Do Rossby-wave critical layers absorb, reflect, or over-reflect?

Peter D. Killworth and Michael E. McIntyre

J. Fluid Mech vol. 161, pp. 449-492 (1985).

This paper studies the `generalized Stewartson-Warn-Warn problem', the simplest class of models explicitly showing, in complete detail, the nature of the interplay between Rossby waves and a `surf zone' where they break (pdf file, 0.9Mbyte). The paper can be downloaded from here as a .pdf (acrobat) file (4 Mbyte, © 1985 Cambridge University Press).

Please note that a correction is needed halfway down page 455. The magnitude of alpha(infinity), which is 3.086, is only half the area of the finely dotted rectangle in figure 1. We forgot the factor 1/2 in equation (2.36), p. 465.

In item (ii) on page 454, we're guilty of using the phrase `sources and sinks of vorticity' in a loose sense. Since the paper was written, it has been more clearly recognized that vorticity and potential vorticity behave more like electric charge, having no net source or sink within a fluid domain. One can have `pair production' but not creation of net charge. For careful discussions of the concepts involved, see Haynes and McIntyre (1990), `On the conservation and impermeability theorems for potential vorticity' J. Atmos. Sci. 47, 2021 (.pdf, 1.1 Mbyte, copyright © American Meteorological Society),  and section 11, pp. 36ff., of the review article `Atmospheric dynamics: some fundamentals' from the 1993 Enrico Fermi School.

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