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Recalculation of surface slopes as forcing for numerical water column models of tidal flow. (English) Zbl 0986.76056
From the summary: We present a method for forcing numerical one-dimensional (1D) water column models of turbulent tidal flows. It needs as an input time series of water depth and velocity at one point in the water column. These time series are here interpreted as indirect measurements of surface slope. The method is based on an operator splitting technique as discretization in time in order to guarantee exact reproduction of the input data. For simple two-dimensional flow in the \(xz\) plane, a parametrization of horizontal advection is given which slightly improves the results. This new method is validated against the performance of a three-dimensional estuarine model from which forcing data for the 1D model have been extracted.

76M20 Finite difference methods applied to problems in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
86A05 Hydrology, hydrography, oceanography
Full Text: DOI
[1] Baumert, H.; Radach, G., Hysteresis of turbulent kinetic energy in nonrotational tidal flows: A model study, J. geophys. res., 97, 3669-3677, (1992)
[2] Burchard, H.; Baumert, H., On the performance of a mixed layer model based on the k-ϵ turbulence closure, J. geophys. res., 100, 8523-8540, (1995)
[3] H. Burchard, Three-dimensional numerical modelling of turbulent flows in estuaries and wadden seas, Theory and test cases, Technical Note No. I.97.180, Space Applications Institute, Joint Research Centre, Ispra, Italy, 1997
[4] Burchard, H.; Petersen, O., Hybridization between σ and z coordinates for improving the internal pressure gradient calculation in marine models with steep bottom slopes, Int. J. num. meth. fluids, 25, 1003-1023, (1997) · Zbl 0898.76072
[5] H. Burchard, O. Petersen, Models of turbulence in the marine environment - A comparative study of two-equation turbulence models, J. Marine Systems, accepted
[6] Burchard, H.; Petersen, O.; Rippeth, T.P., Comparing the performance of the k-ϵ and the mellor – yamada two-equation turbulence models, J. geophys. res., 103, 10543-10554, (1998)
[7] H. Burchard, A. Stips, W. Eifler, K. Bolding, M.R. Villarreal, Numerical simulation of dissipation measurements in non-stratified and strongly stratified estuaries, in: Proceedings of the Ninth Biennial Workshop on Physics in Estuaries and Coastal Seas, Matsuyama, Japan, 24-26 September, submitted
[8] Davies, A.M., On the importance of time varying eddy viscosity in generating higher tidal harmonics, J. geophys. res., 95, 20287-20312, (1990)
[9] E. Deleersnijder, K.G. Ruddick, A generalized vertical coordinate for 3D marine problems, Bulletin de la Société Royale des Sciences de Liège 61 (1992) 489-502
[10] Flather, R.A.; Hubbert, K.P., Tide and surge models for shallow water – morecambe bay revisited in modeling marine systems, Marine systems, 1, 135-166, (1990)
[11] B.A. Kagan, Ocean-Atmosphere Interaction and Climate Modelling, Cambridge University Press, Cambridge, 1995
[12] J.J. Leendertse, A summary of experiments with a model of the Eastern Scheldt, Rep. No. R-3611-NETH, The RAND Corporation, Santa Monica, California, 1988
[13] Luyten, P.J.; Deleersnijder, E.; Ozer, J.; Ruddick, K.G., Presentation of a family of turbulence closure models for stratified shallow water flows and preliminary application to the rhine outflow region, Cont. shelf res., 16, 101-130, (1996)
[14] P.J. Luyten, J.H. Simpson, T.P. Rippeth, Comparison of turbulence models for homogeneous and stratified flows with turbulence measurements in the Irish Sea, paper presented at MAST Workshop on Turbulence Modelling, Bergen, Norway, 8-10 1996
[15] G.I. Marchuk, A.S. Sarkisyan, Mathematical Modelling of Ocean Circulation, Springer, New York, 1988 · Zbl 0712.76006
[16] Phillips, N.A., A coordinate system having some special advantages for numerical forecasting, J. meteorol., 14, 184-185, (1957)
[17] Rodi, W., Examples of calculation methods for flow and mixing in stratified flows, J. geophys. res., 92, 5305-5328, (1987)
[18] Simpson, J.H.; Crawford, W.R.; Rippeth, T.P.; Campbell, A.R.; Cheok, J.V.S., The vertical structure of turbulent dissipation in shelf seas, J. phys. oceanogr., 26, 1579-1590, (1996)
[19] Strang, W.G., On the construction and comparison of difference schemes, SIAM J. numer. anal., 21, 506-517, (1968) · Zbl 0184.38503
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