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ON THE STABILITY OF NATURAL CONVECTION FLOW INDUCED BY TIME-VARYING RADIATIVE THERMAL FORCING

DOI: 10.1615/ICHMT.2014.IntSympConvHeatMassTransf.270
pages 375-386

Tae Hattori
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Australia

John C. Patterson
Centre for Wind, Waves and Water, School of Civil Engineering, The University of Sydney Darlington, NSW 2006, Australia

Chengwang Lei
The University of Sydney

Abstract

In the nearshore regions of natural water reservoirs with slowly varying topography, the daytime thermal forcing associated with incoming solar radiation drives a horizontal convection flow due to differential heating as well as a vertical convection flow in the form of rising plumes due to a Rayleigh-Benard type instability near the bottom boundary as a result of the re-emission of the residual heating absorbed by the boundary. The present study focuses on the Rayleigh-Benard type instability of the flow in response to a sinusoidal thermal forcing. The bottom slope of the natural water bodies is typically small (10−3 ∼ 10−2), therefore no account is taken of the slope. The base flow is perturbed to form a set of linearised perturbation equations. The base temperature solution suggests that in shallow waters, the bottom residual heating is the dominant heating mechanism, and the diffusion time scale over the depth is small, leading to the overall temperature profile being predominantly determined by the time-varying bottom boundary condition. In contrast, the stable stratification is more substantial in deep waters and there is only a little residual heat at the bottom. The critical conditions for the onset of instability are compared at different times and water depths.

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