Existence of solutions to the stommel-charney model of the gulf stream

Journal Article · Tue Nov 01 00:00:00 EST 1988 · SIAM J. Math. Anal.; (United States)

DOI:https://doi.org/10.1137/0519099· OSTI ID:6535636

Barcilon, V ^[1]; Constantin, P ^[2]; Titi, E S ^[2]

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1. Geophysical Sciences, Univ. of Chicago, Chicago, IL (US)
2. Dept. of Mathematics, Univ. of Chicago, IL (US)

This paper discusses the existence of weak solutions to the equations as a model of the Gulf Stream. The method of artificial viscosity is also discussed. Key words: Navier-Stokes equation, artificial viscosity, ocean circulation, DOE. The authors examine the mathematical properties of an equation arising in the theory of ocean circulation. In order to understand the role of this problem in oceanography, a brief review of the subject is given. The first successful attempt to provide a mathematical description of the mid-latitude ocean currents was made by other investigators. It was shown conclusively that a Gulf Stream-like intensification on the western side of an ocean basin could be explained by the so-called ..beta..-effect. This is the geophysical terminology for the latitudinal variation of the normal component of the earth's rotation. Aside from this variable Coriolis force, the other forces which entered into Stommel's model were those due to the pressure gradient, the surface winds, and friction. For the sake of simplicity, this last force was taken to be proportional to the velocity fields. All the effects of density stratification were neglected by making the assumption that the ocean was homogeneous. Finally, by working with vertical averages, Stommel essentially treated the ocean circulation as a two-dimensional horizontal motion. Somewhat surprisingly, Stommel's ad hoc, linear model was shown later to provide an accurate description of an actual experimental setup.

• OSTI ID: 6535636
• Journal Information: SIAM J. Math. Anal.; (United States), Vol. 19:6
• Country of Publication: United States
• Language: English

Related Subjects

58 GEOSCIENCES
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
OCEANIC CIRCULATION
NAVIER-STOKES EQUATIONS
GULF STREAM
MATHEMATICAL MODELS
NONLINEAR PROBLEMS
PRESSURE GRADIENTS
TWO-DIMENSIONAL CALCULATIONS
WIND
CURRENTS
DIFFERENTIAL EQUATIONS
EQUATIONS
PARTIAL DIFFERENTIAL EQUATIONS
WATER CURRENTS
580500* - Oceanography- (1980-1989)
990230 - Mathematics & Mathematical Models- (1987-1989)