Localized convective flows in a nonuniformly heated liquid layer

Within the class of exact solutions of the thermal-convection equations in the Oberbeck-Boussinesq approximation, which assumes a linear dependence of the temperature and the vertical velocity component on the height, a non-self-similar behavior of localized disturbances of a special type in a nonuniformly heated liquid layer is studied. It is shown that in an unstably stratified medium these disturbances can evolve to isothermal vortex structures of Burgers type. In the conditions of stable stratification or uniform heating of the layer, the disturbances considered tend to the state of rest in an oscillating or monotonic manner. New solutions describing self-similar convective vortices are found.