The effects of curvature and β on zonally invariant f-plane dynamics

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 R d = 30 km employed here.