A new well-posed vorticity divergence formulation of the shallow water equations

作者：Nordstrom Jan^*; Ghader Sarmad

来源：Ocean Modelling, 2015, 93: 1-6.

DOI：10.1016/j.ocemod.2015.07.001

• Shallow water equations
• Vorticity
• Divergence
• Energy estimates
• Well posed problems
• Boundary conditions

A new vorticity-divergence formulation of the two-dimensional shallow water equations including boundary conditions is derived. The new formulation is necessary since the conventional one does not lead to a well posed initial boundary value problem for limited-area modelling.
The new vorticity-divergence formulation includes four dependent variables instead of three and requires more equations and boundary conditions than the conventional formulation. On the other hand, it forms a hyperbolic set of equations with well-defined boundary conditions that leads to a well posed problem with bounded energy.

• 出版日期2015-9