Abstract
The response of the ocean to the action of a wind-stress at the surface has been investigated by many scientists since the middle of this century. The pioneering investigations were carried by Sverdrup (1947), Stommel (1948) and Munk (1950): they approximate the real ocean flow induced by the wind at the mid-latitudes in terms of total mass transport of a homogeneous layer of fluid of uniform depth on a beta plane (a projection of the sphere on a tangent plane where the Coriolis parameter is taken to be fo + βy, with fo and β constant, and y the north south coordinate). The fluid is set in motion by a torque which models the effects of the zonally averaged large scale wind pattern of the westerlies and the trades. Thus, the circulation appears as a gyre in which the Coriolis forces balance the pressure gradients and the driving force of the wind stress, in the greater part of the basin (Sverdrup balance); every streamline is going through a boundary layer region, in the western part of the basin, where an important dissipation of vorticity arises: this sink of vorticity is produced by bottom friction in Stommel’s model, and by lateral diffusion of momentum in Munk’s model; some non linear analytical models were then developped to include the inertial effects which are of evidence very important: Munk, Groves and Carrier (1950), Carrier and Robinson (1962), Moore (1963), Il’in and Kamenkovich (1963), Niiler (1966); but these models were questionable on many points: for example they assumed a priori the existence of steady state solutions, without proof. Thus numerical models have been developped to investigate the general time dependent non linear case: Bryan (1963) extended in the non linear and time dependent domain the Munk’s model, Veronis (1966) did the same for the Stommel’s model, Brandford (1971) realized a synthesis of the two. Since these early works, numerous contributions by numerical modellers improved our understanding of the wind induced circulation of the ocean which is impossible to review in this introduction. But, within this paper, it must be pointed out that all these numerical models have been developped on the basis of finite difference technics.
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References
Blandford, R.R. 1971. Boundary conditions in homogeneous ocean models. Deep Sea Research, 18: 739–751.
Bryan, K. 1963 A numerical investigation of a non linear model of a wind driven ocean. J. Atmos. Sciences, 20: 594–606.
Carrier, G.F.; Robinson, A.R. 1962 On the theory of the wind driven ocean circulation. J. Fluid Mech. 12: 49–80.
Ciarlet, P.G.; Glovinsky, R. 1975 Dual iterative techniques for solving a finite element approximation of the bi-harmonic equation. Comp. Math in Applied Mech. in Eng., 5: 277–295.
Fix, G.J. 1975 Finite element models for ocean circulation problems. SIAM J. Appl. Math. 293: 371–387.
Haidvogel, D.B.; Rdbinsdn, A.R.; Schulman, E.E. 1980 The accuracy, Efficiency and Stability of three Numerical Models with application to Open Ocean Problems. Journal of Computational Physics, 34–1–53.
Il’in, A.M.; Kamenkovich, V.M. 1963 On the influence of friction on ocean currents. Dakl. Akad. Nauk, SSSR.: 150–1274–1277.
More, D.W. 1963 Rossby waves in ocean circulation. Deep Sea Research, 10: 735–747.
Munk, W.H. 1950 On the wind driven ocean circulation. Journal of Meteor. 7: 79–93.
Munk, W.H.; Groves, G. and Carrier, G.F. 1950 Note on the dynamics of the Gulf Stream. J. of Marine Res. 9: 218–238.
Niiler, P.P. 1966 On the theory of the wind driven ocean circulation. Deep Sea Research, 13: 597–606.
Stommel, H.M. 1948 The westward intensification of wind driven ocean currents. Trans. Amer. Geoph. Un. 29: 202–206.
Sverdrup, H.U. 1947 Wind driven currents in a barotropic ocean, with application to the equatorial currents of the Eastern Pacific. Proc. U.S. Nat. Acad. Sc. 33: 318–326.
Veronis, G. 1966 Wind driven ocean circulation. Deep Sea Research, 13: 17–29, 31–55.
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© 1982 Springer-Verlag Berlin Heidelberg
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Dumas, E., Le Provost, C., Poncet, A. (1982). Feasability of Finite Element Methods for Oceanic General Circulation Modelling. In: Holz, K.P., Meissner, U., Zielke, W., Brebbia, C.A., Pinder, G., Gray, W. (eds) Finite Elements in Water Resources. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02348-8_26
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DOI: https://doi.org/10.1007/978-3-662-02348-8_26
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