Roughness-Induced Effects on the Quasi-Geostrophic Model

We study in this paper the effect of small-scale irregularities on the quasi-geostrophic model. This study is motivated by some problems related to oceanography, as the Gulf Stream separation, or the impact of the topography on the global circulation. We first consider the role of coastal roughness in the phenomenon of western intensification of boundary currents. We show that the roughness is responsible for a nonlinear dynamics of the boundary layers, governed by a quasilinear elliptic equation. We thus extend substantially the classical derivation of Munk layers 15] and the results of convergence obtained in 10]. We then discuss the effect of a rough topography, by generalizing and justifying some formal computations of 17]. In particular, we derive rigorously a simplified model of oceanic circulation, with a nonlinear and nonlocal dissipative term due to the roughness.Acknowledgement This work has been partially supported by the GDR Amplitude Equations and Qualitative Properties (GDR CNRS 2103: EAQP) and by the IDOPT project in Grenoble.