A Multi-Layer Shallow-Water Model. Applications
to the Strait of Gibraltar and the Alboran Sea.
M.J. Castro, J. Macias' and C. Pares
Dpto. de Analisis Matematico.
Universidad de Malaga.
29071 Malaga. SPAIN.
1 Introduction.
The Strait of Gibraltar, the link between the Atlantic Ocean and the Mediterranean Sea,
plays a major role in the renovation of the Mediterranean water and in the dynamics
of water masses in the Alboran Sea. Therefore, for the numerical simulation of the
hydrodynamic processes that take place in the Alboran Sea a thorough knowledge and
modelling of fluxes through the Strait is needed. This paper is devoted to the numerical
simulation of hydrodynamical processes taking place in both the Strait of Gibraltar and
the Alboran Sea. The main goal is to present the derivation of a multi-layer shallow
water model and its application to this zone of the Mediterranean. This model takes into
account Coriolis force, wind and bottom drag effects, interaction between two adjacent
layers, etc... This has been developed from a shallow-water model developed at the
University of Santiago de Compostela (see[2]).
The presentation of the model is in the form of a brief introduction to shallow water
models in Oceanography: we introduce the basic equations, the simplifications made in
order to obtain the model with a discussion about their meaning and limits of validity.
This presentation is addressed mainly to readers familiar with Partial Differential Equations and their numerical solution with Finite Element Methods, but unfamiliar with the
basic terminology in Oceanography.
Chapter 2 is concerned with one-layer shallow-water models. In their different formulations, these models are obtained from incompressible Navier-Stokes equations, taking
into account some simplifying hypotheses (constant density, hydrostatic pressure, etc ... )
and through a process of vertical integration. In the model considered here, the equations
obtained are first-order and hyperbolic. Some of the main properties of these equations
are recalled in order to introduce the specific vocabulary used in Hydrodynamics.
'Present affiliation: "Climate Modelling & Global Change" project. Centre Europeen de Recherche et
de Formation Avancee en Calenl Scicntifique (CERFACS). 42, Av. Coriolis, 31057-TOULOUSE Cedex
(FRANCE).
NATO ASI Series. Vol. 148
The Mathematics of Models for Climatology
and Environment
Edited by Jesus IIdefonso D{az
© Springer-Verlag Berlin Heidelberg 1997
to the Strait of Gibraltar and the Alboran Sea.
M.J. Castro, J. Macias' and C. Pares
Dpto. de Analisis Matematico.
Universidad de Malaga.
29071 Malaga. SPAIN.
1 Introduction.
The Strait of Gibraltar, the link between the Atlantic Ocean and the Mediterranean Sea,
plays a major role in the renovation of the Mediterranean water and in the dynamics
of water masses in the Alboran Sea. Therefore, for the numerical simulation of the
hydrodynamic processes that take place in the Alboran Sea a thorough knowledge and
modelling of fluxes through the Strait is needed. This paper is devoted to the numerical
simulation of hydrodynamical processes taking place in both the Strait of Gibraltar and
the Alboran Sea. The main goal is to present the derivation of a multi-layer shallow
water model and its application to this zone of the Mediterranean. This model takes into
account Coriolis force, wind and bottom drag effects, interaction between two adjacent
layers, etc... This has been developed from a shallow-water model developed at the
University of Santiago de Compostela (see[2]).
The presentation of the model is in the form of a brief introduction to shallow water
models in Oceanography: we introduce the basic equations, the simplifications made in
order to obtain the model with a discussion about their meaning and limits of validity.
This presentation is addressed mainly to readers familiar with Partial Differential Equations and their numerical solution with Finite Element Methods, but unfamiliar with the
basic terminology in Oceanography.
Chapter 2 is concerned with one-layer shallow-water models. In their different formulations, these models are obtained from incompressible Navier-Stokes equations, taking
into account some simplifying hypotheses (constant density, hydrostatic pressure, etc ... )
and through a process of vertical integration. In the model considered here, the equations
obtained are first-order and hyperbolic. Some of the main properties of these equations
are recalled in order to introduce the specific vocabulary used in Hydrodynamics.
'Present affiliation: "Climate Modelling & Global Change" project. Centre Europeen de Recherche et
de Formation Avancee en Calenl Scicntifique (CERFACS). 42, Av. Coriolis, 31057-TOULOUSE Cedex
(FRANCE).
NATO ASI Series. Vol. 148
The Mathematics of Models for Climatology
and Environment
Edited by Jesus IIdefonso D{az
© Springer-Verlag Berlin Heidelberg 1997