On a stable solute gradient heated from below with prescribed temperature

Abstract

The splitting of a smooth gradient into mixed layers separated by thin interfaces is studied in a constant stable solute gradient heated uniformly from below by raising the temperature at its bottom to a prescribed value above the ambient. The phenomenon under study is characterized by the development of a first mixed layer from the bottom up to a certain height; it is shown that its instantaneous thickness is proportional to the thermal expansion coefficient and the instantaneous temperature difference between the bottom heated plate and the undisturbed far fluid and is inversely proportional to the solute gradient. A second layer starts its formation during the growth of the first one and persists above the bottom layer notwithstanding the advancing interface below. Further layer formation occurs, depending on the prescribed Rayleigh number of the system (which is based on the vertical temperature difference and the initial solute gradient). The secondary layers grow with time and the final thickness of all the layers (except the bottom one) is almost equal. Their average final thickness is found to depend mostly on the solute gradient and the fluid properties. A final quasi-steady state is reached in which the depth of the whole convective region is proportional to the expansion coefficient and the vertical temperature difference and is inversely proportional to the initial solute gradient