Linear and weakly nonlinear internal wave theories applied to “morning glory” waves

Abstract

Detailed comparisons are made between the predictions of Benjamin's weakly nonlinear theory for internal solitary waves in fluids of great depth, with observational data on solitary wave-type disturbances in the lower atmosphere associated with the “morning glory” phenomenon.

It is shown that, while the theory is not wholly unreasonable, neither is it completely satisfactory. In particular, although the calculated wave speeds are generally close to those observed, they are no improvement on those based on linear long wave theory; at the same time the predicted wave half-widths are too large by a factor of two to three. The limitations of the theory appear to be associated with the requirement that wave half-widths are much less than the total fluid depth, a condition not satisfied in the atmospheric case. However, the alternative theory for shallow fluids, based on the Korteweg-de Vries equation is found to be even more unsuitable.

Our analyses highlight some of the problems in comparing theory with observations and bring to the fore some of the present limitations of the data for such purposes.