Multiple Equilibria of a Double-Gyre Ocean Model with Super-Slip Boundary Conditions

Francois W. Primeau
1998 Journal of Physical Oceanography  
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 (δ I , δ S ), 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
more » ... ity. 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 a large Reynolds number, δ I /δ S → ∞, the inertial branch is stable and appears to be unique. This branch is antisymmetric with respect to the midbasin latitude eScholarship provides open access, scholarly publishing services to the University of California and delivers a dynamic research platform to scholars worldwide. like the prescribed wind stress curl. For intermediate values of δ I /δ S , additional pairs of mirror image nonsymmetric equilibria come into existence. These additional equilibria have currents that redistribute relative vorticity across the line of zero wind stress curl. This internal redistribution 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 time-dependent 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 steadystate solutions cease to exist, all the computed time-dependent model trajectories converge to the antisymmetric inertial runaway solution. The internal compensation mechanism, which acts through explicitly simulated eddies, is itself dependent upon an explicit dissipation parameter. 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 (δ I , δ S ), 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 a large Reynolds number, δ I /δ S → ∞, the inertial branch is stable and appears to be unique. This branch is antisymmetric with respect to the midbasin latitude like the prescribed wind stress curl. For intermediate values of δ I /δ S , additional pairs of mirror image nonsymmetric equilibria come into existence. These additional equilibria have currents that redistribute relative vorticity across the line of zero wind stress curl. This internal redistribution 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 time-dependent 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 steadystate solutions cease to exist, all the computed time-dependent model trajectories converge to the antisymmetric inertial runaway solution. The internal compensation mechanism, which acts through explicitly simulated eddies, is itself dependent upon an explicit dissipation parameter. ABSTRACT 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 (␦ I , ␦ S ), 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 a large Reynolds number, ␦ I /␦ S → ϱ, the inertial branch is stable and appears to be unique. This branch is antisymmetric with respect to the midbasin latitude like the prescribed wind stress curl. For intermediate values of ␦ I /␦ S , additional pairs of mirror image nonsymmetric equilibria come into existence. These additional equilibria have currents that redistribute relative vorticity across the line of zero wind stress curl. This internal redistribution 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 time-dependent perturbations. Time-averaged 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 time-dependent model trajectories converge to the antisymmetric inertial runaway solution. The internal compensation mechanism, which acts through explicitly simulated eddies, is itself dependent upon an explicit dissipation parameter.
doi:10.1175/1520-0485(1998)028<2130:meoadg>2.0.co;2 fatcat:7qfqykjwkzct3omclyqorlibya