Geostrophic energetics and the small viscosity behaviour of an idealized ocean circulation model.

摘要

The role of the mechanical energy budget is analyzed in relation to the small viscosity behaviour of an idealized model of the wind-driven circulation. This is addressed theoretically and numerically in part one. In part two the connection to the real ocean is made through an analysis of the energy source with real data.; The theoretical arguments based on the QG energy equation 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 numerical study is focused on insensitivity to frictional parameters in the nonlinear Stommel-Munk model. Dependence of the multiple solutions of the steady state model on the boundary layer Reynolds number, Re, are investigated by varying the eddy viscosity for fixed wind forcing. An important finding is the tendency to decrease the energy source for solutions that are nonsymmetric about the centre latitude. Antisymmetric solutions display the opposite behaviour, and diverge more quickly with increasing Re. Also interesting is the tendency for the total energy and transport to become less sensitive to eddy viscosity with increasing Re. The robustness of the results to dynamic boundary condition, symmetry and strength of wind stress, time dependence and bottom friction are tested. A significant, though not surprising, result is that the no slip condition leads to high Rossby number in the boundary layer at much lower Re than for the free slip condition.; It is demonstrated that recent advances in altimetry measurements allow for a reasonable estimate of the rate of mechanical energy transfer from the atmospheric winds to the surface geostrophic velocity integrated over large regions. (Local values are highly uncertain due to the very large uncertainty in the marine geoid undulation field.) The feasibility and methodology of a quantitative uncertainty estimate is also demonstrated. The estimate of the energy source term allows comparison of the theoretical and numerical results with the real ocean.