The evolution of the critical layer of a rossby wave. Part II
Abstract
In Part I of this paper with the same title [Stewartson (1978)] the evolution of a Rossby wave of amplitude O() forced on a uniform shear was studied. Times t were considered such that t = O (1) and ½t= O (1) and it was shown that as ½t→ ∞ the vorticity in the neighbourhood of the critical layer does not tend to a limit though the velocity jump across it tends to zero. The discussion concentrated on inviscid flow so that λ= R -1 ɛ -3/2 was zero. In the present paper the unsteady investigation is extended to values of λ << 1, and it is shown that the vorticity in the critical layer diffuses outwards until it has an effect on the imposed shear which is larger by a factor ɛ-½ than that due of the wave disturbance. This is corroborated by a closer examination of the Benney-Bergeron theory for λ << 1 in which the correctness of the conjecture of Haberman that the vorticity must be continuous across the critical layer is demonstrated. Thus in this limit also there is an O (ɛ) modification to the imposed shear.
- Publication:
-
Geophysical and Astrophysical Fluid Dynamics
- Pub Date:
- 1978
- DOI:
- 10.1080/03091927808242627
- Bibcode:
- 1978GApFD..10....1B