Double-diffusive convection in a horizontally infinite layer of a unit height in a large Rayleigh numbers limit is considered. From linear stability analysis it is shown, that the convection tends to have a form of travelling tall thin rolls with height 10-30 times larger than width. Amplitude equations of ABC type for vertical variations of amplitude of these rolls and mean values of diffusive components are derived. As a result of its numerical simulation it is shown, that for a wide variety of parameters considered ABC system have solutions, known as diffusive chaos, which can be useful for explanation of fine structure generation in some important oceanographical systems like thermohaline staircases.
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