Abstract
This section of the chapter extends the spectral method developed earlier to deal with the problem of formulating a full three-dimensional spectral model for wind induced circulation. Some simple examples are considered to illustrate the accuracy of the method and to show how the approach can be used to gain some insight into the factors controlling wind induced current profiles. In the final section references to the literature are used to indicate the range of models which have employed spectral methods in shallow sea problems. The aim is to produce a self-contained text which will introduce the topic to a student or research scientist who is not familiar with the spectral approach.
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References
Carter, D. J. T., Prediction of wave height and period for a constant wind velocity using the JONSWAP results, Ocean Engng, 9, 17–33, 1982.
Cooper, C. K., and B. Pearce, Numerical Simulations of hurricangenerated currents, J. of Phys. Oceano., 12, 1071–1091, 1982.
Davies, A. M., Application of a Galerkin-Eigenfunetion method to computing currents in homogeneous and stratified seas, in Numerical Methods for Fluid Dyn., edited by K. W. Morton and M. J. Baines, Academic Press, 1982a.
Davies, A. M., Meteorologically-induced circulation on the north west European continental shelf: from a three dimensional numerical mode, Oceanologica Acta, 5, 269–280, 1982b.
Davies, A. M., Comparison of computed and observed residual currents during JONSDAP’76, in Physical Oceanography of Coastal and Shelf Seas, edited by B. Johns, Elsevier Oceanography Series, 35, 1983a.
Davies, A. M., Formulation of a linear three-dimensional hydrodynamic sea model using a Galerkin-Eigenfunction method, Int. J. Num. Meth. in Fluids 3, 33–60, 1983b.
Davies, A. M., Numerical modelling of stratified flow: a spectral approach, Continental Shelf Research, 2, 275–300, 1983c.
Davies, A. M., A three dimensional modal model of wind induced flow in a sea region, in press, Progress in Oceanography 1985a.
Davies, A. M., Spectral models in Continental Shelf Sea Oceanography, in press, AGU Coastal and Estuarine Regimes Monograph Series edited by N.S. Heaps, 1985b.
Davies, A. M., Mathematical formulation of a spectral tidal model, this volume, 1986a.
Davies, A. M., and C. V. Stephens, Comparison of the finite difference and Galerkin methods as applied to the solution of the hydrodynamic equations, Applied Mathematical Modelling, 7, 226–240, 1983.
Dobroklonskiy, S. V., Drift current in the sea with an exponentially decaying eddy viscosity coefficient, Oceanology, 9, 19–25, 1969.
Dyke, P. P. G., A simple ocean surface layer model, Rivista Italiana di Geofisica, 4, 31–34, 1977.
Gordon, R. B., Wind Driven circulation in Narragansett Bay, Ph.D. Thesis, University of Rhode Island, 1982.
Gordon, R. L., Coastal ocean current response to storm winds, J. Geophys. Res., 87, 1939–1951, 1982.
Heaps, N. S., On the numerical solution of the three-dimensional hydrodynamical equations for tides and storm surges, Mem. Soc. r. Sci Liege Ser 6, 2, 143–180, 1972.
Huang, N. E., On surface drift currents in the ocean, J. Fluid Mech., 91, 191–208, 1979.
Ichiye, T., Upper ocean boundary-layer flow determined by dye diffusion, Phys. Fluids Suppl., 10, 270–277, 1967.
Kullenberg, G. E. G., On vertical mixing and the energy transfer from the wind to the water, Tellus, 28, 159–165, 1976.
Lai, R. Y. S. and D. B. Rao, Wind drift currents in the deep sea with variable eddy viscosity, Arch. Met. Geophys. Bioklim, A, 25, 131–140, 1976.
Neumann, G. and W. J. Pierson, Principles of Physical Oceanography, Prentice Hall, 1964.
Thorpe, S. A., On the determination of Kv in the near-surface ocean from acoustic measurements of bubbles, Journal of Physical Oceanography, 14, 855–863, 1984.
Weber, J. E., Ekman currents and mixing due to surface gravity waves, Journal of Physical Oceanography, 1, 1431–1435, 1981.
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Davies, A.M. (1986). Mathematical Formulation of a Spectral Circulation Model. In: O’Brien, J.J. (eds) Advanced Physical Oceanographic Numerical Modelling. NATO ASI Series, vol 186. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0627-8_22
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DOI: https://doi.org/10.1007/978-94-017-0627-8_22
Publisher Name: Springer, Dordrecht
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