The Eulerian- and Lagrangian-Mean Flows Induced by Stationary, Dissipating Planetary Waves

[摘要] The Eulerian- and the Lagrangian-mean flows induced by stationary, dissipating pianetary waves are discussed by using a simple channel model on a beta-plane. The wave is assumed to be excited by the bottom undulation and to be dissipated by Newtonian cooling with relaxa-tion time α and by Rayleigh friction with, λα(λ being constant). Three cases with, λ=1 are mainly discussed; (1) the basic zonal wind U0 and the dissipation rate a are both constant, (2) U0 varies with height, while α is constant and (3) U0 and α vary with height. In Case (1), it is shown how the Eulerian- and the Lagrangian-mean fields depend on the difference be-tween the dissipation scale-height and the density scale-height (cf. Dunkerton, 1979; Uryu, 1980). In Case (2) and Case (3), it is shown how the results for Case (1) are modified under slightly more realistic situations.The assumption, often used in the study of vertical propagation of planetary waves (cf. Dickinson, 1969a), that planetary waves are dissipated by Newtonian cooling only (λ=0) is re-examined. In Case (1), it is shown that unless λ«|(UR-U0)/U0|(where UR is the speed of two dimensional Rossby wave), the Rayleigh friction term cannot be neglected in the poten-tial vorticity equation. In addition, if this assumption is incorporated with the assumption that the Eulerian-mean zonal flow is damped by Rayleigh friction (cf. Dickinson, 1969b; Uryu, 1980), the resulting Lagrangian-mean flows become quite different from those obtained when the wave-dissipation mechanism includes Rayleigh friction, except for the case where the basic zonal wind is very small; for example, the Lagrangian-mean meridional circuation is of 3-cell structure in the meridional direction when U0=30m/sec and α=1/7 day-1. It is noted that the Eulerian-mean flows do not show any qualitative difference. This suggests that the plausibility of assumptions used should be examined also by the Lagrangian-mean dynamics.

[学科分类] 大气科学