Unsteady natural convection in a reservoir induced by constant surface cooling

This article concerns numerical simulations of unsteady natural convection induced by constant cooling at the water surface of a reservoir. Numerical computations reveal the occurrence of sinking cold water plumes soon after the initiation of cooling. These sinking plumes are responsible for an initial mixing over the local water depth, resulting later in a distinct horizontal temperature gradient with the water temperature decreasing toward the shallow region due to the presence of a sloping boundary. Simulations also show that the relatively higher cooling rate in the shallow water causes a cold water current flowing downwards along the sloping bottom and penetrating into the deeper regions. After a sufficient time a quasi-steady state is attained and at the end two main fluid layers are developed: a relatively stable undercurrent, and a very unstable return flow just below the water surface. Numerical results for different Grashof numbers are discussed. Understanding of the flow mechanisms pertinent to this flow is important for predicting the transport of nutrients and pollutants across the reservoir. References G. M. Horsch, H. G. Stefan, Convective circulation in littoral water due to surface cooling, Limnol. Oceanogr., 33, 1998, 1068--1083. C. Lei, J. C. Patterson, Unsteady natural convection in a triangular enclosure induced by surface cooling, Int. J. Heat and Fluid Flow, 26, 2005, 307--321. C. Lei, J. C. Patterson, A direct three-dimensional simulation of radiation-induced natural convection in a shallow wedge, Int. J. Heat and Mass Transfer, 46, 2003, 1183--1197. doi:10.1016/S0017-9310(02)00401-5 C. Lei, J. C. Patterson, Natural convection induced by diurnal heating and cooling in a reservoir with slowly varying topography, JSME International Journal, Series B: Fluids and Thermal Engineering, 49(3), 2006, 605--615. doi:10.1299/jsmeb.49.605 E. E. Adams, S. A. Wells, Field measurements on side arms of Lake Anna Va, J.Hydraulic Eng., 110, 1984, 773--793. S. G. Monismith, J. Imberger, M. L. Morison, Convective motions in the sidearm of a small reservoir, Limnol. Oceanogr., 35(8), 1990, 1676--1702. D. E. Farrow, J. C. Patterson, On the response of a reservoir sidearm to diurnal heating and cooling, J. Fluid Mech., 246, 1993, 143--161. doi:10.1017/S0022112093000072 D. Farrow, Periodically forced natural convection over slowly varying topography, J. Fluid Mech., 508, 2004, 1--21. doi:10.1017/S002211200400847X FLUENT 6.2 User's guide, Fluent Inc., Lebanon, 2005. H. K. Versteeg, W. Malalasekera, An introduction to computational fluid dynamics: the Finite Volume method, Longman Scientific and Technical, 1995. T. P. Bednarz, C. Lei, J. C. Patterson, An experimental study of unsteady natural convection in a reservoir model cooled from the water surface, Experimental Thermal and Fluid Science, in press, 2007. doi:10.1016/j.expthermflusci.2007.10.00