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On wind driven geophysical flows without bottom friction

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In questo lavoro studiamo il moto di un fluido in un dominio sottile soggetto all’azione del vento in superficie ed a condizioni di slipping sul fondo. Viene derivato, dalle equazioni di Navier-Stokes in presenza della forza di Coriolis, un modello asintotico nel limite in cui il rapporto tra la profondità e la larghezza del dominio tende a zero, per numeri di Reynolds non troppo grandi.

Abstract

The motion of a fluid in a thin domain subject to wind traction at the surface and to slipping at the bottom is investigated. An asymptotic model is derived from Navier-Stokes equations with Coriolis force as the aspect ratio δ=depth/width of the domain go to 0, for not too large Reynolds number.

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References

  1. O. Besson—M. R. Laydi,Some estimates for the anisotropic Navier-Stokes equations and for the hydrostatic approximation M2AN,26, no. 7 (1992), pp. 855–865.

    MATH  MathSciNet  Google Scholar 

  2. R. Blumberg—L. Mellor,A description of a three dimensionnal coastal ocean circulation model, Three dimensional coastal ocean models, Borman Heaps, 1987.

  3. D. Bresch—J. Lemoine—J. Simon,A vertical diffusion model for lakes, SIAM J. Math. Anal.,30, 3 (1999), pp. 603–622.

    Article  MATH  MathSciNet  Google Scholar 

  4. D. Bresch—J. Lemoine—J. Simon,A geostrophic model with vertical diffusion, Nonlinear Anal.,43, 4 (2001), pp. 449–470.

    Article  MATH  MathSciNet  Google Scholar 

  5. D. Bresch—J. Simon,On the effect of friction on wind driven shallow lakes, J. Math. Fluid Mech. (to appear).

  6. T. Colin—P. Fabrie,Rotating fluid at high Rossby number driven by a surface stress: existence and convergence, Adv. Differential Equations,2, 5 (1997), pp. 715–751.

    MATH  MathSciNet  Google Scholar 

  7. A. E. Gill,Atmosphere-Ocean Dynamics, Academic press, 1982.

  8. E. Grenier—N. Masmoudi,Ekman Layers of rotating fluids, the case of well prepared initial data, Commun. Partial Diff. Eq.,22 (1997), pp. 953–975.

    MATH  MathSciNet  Google Scholar 

  9. G. N. Ivey—J. C. Patterson,A model of the vertical mixing in lake Erie in Summer, Limnol. Oceanogr.,29 (1984), pp. 553–563.

    Article  Google Scholar 

  10. Z. Kowalik—T. Smurty,Numerical modeling of Ocean Dynamics, Mon. Wea. Rev.,7 (1993), pp. 916–929.

    Google Scholar 

  11. R. Lewandowski,Analyse Mathématique et océanographie, Masson, Paris, 1997.

    Google Scholar 

  12. R. Temam—M. Ziane,Navier-Stokes equations in three-dimensional thin domains with various boundary conditions, Adv. Differential Equations,1 (1996), pp. 499–546.

    MATH  MathSciNet  Google Scholar 

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  1. Didier Bresch & Jacques Simon

    Present address: Laboratoire de Mathématiques Appliquées, CNRS (UMR 6620), Université Blaise Pascal (Clermont-Ferrand 2), 63177, Aubière cedex, France

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    1. Didier Bresch
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    2. Jacques Simon
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    Bresch, D., Simon, J. On wind driven geophysical flows without bottom friction. Ann. Univ. Ferrara 46, 101–113 (2000). https://doi.org/10.1007/BF02837292

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    • DOI: https://doi.org/10.1007/BF02837292

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