Murdoch University Research Repository

Welcome to the Murdoch University Research Repository

The Murdoch University Research Repository is an open access digital collection of research
created by Murdoch University staff, researchers and postgraduate students.

Learn more

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

Farrow, D.E. and Patterson, J.C. (1993) On the stability of the near shore waters of a lake when subject to solar heating. International Journal of Heat and Mass Transfer, 36 (1). pp. 89-100.

Link to Published Version:
*Subscription may be required


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. Previous work suggests that the preferred mode for the instability consists of longitudinal rolls with their axes aligned with the slope. As the bottom slope becomes small, the stability problem becomes independent of the base flow and the originally threedimensional (3-D) problem is reduced to a two-dimensional (2-D) problem between horizontal and parallel plates. A quasi-static, linear stability analysis suggests that, for geophysical parameters, the model is locally unstable in a region centred away from the shore.

Item Type: Journal Article
Publisher: Elsevier Limited
Copyright: © 1993 Published by Elsevier Ltd.
Item Control Page Item Control Page