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, R_d, 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.