On the stability of the near shore waters of a lake when subject to solar heating (Q1207100)

During the day, water in a lake or reservoir absorbs solar radiation according to Beer's law. As the depth decreases towards the shore, more of the radiation penetrates to the bottom, leading to a region of warmer water attached to the lower boundary which is a potentially unstable temperature profile. This situation is modelled by a fluid contained in a triangular domain with a horizontal upper surface. The fluid is subject to internal heating associated with Beer's law and a bottom boundary heat flux associated with the radiation that is not absorbed by the water column. A quasi-static, linear stability analysis suggests that, for geophysical parameters, the model is locally unstable in a region centred away from the shore.