6533b855fe1ef96bd12b1b53
RESEARCH PRODUCT
A shallow water model with eddy viscosity for basins with varying bottom topography
C. David LevermoreMarco Sammartinosubject
Cauchy stress tensorApplied MathematicsTurbulence modelingGeneral Physics and AstronomyStatistical and Nonlinear PhysicsMechanicsStructural basinPhysics::Fluid DynamicsWaves and shallow waterCompressibilityAnisotropyPhysics::Atmospheric and Oceanic PhysicsMathematical PhysicsMathematicsdescription
The motion of an incompressible fluid confined to a shallow basin with a varying bottom topography is considered. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model to derive a two-dimensional shallow water model. The global regularity of the resulting model is proved. The anisotropic form of the stress tensor in our three-dimensional eddy viscosity model plays a critical role in ensuring that the resulting shallow water model dissipates energy.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2001-09-18 | Nonlinearity |