Multiple equilibria and low-frequency variability of wind-driven ocean models

Abstract

The steady states of two models of the double-gyre wind-driven ocean circulation are studied. The link between the steady state solutions of the models and their time-mean and low-frequency 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 double-gyre ocean model in which the wind-stress 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 anti-symmetric with respect to the mid-basin latitude like the prescribed wind-stress curl. For intermediate values of δI,δS, additional pairs of mirror image non-symmetric equilibria come into existence. These additional equilibria have currents which redistribute relative vorticity across the line of zero wind-stress curl. This internal redist~ibution of vorticity prevents the solution from developing the large transports that are necessary for the anti-symmetric solution to achieve a global vorticity balance. Beyond some critical Reynolds number, the nonsymmetric solutions are unstable to time-dependent perturbations. Time-averaged solutions in' this parameter regime have transports comparable in magnitude to those of the non-symmetric steady state branch. Beyond a turning point, where the non-symmetric steady state solutions cease to exist, all the computed time-dependent model trajectories converge to the anti-symmetric inertial runaway solution. The internal compensation mechanism which acts through explicitly simulated eddies is itself dependent explicit dissipation parameter. Using the reduced-gravity quasigeostrophic model an investigation of the link between the steady state solutions and the model's low-frequency variability is conducted. If the wind-stress curl is kept anti-symmetric, successive pairs of non-symmetric equilibria come into existence via symmetry-breaking 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 inter-gyre fluxes of vorticity. Those solutions with weak inter-gyre fluxes of vorticity have large and energetic recirculation cells which remove excess vorticity through bottom friction. Those solutions with strong inter-gyre 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 time-mean 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 low-frequencies, showing that these modes are linked to the low-frequency variability of the model. Furthermore, the time-averaged flow fields within distinct energy ranges show distinct patterns which are in turn similar to the distinct steady state solutions.