Insensitivity to turbulent closure in the wind-driven nonlinear Stommel-Munk model is addressed theoretically and numerically. The QG energy equation is used to show that, with the assumption that the maximum velocities occur at inertial length scales or smaller, a Sverdrup interior is consistent with the small Rossby number assumption only when the frictional parameters exceed critical values. For frictional parameters smaller than these values, valid solutions must decrease the energy source. This is possible for non-Sverdrup solutions since the energy source is dependent on the solution. The steady-state behavior of the model was investigated via a pseudo-arclength continuation algorithm. Dependence on the boundary layer Reynolds number, Re, was investigated by varying the eddy viscosity for fixed wind forcing. A tendency to decrease the energy source was found for solutions that are nonsymmetric about the center latitude. Antisymmetric solutions displayed the opposite behavior and diverged more quickly with increasing Re. The robustness of the results to dynamic boundary condition, symmetry and strength of wind stress, time dependence and bottom friction were tested. Some aspects of the nonsymmetric solutions appeared insensitive to Re.
Scott, Robert B., and David N. Straub. 1998. "Small viscosity behavior of a homogeneous, quasi-geostrophic, ocean circulation mode." Journal of Marine Research 56, (6). https://elischolar.library.yale.edu/journal_of_marine_research/2305