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Unsteady natural convection in a triangular enclosure induced by absorption of radiation – a revisit by improved scaling analysis

Published online by Cambridge University Press:  10 March 2009

YADAN MAO ,
CHENGWANG LEI  and
JOHN C. PATTERSON
YADAN MAO*
Affiliation:
School of Engineering, James Cook University, Townsville, QLD 4811, Australia
CHENGWANG LEI
Affiliation:
School of Engineering, James Cook University, Townsville, QLD 4811, Australia
JOHN C. PATTERSON
Affiliation:
School of Engineering, James Cook University, Townsville, QLD 4811, Australia
*
†Email address for correspondence: yadan.mao@jcu.edu.au
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Abstract

The present study is concerned with radiation-induced natural convection in a water-filled triangular enclosure with a sloping bottom, which is directly relevant to buoyancy-driven flows in littoral regions. An improved scaling analysis is carried out to reveal more detailed features of the flow than a previously reported analysis. Two critical functions of the Rayleigh number with respect to the horizontal position are derived from the scaling for identifying the distinctness and stability of the thermal boundary layer. Four flow scenarios are possible, depending on the bottom slope and the maximum water depth. For each flow scenario, the flow domain may be composed of multiple subregions with distinct thermal and flow features, depending on the Rayleigh number. The dividing points between neighbouring subregions are determined by comparisons of the critical functions of the Rayleigh number with the global Rayleigh number. Position-dependent scales have been established to quantify the flow properties in different subregions. The different flow regimes for the case with relatively large bottom slopes and shallow waters are examined in detail. The present scaling results are verified by numerical simulations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 622 , 10 March 2009 , pp. 75 - 102
Copyright
Copyright © Cambridge University Press 2009

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