The Trapeze Instability on an Open Domain

Abstract

The ?trapeze instability? of Orlanski is investigated in the absence of a reflecting lid above the fluctuating layer. An expansion of the exact solution as a power series in a parameter representing the ratio of the fluctuating to the mean stability is made, and the first two terms calculated, both of which grow only for a finite length of time, after which they level off. This is quite unlike what occurs in the closed case. On the basis of a plausible conjecture about the behavior of higher order terms, we conclude that only waves whose vertical wavelength is small compared to the depth of the active layer will be amplified by the trapeze instability. When estimates of the effects of eddy viscosity are included, waves of horizontal wavelength of the order of 200?400 km and a period of two days are expected to be most unstable.