Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T14:03:19.981Z Has data issue: false hasContentIssue false
  • English
  • Français

On the response of a reservoir sidearm to diurnal heating and cooling

Published online by Cambridge University Press:  26 April 2006

D. E. Farrow  and
J. C. Patterson
D. E. Farrow
Affiliation:
Centre for Water Research. University of Western Australia, Nedlands, WA 6009, Australia Present address: Department of Applied Mathematics, University of Adelaide. Adelaide SA 5001, Australia.
J. C. Patterson
Affiliation:
Centre for Water Research. University of Western Australia, Nedlands, WA 6009, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

During the day, the shallower regions of a reservoir sidearm absorb more heat per unit volume than the deeper parts, leading to a horizontal pressure gradient that drives a circulation in the sidearm. At night, the shallow regions cool more rapidly, leading to a circulation in the opposite direction. Since the spin-up time of a typical sidearm is at least of the same order as a day, the flow within a diurnally forced sidearm is principally an inertia–buoyancy balance. In this paper, a diurnally forced sidearm is modelled by periodically forced natural convection in a triangular cavity. The periodic forcing enters the model via an internal heating/cooling term in the temperature equation. Reservoir sidearms typically have small bottom slopes and this fact can be exploited to obtain asymptotic solutions of the resulting equations. These solutions clearly demonstrate the transition from the viscous-dominated flow in the shallows to the inertia-dominated flow in the deeper parts. In the inertia-dominated region, the flow response significantly lags the forcing. Numerical solutions of the full nonlinear problem are consistent with the asymptotic solutions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 246 , January 1993 , pp. 143 - 161
Copyright
© 1993 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adams, E. E. & Wells, S. A. 1984 Field measurements on side arms of Lake Anna, Va. J. Hydraul. Engng 110, 773– 793.Google Scholar
Armfield, S. W. 1991 Finite-difference solutions of the Navier–Stokes equations on staggered and non-staggered grids. Computers Fluids 20, 1– 17Google Scholar
Brocard, D. N. & Harleman, D. R. F. 1980 Two-layer model for shallow convective circulation. J. Fluid Mech. 100, 129– 156.Google Scholar
Cormack, D. E., Leal, L. G. & Imberger, J. 1974 Natural convection in a shallow cavity with differentially heated end walls. Part 1. Asymptotic theory. J. Fluid Mech. 65, 209– 229.Google Scholar
Cormack, D. E., Stone, G. P. & Leal, L. G. 1975 The effect of upper surface conditions on convection in a shallow cavity with differentially heated end-walls. Intl J. Heat Mass Transfer 18, 635– 648.Google Scholar
Horsch, G. M. & Stefan, H. G. 1988 Convective circulation in littoral water due to surface cooling. Limnol. Oceanogr. 33, 1068– 1083.Google Scholar
Imbehger, J. & Patterson, J. C. 1990 Physical limnology. Adv. Appl. Mech. 27, 303– 475.Google Scholar
Jain, S. C. 1982 Buoyancy-driven circulation in free-surface channels. J. Fluid Mech. 122, 1– 12.Google Scholar
Kirk, J. T. O. 1986 Optical limnology – a manifesto. In Limnology in Australia (ed. P. de Dekker & W. D. Williams), pp. 33– 62. CSIRO Publications Sales.
Monismith, S. G., Imberger, J. & Morison, M. L. 1990 Convective motions in the sidearm of a small reservoir. Limnol. Oceanogr. 35, 1676– 1702.Google Scholar
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. Hemisphere.
Patankar, S. V. 1988 Recent developments in computational heat transfer. Trans. ASME C: J. Heat Transfer 110, 1037– 1045.Google Scholar
Patterson, J. C. 1984 Unsteady natural convection in a cavity with internal heating and cooling. J. Fluid Mech. 140, 135– 151.Google Scholar
Patterson, J. C. 1987 A model for convective motions in reservoir sidearm. In Proc. XXII Congress IAHR, Laussane, 1987, pp. 68– 73.
Poulikakos, D. & Bejan, A. 1983 The fluid mechanics of an attic space. J. Fluid Mech. 131, 251– 269.Google Scholar
Scott, C. F. 1988 On the circulation and classification of shallow estuaries. Ph.D. thesis, Western Australia.
Scott, C. F. & Imberger, J. 1988 Three-dimensional estuary circulation and classification. In Proc. Intl Conf. Physics of Shallow Estuaries and Bays (ed. R. Cheng). Springer.
Sturm, T. W. 1981 Laminar convection of heat in dead-end channels. J. Fluid Mech. 110, 99– 114.Google Scholar