Numerical study of the primitive equations in the small viscosity regime. (English) Zbl 1431.35125
Summary: In this paper we study the flow dynamics governed by the primitive equations in the small viscosity regime. We consider an initial setup consisting on two dipolar structures interacting with a no slip boundary at the bottom of the domain. The generated boundary layer is analyzed in terms of the complex singularities of the horizontal pressure gradient and of the vorticity generated at the boundary. The presence of complex singularities is correlated with the appearance of secondary recirculation regions. Two viscosity regimes, with different qualitative properties, can be distinguished in the flow dynamics.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 76F40 | Turbulent boundary layers |
| 35A21 | Singularity in context of PDEs |
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 86A05 | Hydrology, hydrography, oceanography |
| 86A10 | Meteorology and atmospheric physics |
| 35Q86 | PDEs in connection with geophysics |
| 76V05 | Reaction effects in flows |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 41A50 | Best approximation, Chebyshev systems |
Software:
MatlabReferences:
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