Some Remarks on the Frictional Steady Topographical Perturbation of a Zonal Current

Abstract

The author deals herewith, by the linear theory, the large-scale or even ultra large-scale steady topographical perturbation of a two-dimensional zonal current with friction in the rotating system for the rotating dishpan model experiment and the atmospheric prototype under the different conditions of the upper boundary, free or bounded, of the lateral boundary, periodic or infinite-distantly vanishing, and of the β-term, included or not included.
Two types of analytical solution are obtained, periodic and exponentially damping, according to the periodic and infinite-distantly vanishing lateral boundary conditions.
Using these two types of analytical solution, following three main results have been derived.
Firstly, under the upper free boundary condition without theβ-term, the frcitional effect upon the large-scale steady topographical perturbation of a zonal current is not so much of amount as pointed out previously by several authors. This treatment is the most fitted for the topographical perturbation of this scale of the atmospheric prototype.
Secondly, the result of customary use of constant height or upper-bounded treatment for this kind of perturbation is much deviated from that of the upper free one mentioned above and consequently seems to be unreasonable for the prototype. The frictional effect becomes large in this case.
Thirdly, within the framework of the present study the two-dimensional topographical perturbation of the prototype is not appropriate to be treated on the β-plane since the behaviors of perturbation become quite fictitious in this case. The frcitional effect is also very large.