On the stable convection in a differentially spot-heated loop near the temperature of maximum density

Welander’s approach to study convective motions in a differentially spot-heated loop is reformulated for the case of fluid near the temperature of maximum density. The existence of this temperature is of great importance to understand dynamics of temperate lakes. The key character of the case of interest is that heat exchange takes place only within small spots at the bottom and the top of the loop. This study aims to reveal what happens with convective motions when fluid is near a state with the zero coefficient of thermal expansion. A somehow surprising conclusion is that steady regimes of convection, when they exist, turn out to be stable. This outcome differs from the case when heat exchange with the environment in line with Newton’s law of cooling takes place in a whole range of the loop. The findings of theoretical analysis are supported by the results of numerical studies. The reported outcomes allow us to estimate peculiarities of building more complex models of thermal convection. In particular, the role of spot-heated character of exchange with the environment is demonstrated. This feature should be kept in mind in attempts to simulate natural convection on the base of idealized models.