Hostname: page-component-7dd5485656-tbj44 Total loading time: 0 Render date: 2025-10-23T11:52:23.291Z Has data issue: false hasContentIssue false
  • English
  • Français

Roe Scheme for Two-layer Shallow Water Equations:Application to the Strait of Gibraltar

Published online by Cambridge University Press:  02 October 2009

M. Chakir ,
D. Ouazar  and
A. Taik
M. Chakir
Affiliation:
Information Management and Technology, GIS Branch, New Brunswick, Department of Transportation, Kings Place, 440 King Street Fredericton N-B E3B-5H8, Canada
D. Ouazar
Affiliation:
Univ. Mohammed V, EMI, LASH, Av. Ibn Sina, B.P. 765 Agdal, Rabat, Morocco
A. Taik*
Affiliation:
Department of Mathematics, FSTM, HassanII-Mohammedia University, Morocco
*
taik_ahmed@yahoo.fr
Get access

Abstract

The flow trough the Strait of Gibraltar could be analyzed as a problem oftwo-layerhydraulic exchange between the Atlantic ocean and the Mediterranean sea. Theshallow waterequations in both layers coupled together are an important tool to simulate thisphenomenon. Inthis paper we perform an upwind schemes for hyperbolic equations based on theRoe approximateRiemann solver, to study the resulting model. The main goal assigned was topredict the locationof the interface between the two layers. Therefore the computational resultsobtained are comparedto previous results and experiments.

Keywords

Strait of GibraltarAtlantic ocean layerMediterranean sea layerinterface betweenlayersshallow water modelfinite volume methodRoe approximate Riemannsolver

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

D. Ambrosi. Approximation of shallow water equations by Riemann solvers. Inter. Journ. for Numerical Methods in Fluids,(1995) 20, 157–168.
L. Armi, D. Farmer. The internal hydraulics of the Strait of Gibraltar and associated sills land narrows. Oceanologia Acta 8, (1985), 37–46.
L. Armi, D. Farmer. The flow of Mediterranean water through the Strait of Gibraltar. Prog. Oceanogr., 21, (1988), 1–105.
N. Benmansour. Resultats de la Compagne CTD sur le Lynch-2 Gibraltar Experiments. Rapport de mission, Ecole Mohammadia d'Ingenieurs, (1985).
N. Benmansour. Boundary element solution to stratified shallow water wave equations (with application to the strait of Gibraltar). PHD Thesis, Wesses Institute of Technology, University of Portsmouth, (1993).
H. L. Bryden, T. H. Kinder. Gibraltar experiment. A plan for dynamics and kinematic investigations of strait mixing, exchange and turbulence. WHOI-86-29, (1986).
H. L. Bryden, T. H. Kinder. The 1985-1986 Gibraltar Experiment : Data collection and preliminary results. Eos Trans. AGU, 68, 786-787, 793–795.
H. L. Bryden, T. H. Kinder. Gibraltar experiment. Summary and initial results of Gibraltar experiments. WHOI-88-30, (1988).
H. L. Bryden, T. H. Kinder. Measurements of the flow throught the Strait of Gibraltar. Proc. 1st Int. Conf. in Africa on Computer Methods and Water Resources, Vol.2 Computational Hydraulics, Ed. D. Ouazar et al, CMP and CMP and Spring-Verlag, (1988), 347–362.
Bryden, H. L., Stommel, H. M.. Limiting process that determines basic features of circulation in the Mediterranean sea. Oceanoligica Acta, 7 (1984), 286–296.
M. Chakir, F. Benkhalodoun, L. Monthe, D. Ouazar, A. Belghit. A nine points finite volume Roe scheme for shallow water equations coupled to pollutant transport including source terms. Proc. of 1st Int. Symposium on Finite Volumes for Complex Applications, (1996), 625–633.
L. Gonzalez Alonso. Liaison fixe à travers le détroit de Gibraltar: la solution ferroviaire = fixed connexion between Gibraltar channel: the railway solution. Rail international ISSN 1022-4076 CODEN RAIIAF, (1984), No. 8-9, 30–31.
Gonzalez, M., Seaid, M.. Finite element modified method of characterstics for shallow water flows: application to the strait of Gibraltar, Progress in Industrial Mathematics, 8 (2005), 512–522.
H. Lacombe, C. Richez. The regime of the strait of Gibraltar. Proc. Hydrodynamics of Semi-Enclosed Seas. Ed. J.C.J. Nihoul, Elservier, Amsterdam, (1982), 13–74.
H. Lacombe, C. Richez. Hydrography and currents in the strait Gibraltar. Sea Straits Research Atlas SSR-3. National Ocean Research and development Activity, NSTL Mississippi 39529.
P.E. La Violette, T.H. Kinder, D.W. Green, Measurements of internal waves in the Strait of Gibraltar using a shore-based radar. Tech. Rep. 118,13 pp., Nav. Ocean Res. and Develop. Activ., Natl. Space Technol. Lab., Bay St Louis, Miss. (1986)
Leveque, R. J.. A study of numerical methods for hyperbolic conservation laws with stiff source terms. Journal of Computational Physics, 86 (1979), 187–210. CrossRef
R. J. Leveque. Numerical methods for conservation laws. Lectures in Mathematics ETH Zurich, Birhauser Verlag, 1992.
F. Madelain. Influence de la Topographie du fond sur l'écoulement Méditerraneen entre le Détroit de Gibraltar et le Cap Saint-Vincent. Cahiers Océanographiques, 22 (1970), No 1.
M. Mahboub. Modèle Numérique Eléments finis du Détroit de Gibraltar, EMI, Graduation Thesis, Rabat, (1988).
L. Moutya. Modèle Unidimensionnel Bi-couche du Détroit de Gibraltar, pp VII. 11-1/11-13, Proc. 1er Colloque Maghrébin sur les Modèles Numériques de l'Ingénieur, Algeria, (1987).
D. Ouazar, N. Benmansour, C. A. Brebbia. Towards a numerical model of strait of Gibraltar, Software for hydraulics, hydrology and hydrodynamics, volume, No. 3, (1989).
P. L. Roe. Approximate Riemann solvers, parameter vectors, and difference scheme. Journal of computational physics 43 (1981), 357–372.
A. Taik. Modélisation et analyse numérique des écoulements à surface libre par un schema volumes finis et par la méthode des éłéments finis. thèse de Doctorat d'Etat, (2002), EMI-Rabat, Maroc.
M. Taik. Projet de liaison fixe à travers le Détroit de Gibraltar: Projet de pont et navigation maritime. International navigation congress No 28, Seville, Espagne (22/05/1994) 1994, No. 83-84, 140–144, ISSN 0374-1001.
H. G. Yee. A Class of high-resolution explicit and implicit shock-capturing methods. NASA Technical Memorandum 101088, 1989.