Geostrophic adjustment and frontogenesis in stratified two-component media

A nonlinear problem of geostrophic adjustment in an ideal rotating two-component fluid in the field of gravity is studied analytically. The stratification of the fluid’s density is composed of its temperature stratification and stratification of the concentration of an admixture (in particular, these are salt seawater and moist air). Stationary states, which are reached after the adjustment process is terminated, are found with the use of Lagrange conservation laws. If the amplitudes of smooth initial disturbances are sufficiently large, discontinuity surfaces can appear in the course of evolution. Allowance for a two-component character of the medium makes qualitative properties of such surfaces especially varied. For example, a jump may be strongly marked in the field of one substance alone. It is shown that, if the initial ageostrophic property is related to temperature and/or admixture-concentration disturbances, the evolution of the fields of these substances can differ qualitatively from classical solutions to adjustment problems. For example, in the course of adjustment, the initial heat pulse can lead to the formation of a stationary temperature disturbance with a larger amplitude and/or the opposite sign. During the evolution of a smoothed temperature “step,” nonmonotonic distributions of temperature whose amplitudes are much greater than the amplitude of the initial step may appear. Some of such effects can manifest themselves even in a linear approximation.