Nathan Paldor

The modification of the dynamics on the f-plane due to the inclusion of the latitudinal variation of the Coriolis frequency, quantified by β, is examined by comparing steady and time-dependent solutions for different values of β, including 0. The comparisons are made for analytic expressions and numerical simulations of the solutions of two physical problems: geostrophic adjustment and Ekman transport. By varying the extent of the meridional domain, L, and the value of β, while keeping the same value of the deformation radius, Rd, we find that the relative change of the Coriolis frequency across L is not a uniformly valid predictor of the effect of β on the dynamics. Instead, the magnitude of this effect varies with the physical problem, the type of dynamics, i.e., steady or time dependent, and with the particular values of β and L. In contrast to the effect of β, the effect of curvature on the zonally invariant f-plane dynamics is negligible in all cases for L≤1200 km and Rd=30 km employed here.

The dynamics of a water column at the surface of the ocean on the rotating spherical Earth forced by zonal wind stress is analyzed by substituting the angular momentum for the zonal velocity as one of the system's dependent variables. This substitution results in a model of the column's trajectory as a quasiparticle in a time dependent potential well. Explicit solutions are derived for the temporal changes in the angular momentum and the associated minima of the potential well as well as for the oscillations about these minima. The analytic results are confirmed by numerical solutions of the fourth-order nonlinear system of ordinary differential equations. For the eastward directed wind stress, our results provide exact formulas for the time it takes a column to reach the equator, where the dynamics is trivially described by the non-rotating paradigm of a particle subject to a constant force. In mid-latitudes, the analysis underscores the pivotal role played by the latitude where the wind-stress changes sign. Columns originating north or south of this latitude either converge to it or diverge away from it depending on whether the latitudinal change of the wind stress at this latitude is positive or negative. The oscillatory motion about this latitude is linearly unstable, and the growth rate of the amplitude is proportional to the gradient of the wind stress at that latitude.