocean circulation are
studied. The link between the steady state solutions of the models and their timemean
and lowfrequency variability is explored to test the hypothesis that both stable and
unstable fixed points influence shape the model's attractor in phase space.
The steady state solutions of a barotropic doublegyre ocean model in which the
windstress curl input of vorticity is balanced primarily by bottom friction are studied.
The bifurcations away from a unique and stable steady state are mapped as a function of
two nondimensional parameters, (δI,δS), which can be thought of as measuring respectively
the relative importance of the nonlinear advection and bottom damping of relative
vorticity to the advection of planetary vorticity.
A highly inertial branch characterized by a circulation with transports far in excess of
those predicted by Sverdrup balance is present over a wide range of parameters including
regions of parameter space where other solutions give more realistic flows. For the range
of parameters investigated, in the limit of large Reynolds number, δI,δS → ∞, the inertial
branch is stable and appears to be unique. This branch is antisymmetric with respect
to the midbasin latitude like the prescribed windstress curl. For intermediate values
of δI,δS, additional pairs of mirror image nonsymmetric equilibria come into existence.
These additional equilibria have currents which redistribute relative vorticity across the
line of zero windstress curl. This internal redist~ibution of vorticity prevents the solution
from developing the large transports that are necessary for the antisymmetric solution
to achieve a global vorticity balance. Beyond some critical Reynolds number, the nonsymmetric
solutions are unstable to timedependent perturbations. Timeaveraged solutions
in' this parameter regime have transports comparable in magnitude to those of the
nonsymmetric steady state branch. Beyond a turning point, where the nonsymmetric
steady state solutions cease to exist, all the computed timedependent model trajectories
converge to the antisymmetric inertial runaway solution. The internal compensation
mechanism which acts through explicitly simulated eddies is itself dependent explicit
dissipation parameter. Using the reducedgravity quasigeostrophic model an investigation of the link between
the steady state solutions and the model's lowfrequency variability is conducted. If the
windstress curl is kept antisymmetric, successive pairs of nonsymmetric equilibria come
into existence via symmetrybreaking pitchfork bifurcations as the model's biharmonic
viscosity is reduced. Succesive pairs of mirror image equilibria have an additional half
meander in the jet. The distinct energy levels of the steady state solutiOris can be understood
in part by there different intergyre fluxes of vorticity. Those solutions with weak
intergyre fluxes of vorticity have large and energetic recirculation cells which remove
excess vorticity through bottom friction. Those solutions with strong intergyre fluxes of
vorticity have much smaller and ·less energetic recirculation cells.
A significant fraction of the variance (30%) of the interface height anomaly can be
accounted by four coherent structures which point away from the timemean state and
towards four steady state solutions in phase space. After removing the variance which
projects onto the four modes, the remaining variance is reduced predominantly at lowfrequencies,
showing that these modes are linked to the lowfrequency variability of the
model. Furthermore, the timeaveraged flow fields within distinct energy ranges show
distinct patterns which are in turn similar to the distinct steady state solutions.
Description
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 1998
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