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Mixing in internally heated natural convection flow and scaling for a quasi-steady boundary layer

Published online by Cambridge University Press:  17 December 2014

Tae Hattori ,
John C. Patterson  and
Chengwang Lei
Tae Hattori*
Affiliation:
School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
John C. Patterson
Affiliation:
School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
Chengwang Lei
Affiliation:
School of Civil Engineering, The University of Sydney, Sydney, NSW 2006, Australia
*
†Email address for correspondence: tae.hattori@sydney.edu.au
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Abstract

This study considers the natural convection flow in a water body subjected to heating by solar radiation. The investigation into this type of natural convection flow has been motivated by the fact that it is known to play a crucial role in the daytime heat and mass transfer in shallow regions of natural water reservoirs and lakes, with a resultant impact on biological activity. An analytical solution for temperature in such an internally heated system shows that the temperature stratification consists of an upper stable stratification and a lower unstable stratification. One of the important consequences of such a nonlinear temperature stratification is the limitation of the mixing driven by rising thermal plumes with the penetration length scale of the plumes determining the lower mixed layer thickness. A theoretical analysis conducted in the present study suggests that in relatively deep waters, the lower mixed layer thickness is equal to the attenuation length of the radiation, which has important implications for water quality, including the transport of pollutants and nutrients in the water body. Scalings are also obtained for the quasi-steady boundary layer. The theoretical analysis is validated against numerical simulations.

JFM classification

Boundary Layers: Boundary Layers Convection: Buoyancy-driven instability Convection: Convection
Type
Papers
Information
Journal of Fluid Mechanics , Volume 763 , 25 January 2015 , pp. 352 - 368
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Copyright
© 2014 Cambridge University Press 

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