The problem of transient natural convection in a cavity of aspect ratio A [les ] 1 with differentially heated end walls is considered. Scale analysis is used to show that a number of initial flow types are possible, collapsing ultimately onto two basic types of steady flow, determined by the relative value of the non-dimensional parameters describing the flow. A number of numerical solutions which encompass both flow types are obtained, and their relationship to the scale analysis is discussed.
During the day, the shallower regions of a reservoir sidearm absorb more heat per unit volu1ne than the deeper parts, leading to a horizontal pressure gradient that drives a circulation in the sideann. At night, the shallow regions cool more rapidly, leading to a circulation in the opposite direction. Since the spin-up ti1ne of a typical sideann is at least of the sa1ne order as a day, the flmv -vvithin a diurnally forced sideann is principally an inertia-buoyancy balance. In this paper, a diurnally forced sideann is 1nodellecl by periodically forced natural convection in a triangular cavity. The periodic forcing enters the 1nodel via an internal heating/ cooling tenn in the tmnperature equation. Reservoir sideanns typically have small bottmn slopes and this fact can be exploited to obtain asy1nptotic solutions of the resulting equations. These solutions clearly dmnonstrate the transition frmn the viscous-dmninated flmv in the shallows to the inertia-dmninated flow in the deeper parts. In the inertiadmninated region, the flow response significantly lags the forcing. Nu1nerical solutions of the full nonlinear problmn are consistent with the asymptotic solution~.
A one-dimensional thermodynamic model of a two-component ice and snow cover is added to an existing one-dimensional lake mixing model. Emphasis is placed on the thermodynamic coupling between the ice and mixing models-absent in previous models. The two-dimensional effects of partial ice cover are incorporated into this one-dimensional framework by using a minimum ice thickness. The model is applied to Lake Laberge, Yukon Territory, and to Babine Lake, British Columbia, for periods covering the formation and demise of full ice cover. The results of the model are compared to snow and ice measurements in the first case and to water column data during the spring period in the second. The comparisons are good, implying that the ice and snow model is performing satisfactorily and emphasizing the importance of the coupling between the ice and the underlying water. The successful simulation of the observed mixed layer under the ice, driven by convective stirring caused by short-wave heating below the temperature of maximum density, is an example of the ability of the model to provide physical insight into processes occurring in lakes.
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