A Study of the Time-Dependent Wind-Driven Ocean Circulation

This investigation is concerned with the large-scale wind-driven motions of the ocean and their responses to a time variation in the wind. Starting from the equations of motion for an inhomogeneous fluid, a detailed formulation of the problem is presented, including the listing and discussion of the assumptions and simplifications necessary to reduce the general mathematical model to one which may be successfully attacked analytically. Since the real ocean is baroclinic, the problem is formulated to include a non-uniform density distribution. Two special cases are considered. (i) An ocean consisting of two superposed layers of constant density is assumed and the equations are integrated over each layer to simplify the analysis, Attempts at an analytical solution for this case were unsuccessful. (ii) A more general density distribution is then assumed, but a more restrictive assumption is made concerning the vertical variation of velocity. In particular, it is assumed that there exists a (variable) depth below which the velocities are negligible. As a result of this assumption, a direct relation is found between the thermocline and the free surface. The equations are integrated from this depth up to the free surface. The linearized equations are then subjected to an analytical treatment consisting of a perturbation expansion in terms of a parameter which is proportional to the frequency of the wind variation. The resulting equations are solved by boundary layer technique. Results are derived for the response of the mass transport to slowly varying winds and the effect of the wind on the intensified stream near the western boundary is discussed in detail. The two-layer steady problem is also solved and the steady position of the thermocline is determined.