Ekman boundary layers in rotating fluids

Jean-Yves Chemin; Benoît Desjardins; Isabelle Gallagher; Emmanuel Grenier

ESAIM: Control, Optimisation and Calculus of Variations (2002)

  • Volume: 8, page 441-466
  • ISSN: 1292-8119

Abstract

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In this paper, we investigate the problem of fast rotating fluids between two infinite plates with Dirichlet boundary conditions and “turbulent viscosity” for general L 2 initial data. We use dispersive effect to prove strong convergence to the solution of the bimensionnal Navier-Stokes equations modified by the Ekman pumping term.

How to cite

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Chemin, Jean-Yves, et al. "Ekman boundary layers in rotating fluids." ESAIM: Control, Optimisation and Calculus of Variations 8 (2002): 441-466. <http://eudml.org/doc/244759>.

@article{Chemin2002,
abstract = {In this paper, we investigate the problem of fast rotating fluids between two infinite plates with Dirichlet boundary conditions and “turbulent viscosity” for general $L^2$ initial data. We use dispersive effect to prove strong convergence to the solution of the bimensionnal Navier-Stokes equations modified by the Ekman pumping term.},
author = {Chemin, Jean-Yves, Desjardins, Benoît, Gallagher, Isabelle, Grenier, Emmanuel},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Navier–Stokes equations; rotating fluids; Strichartz estimates; Navier-Stokes equations},
language = {eng},
pages = {441-466},
publisher = {EDP-Sciences},
title = {Ekman boundary layers in rotating fluids},
url = {http://eudml.org/doc/244759},
volume = {8},
year = {2002},
}

TY - JOUR
AU - Chemin, Jean-Yves
AU - Desjardins, Benoît
AU - Gallagher, Isabelle
AU - Grenier, Emmanuel
TI - Ekman boundary layers in rotating fluids
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2002
PB - EDP-Sciences
VL - 8
SP - 441
EP - 466
AB - In this paper, we investigate the problem of fast rotating fluids between two infinite plates with Dirichlet boundary conditions and “turbulent viscosity” for general $L^2$ initial data. We use dispersive effect to prove strong convergence to the solution of the bimensionnal Navier-Stokes equations modified by the Ekman pumping term.
LA - eng
KW - Navier–Stokes equations; rotating fluids; Strichartz estimates; Navier-Stokes equations
UR - http://eudml.org/doc/244759
ER -

References

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  1. [1] A. Babin, A. Mahalov and B. Nicolaenko, Global regularity of 3D rotating Navier–Stokes equations for resonant domains. Indiana Univ. Math. J. 48 (1999) 1133-1176. Zbl0932.35160
  2. [2] A. Babin, A. Mahalov and B. Nicolaenko, Global splitting, integrability and regularity of 3 D Euler and Navier–Stokes equations for uniformly rotating fluids. European J. Mech. B Fluids 15 (1996) 291-300. Zbl0882.76096
  3. [3] J.-Y. Chemin, B. Desjardins, I. Gallagher and E. Grenier, Fluids with anisotropic viscosity. Modél. Math. Anal. Numér. 34 (2000) 315-335. Zbl0954.76012MR1765662
  4. [4] J.-Y. Chemin, B. Desjardins, I. Gallagher and E. Grenier, Anisotropy and dispersion in rotating fluids. Preprint of Orsay University. Zbl1034.35107MR1935994
  5. [5] B. Desjardins, E. Dormy and E. Grenier, Stability of mixed Ekman–Hartmann boundary layers. Nonlinearity 12 (1999) 181-199. Zbl0939.35151
  6. [6] I. Gallagher, Applications of Schochet’s methods to parabolic equations. J. Math. Pures Appl. 77 (1998) 989-1054. Zbl1101.35330
  7. [7] H.P. Greenspan, The theory of rotating fluids, Reprint of the 1968 original. Cambridge University Press, Cambridge-New York, Cambridge Monogr. Mech. Appl. Math. (1980). Zbl0443.76090MR639897
  8. [8] E. Grenier, Oscillatory perturbations of the Navier–Stokes equations. J. Math. Pures Appl. 76 (1997) 477-498. Zbl0885.35090
  9. [9] E. Grenier and N. Masmoudi, Ekman layers of rotating fluids, the case of well prepared initial data. Comm. Partial Differential Equations 22 (1997) 953-975. Zbl0880.35093MR1452174
  10. [10] N. Masmoudi, Ekman layers of rotating fluids: The case of general initial data. Comm. Pure Appl. Math. 53 (2000) 432-483. Zbl1047.76124MR1733696
  11. [11] Pedlovsky, Geophysical Fluid Dynamics. Springer-Verlag (1979). Zbl0429.76001

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