### Abstract

This paper is devoted to the establishment of a friction boundary condition associated with the hydrostatic Navier-Stokes equations (also called the primitive equations). Usually the Navier boundary condition is used, as a wall law, for a fluid governed by the Navier-Stokes equations when we want to modelize roughness. We consider here an anisotropic Navier boundary condition corresponding to the anisotropic Navier-Stokes equations. By an asymptotic analysis with respect to the aspect ratio of the domain, we obtain a friction boundary condition for the limit system, that is the primitive equations. This asymptotic boundary condition only concerns the trace of the horizontal components of the velocity field and the trace of its vertical derivative.

Original language | English (US) |
---|---|

Pages (from-to) | 237-259 |

Number of pages | 23 |

Journal | Asymptotic Analysis |

Volume | 33 |

Issue number | 3-4 |

State | Published - Mar 2003 |

### Fingerprint

### Keywords

- Asymptotic analysis
- Navier boundary conditions
- Primitive equations

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Asymptotic Analysis*,

*33*(3-4), 237-259.

**Asymptotic derivation of a Navier condition for the primitive equations.** / Bresch, D.; Guillén-González, F.; Masmoudi, N.; Rodríguez-Bellido, M. A.

Research output: Contribution to journal › Article

*Asymptotic Analysis*, vol. 33, no. 3-4, pp. 237-259.

}

TY - JOUR

T1 - Asymptotic derivation of a Navier condition for the primitive equations

AU - Bresch, D.

AU - Guillén-González, F.

AU - Masmoudi, N.

AU - Rodríguez-Bellido, M. A.

PY - 2003/3

Y1 - 2003/3

N2 - This paper is devoted to the establishment of a friction boundary condition associated with the hydrostatic Navier-Stokes equations (also called the primitive equations). Usually the Navier boundary condition is used, as a wall law, for a fluid governed by the Navier-Stokes equations when we want to modelize roughness. We consider here an anisotropic Navier boundary condition corresponding to the anisotropic Navier-Stokes equations. By an asymptotic analysis with respect to the aspect ratio of the domain, we obtain a friction boundary condition for the limit system, that is the primitive equations. This asymptotic boundary condition only concerns the trace of the horizontal components of the velocity field and the trace of its vertical derivative.

AB - This paper is devoted to the establishment of a friction boundary condition associated with the hydrostatic Navier-Stokes equations (also called the primitive equations). Usually the Navier boundary condition is used, as a wall law, for a fluid governed by the Navier-Stokes equations when we want to modelize roughness. We consider here an anisotropic Navier boundary condition corresponding to the anisotropic Navier-Stokes equations. By an asymptotic analysis with respect to the aspect ratio of the domain, we obtain a friction boundary condition for the limit system, that is the primitive equations. This asymptotic boundary condition only concerns the trace of the horizontal components of the velocity field and the trace of its vertical derivative.

KW - Asymptotic analysis

KW - Navier boundary conditions

KW - Primitive equations

UR - http://www.scopus.com/inward/record.url?scp=84887242690&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887242690&partnerID=8YFLogxK

M3 - Article

VL - 33

SP - 237

EP - 259

JO - Asymptotic Analysis

JF - Asymptotic Analysis

SN - 0921-7134

IS - 3-4

ER -