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

Jan Nordström; Sarmad Ghader

doi:10.1016/j.ocemod.2015.07.001

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

Jan Nordström, Sarmad Ghader

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1-6
Number of pages	6
Journal	Ocean Modelling
Volume	93
DOIs	https://doi.org/10.1016/j.ocemod.2015.07.001
Publication status	Published - 1 Sept 2015
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Computer Science (miscellaneous)
Oceanography
Geotechnical Engineering and Engineering Geology
Atmospheric Science

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10.1016/j.ocemod.2015.07.001

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title = "A new well-posed vorticity divergence formulation of the shallow water equations",

abstract = "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.",

keywords = "Boundary conditions, Divergence, Energy estimates, Shallow water equations, Vorticity, Well posed problems",

author = "Jan Nordstr{\"o}m and Sarmad Ghader",

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T1 - A new well-posed vorticity divergence formulation of the shallow water equations

AU - Nordström, Jan

AU - Ghader, Sarmad

PY - 2015/9/1

Y1 - 2015/9/1

N2 - 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.

AB - 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.

KW - Boundary conditions

KW - Divergence

KW - Energy estimates

KW - Shallow water equations

KW - Vorticity

KW - Well posed problems

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VL - 93

SP - 1

EP - 6

JO - Ocean Modelling

JF - Ocean Modelling

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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