Modal Response of Reservoirs to Wind Stress
Publication: Journal of Hydraulic Engineering
Volume 113, Issue 10
Abstract
An analysis of the response of a density‐stratified reservoir to surface shear stress is presented. The reservoir is assumed to be two‐dimensional and to have a constant depth. In the limit that the bulk Wedderburn number and the bulk Richardson number are both infinite, the resulting equations are linear and solutions can be found in terms of the individual responses of a set of orthogonal normal modes. For the case of a steady wind stress, the solution consists of periodic motions and steady isopycnal displacements. However, the steady‐state isopycnal slope at the base of the mixed layer is infinite, implying that upwelling can occur when the Wedderburn number is quite large. This is attributed to blocking of the stratified fluid below the mixed layer by the endwall. The modal theory presented in this paper is compared with experimental observations made using a belt to impart shear stress to a stratified fluid contained in a box. The comparison shows that the present theory is qualitatively correct in that upwelling is observed when However, the modal theory best predicts the first‐mode seiche amplitude; the higher‐mode response is not accurately predicted.
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References
1.
Church, J. A., and Thompson, R. O. R. Y. (1982). “Cloud‐in‐cell and finite difference models for a stratified lake.” Numerical Solutions of Partial Differential Equations, J. Noye, ed., North Holland.
2.
Csanady, G. T. (1972). “Response of large stratified lakes to wind.” J. Phys. Oceanogr, 2(1), 3–13.
3.
Findikakis, A. N., and Street, R. L. (1982a). “Finite element simulation of stratified turbulent flows.” J. Hyd. Div., ASCE, 108(HY8), 904–920.
4.
Findikakis, A. N., and Street, R. L. (1982b). “;Vertical structure of internal modes in stratified flows.” J. Eng Mech. Div., ASCE, 108(EM4), 583–594.
5.
Fischer, H. B., and Smith, R. D. (1983). “Observations of transport to surface waters from a plunging inflow to Lake Mead.” Limnol Oceanogr., 28(2), 258–272.
6.
Gill, A. E., and Clarke, A. J. (1974). “Wind‐induced upwelling, coastal currents and sea‐level changes.” Deep‐Sea Res., 21, 325–345.
7.
Heaps, N. S., and Ramsbottom, A. E. (1966). “Wind effects on water in a narrow two‐layered lake.” Phil. Trans. Roy. Soc. London, Ser. A, 259, 391–430.
8.
Imberger, J. (1985). “The diurnal mixed layer.” Limnol Oceanogr., 30, 737–770.
9.
Imberger, J., and Hamblin, P. (1982). “Dynamics of lakes, reservoirs and cooling ponds.” Ann. Rev. of Fluid Mech., 14, 153–187.
10.
Kit, E., Berent, E., and Vadja, M. (1980). “Vertical mixing induced by wind and a rotating screen in a stratified fluid in a channel.” J. Hyd. Res., 18(1), 35–57.
11.
Kranenburg, C. (1985). “Mixed‐layer deepening in lakes after wind set‐up.” J. Hyd. Div., ASCE, 111(HY9), 1279–1297.
12.
Lazier, S. A., and Sandstrom, H. (1978). “Migrating thermal structure in a fresh water thermocline.” J. Phys. Oceanogr., 8, 144–155.
13.
Lighthill, M. J. (1969). “Dynamic response of the Indian Ocean to the Southwest Monsoon.” Phil. Trans. Roy. Soc. London, Ser. A, 265, 45–92.
14.
McCreary, J. P. (1981). “A linear stratified ocean model of the equatorial undercurrent.” Phil. Trans. Roy. Soc. London, Ser. A, 298, 603–665.
15.
Monismith, S. G. (1983). “The dynamic response of stratified reservoirs to surface shear stress,” thesis presented to the University of California, at Berkeley, Calif., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
16.
Monismith, S. G. (1985). “Wind induced motions in stratified lakes and their effect on mixed‐layer shear.” Limnol Oceanogr., 30, 771–783.
17.
Monismith, S. G. (1986). “An experimental study of the upwelling response of stratified reservoirs to surface shear stress.” J. Fluid Mech., 171, 407–439.
18.
Mortimer, C. H. (1952). “Water movements in lakes during summer stratification. Evidence from the distribution of temperature in Windmere.” Phil. Trans. Roy. Soc. London, Ser. B, 236, 255–104.
19.
Patterson, J. C., Hamblin, P. F., and Imberger, J. (1984). “Classification and dynamic simulation of the vertical density structure of lakes.” Limnol Oceanogr., 29, 845–861.
20.
Rodi, W. (1987). “Examples of calculation methods for flow and mixing in stratified fluids.” J. Geophys. Res., 92(C5), 5305–5328.
21.
Schladow, G. (1984). “The upper mixed zone of a salt‐gradient solar pond: its dynamics, prediction and control.” Solar Energy, 33, 417–426.
22.
Spigel, R. H. (1978). “Wind mixing in lakes,” thesis presented to the University of California, at Berkeley, Calif., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
23.
Spigel, R. H. (1980). “Coupling of internal wave motions with entrainment at the density interface of a two‐layered lake.” J. Phys. Oceanogr., 10(1), 144–154.
24.
Spigel, R. H., and Imberger, J. (1980). “The classification of mixed layer dynamics in lakes of small to medium size.” J. Phys. Oceanogr., 10(7), 1104–1121.
25.
Thompson, R. O. R. Y., and Imberger, J. (1980). “Response of a numerical model of a stratified lake to wind stress.” Proc. 2nd Int. Symp. on. Stratified Flows, Trondheim, Norway, Vol. 1, 562–570.
26.
Thorpe, S. A. (1966). “On the shape of progressive internal waves.” Phil. Trans. Roy. Soc. London, Ser A, 263, 563–613.
27.
Turner, J. S. (1973). Buoyancy Effects in Fluids, Cambridge University Press.
28.
Wedderburn, E. M. (1912). “Temperature observations in Loch Earn with a further contribution to the hydrodynamical theory of temperature seiches.” Trans. Roy. Soc. Edinburgh, 48, 629–695.
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Published In
Journal of Hydraulic Engineering
Volume 113 • Issue 10 • October 1987
Pages: 1290 - 1304
Copyright
Copyright © 1987 ASCE.
History
Published online: Oct 1, 1987
Published in print: Oct 1987
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