Derivation of a two-layer non-hydrostatic shallow water model
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1995-08
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Water Resources Research Center, University of Hawaii at Manoa
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Abstract
A theoretical non-hydrostatic model is developed to describe the dynamics of a two-layer shallow water system in the presence of viscous and Coriolis effects. The Navier-Stokes equations are integrated over the water depth in each layer to obtain the layer-mean equations. To close the resulting equation set, perturbation expansions of the vertical momentum equation are used and the dynamic pressures are solved in terms of wave elevations and horizontal velocities. A preliminary analysis is also carried out and a result for the quasigeostrophic problems is given based on an previous study. Our final model is of the Bousinesq class which is nonlinear and dispersive, and includes the effects of surface wind stress, bottom friction, eddy diffusion and earth rotation. It is shown that our new model can be readily reduced to previous inviscid non-hydrostatic models. Our model can be used in numerical simulations to study real ocean problems such as hurricane generated waves, tidal induced current, and interactions among surface waves, internal waves and variable topographies.
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Hydrodynamics--Mathematical models, Fluid dynamics—Mathematical models., Hydrodynamics--Mathematical models.
Citation
Feng Y. 1995. Derivation of a two-layer non-hydrostatic shallow water model. Honolulu (HI): Water Resources Research Center, University of Hawaii at Manoa. WRRC unedited report, 95-03.
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x, 59 pages
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Related To
Theses for the degree of Master of Science (University of Hawaii at Manoa). Civil Engineering; no. 3088
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