FRONTAL WAVE STABILITY DURING MOIST DEFORMATION FRONTOGENESIS .2. THESUPPRESSION OF NONLINEAR-WAVE DEVELOPMENT

In this paper, the role of horizontal deformation and the associated f rontogenetic ageostrophic circulation in suppressing the development o f nonlinear waves is assessed. Unless linear barotropic frontal waves can become nonlinear, the associated horizontal transports of momentum will not be sufficient to halt frontogenesis or to create nonlinear m ixing processes such as vortex roll-up. The analysis of Dritschel et a l. suggests that such nonlinear phenomena will not occur if the wave s lope remains small. For the linear model described in Part I, a simple relationship between optimal wave slope amplification over a specifie d time period and the amplification of an initially isolated edge wave is found. Using this relationship, the mechanisms by which strain aff ects the dependence of optimal wave slope amplification on wavelength and the time of entry of disturbances to the front are investigated. I t is found that waves entering the frontal zone when it is intense can experience greater steepening than those appearing earlier in the dev elopment of the front. The most rapidly growing waves enter the front with a wavelength about three times the width of the front. As the fro nt collapses, the ratio of wavelength to frontal width rapidly increas es. For strain rates greater than 0.6 x 10(-5) s-1, the model predicts that wave slope amplification greater than a factor of e is impossibl e. The variation of optimal growth with wavenumber and the time of ent ry of disturbances to the front is explained using diagnostics based o n a mathematical model of Bretherton's qualitative description of wave growth in terms of the interaction of counterpropagating edge waves. These diagnostics yield a simple formula for the frontogenesis rate re quired to completely eliminate wave steepening. For the front consider ed in Part I, the formula predicts that no amplification is possible f or strain rates greater than one-quarter of the Coriolis parameter. Di agnostics of this sort may aid attempts to predict, from the large-sca le forcing, the minimum attainable cross-frontal scale of a front.