We have applied the methods of classical statistical mechanics to derive the inviscid equilibrium states for one- and two-layer nonlinear quasi-geostrophic flows, with and without bottom topography and variable rotation rate. In the one-layer case without topography we recover the equilibrium energy spectrum given by Kraichnan (1967). In the two-layer case, we find that the internal radius of deformation constitutes an important dividing scale: at scales of motion larger than the radius of deformation the equilibrium flow is nearly barotropic, while at smaller scales the stream functions in the two layers are statistically uncorrelated. The equilibrium lower-layer flow is positively correlated with bottom topography (anticyclonic flow over seamounts) and the correlation extends to the upper layer at scales larger than the radius of deformation. We suggest that some of the statistical trends observed in non-equilibrium flows may be looked on as manifestations of the tendency for turbulent interactions to maximize the entropy of the system.

Laplace's Tidal Equations (LTE) are modified to allow for the yielding of the solid Earth to tide generating forces and to the weight of the oceanic tidal column as well as for oceanic gravitational self-attraction. A realistic cotidal-corange chart for the global M , tide is used to show that the first effect is the order of the astronomical potential itself while the second and third are roughly one order of magnitude smaller. However, the later potential perturbations produce order one effects in the computed tide because they are much richer in high spherical harmonics than is the astronomical potential. The existence of an appreciable solid Earth tide significantly modifies the usual expressions for stored tidal energy, for tidal energy flux and for the rate of working on the oceans by tide generating bodies. An unexpectedly high value of Q(-34) is found for the global M , tide.

[1] The coastal circulation in the Santa Barbara Channel (SBC) and the southern central California shelf is described in terms of three characteristic flow patterns. The upwelling pattern consists of a prevailing equatorward flow at the surface and at 45 m depth, except in the area immediately adjacent to the mainland coast in the SBC where the prevailing cyclonic circulation is strong enough to reverse the equatorward tendency and the flow is toward the west. In the surface convergent pattern, north of Point Conception, the surface flow is equatorward while the flow at 45 m depth is poleward. East of Point Conception, along the mainland coast, the flow is westward at all depths and there results a convergence at the surface between Point Conception and Point Arguello, with offshore transport over a distance on the order of 100 km. Beneath the surface layer the direction of the flow is consistently poleward. The relaxation pattern is almost the reverse of the upwelling pattern, with the exception that in the SBC the cyclonic circulation is such that the flow north of the Channel Islands remains eastward, although weak. The upwelling pattern is more likely to occur in March and April, after the spring transition, when the winds first become upwelling favorable and while the surface pressure is uniform. The surface convergent pattern tends to occur in summer, when the wind is still strong and persistently upwelling favorable, and the alongshore variable upwelling has build up alongshore surface pressure gradients. The relaxation pattern occurs in late fall and early winter, after the end of the period of persistent upwelling favorable winds.INDEX TERMS: 4516 Oceanography: Physical: Eastern boundary currents; 4219 Oceanography: General: Continental shelf processes; 4532 Oceanography: Physical: General circulation; KEYWORDS: coastal circulation, upwelling, Santa Barbara Channel, bio-geographical boundaries, transport pathways Citation: Winant, C. D., E. P. Dever, and M. C. Hendershott, Characteristic patterns of shelf circulation at the boundary between central and southern California,