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Wind-driven currents in a sea with a variable eddy viscosity calculated via a sinc-Galerkin technique. (English) Zbl 0984.76066

Summary: The sinc-Galerkin method is presented as a new and potentially useful extension of spectral method in numerical oceanography. To describe and illustrate the technique, a sinc-Galerkin procedure is used to infer the sensitivity of wind-driven sub-surface currents in coastal regions and semi-enclosed seas, when the vertical eddy viscosity coefficient is represented as a continuously differentiable function of depth. Problems with exact solutions are used to explore the accuracy and exponential convergence of expansions using composite translated sinc functions as a basis set. To illustrate the essential idea, we describe applications of sinc-Galerkin technique to modifications of Ekman wind-drift current problem.

MSC:

76M22 Spectral methods applied to problems in fluid mechanics
76U05 General theory of rotating fluids
86A05 Hydrology, hydrography, oceanography
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[1] Ekman, Royal Swedish Academy of Science, Arkiv foer matematik, astronomi och fysik 2 pp 1– (1905)
[2] Physical Oceanography, vol. 1. Pergamon Press: Oxford, 1961.
[3] Heaps, Memoirs of the Society of Science, Liege, Series 6 1 pp 143– (1971)
[4] Heaps, Rapp Rev Reun Cons Int Explor Mer, Sec 3; Models 167 pp 147– (1974)
[5] Heaps, Geophysical Journal of the Royal Astronomical Society 64 pp 291– (1981) · doi:10.1111/j.1365-246X.1981.tb02669.x
[6] The numerical solution of the three-dimensional hydrodynamical equations using a B-spline representation of the vertical current profile. In Bottom Turbulence, (ed.). Elsevier: New York, 1977; 1-25.
[7] Davies, Applied Mathematical Modelling 3 pp 421– (1979) · Zbl 0437.76014 · doi:10.1016/S0307-904X(79)80024-4
[8] Spectral models in continental shelf oceanography. In Three-Dimensional Coastal Ocean Models, (ed.). American Geophysical Union: Washington, DC, 1987; 77-106.
[9] Bowers, Numerical Methods for Partial Differential Equations 11 pp 399– (1995) · Zbl 0837.65106 · doi:10.1002/num.1690110408
[10] Sinc Methods for Quadrature and Differential Equations. SIAM: Philadelphia, PA, 1992. · doi:10.1137/1.9781611971637
[11] Stenger, SIAM Review 23 pp 165– (1981) · Zbl 0461.65007 · doi:10.1137/1023037
[12] Numerical Methods Based on Sinc and Analytic Functions. Springer: New York, 1993. · Zbl 0803.65141 · doi:10.1007/978-1-4612-2706-9
[13] Turbulence energy models in shallow sea oceanography. In Quantitative Skill Assessment for Coastal Ocean Models, Coastal and Estuarine Studies, vol. 47, (eds). American Geophysical Union: Washington, DC, 1995; 97-123.
[14] A turbulent boundary layer model for the linearized shallow water equations, NUBBLE USER’S MANUAL (Release 1.1). Technical Report NML-96-1, Dartmouth College, 31 July, 1996.
[15] Large, Journal of Physical Oceanography 11 pp 324– (1981) · doi:10.1175/1520-0485(1981)011<0324:OOMFMI>2.0.CO;2
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