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A free-surface hydrodynamic model for density-stratified flow in the weakly to strongly non-hydrostatic regime. (English) Zbl 1115.76310

Summary: A non-hydrostatic density-stratified hydrodynamic model with a free surface has been developed from the vorticity equations rather than the usual momentum equations. This approach has enabled the model to be obtained in two different forms, weakly non-hydrostatic and fully non-hydrostatic, with the computationally efficient weakly non-hydrostatic form applicable to motions having horizontal scales greater than the local water depth. The hydrodynamic model in both its weakly and fully non-hydrostatic forms is validated numerically using exact nonlinear non-hydrostatic solutions given by the Dubriel-Jacotin-Long equation for periodic internal gravity waves, internal solitary waves, and flow over a ridge. The numerical code is developed based on a semi-Lagrangian scheme and higher order finite-difference spatial differentiation and interpolation. To demonstrate the applicability of the model to coastal ocean situations, the problem of tidal generation of internal solitary waves at a shelf-break is considered. Simulations carried out with the model obtain the evolution of solitary wave generation and propagation consistent with past results. Moreover, the weakly non-hydrostatic simulation is shown to compare favorably with the fully non-hydrostatic simulation. The capability of the present model to simulate efficiently relatively large scale non-hydrostatic motions suggests that the weakly non-hydrostatic form of the model may be suitable for application in a large-area domain while the computationally intensive fully non-hydrostatic form of the model may be used in an embedded sub-domain where higher resolution is needed.

MSC:

76B07 Free-surface potential flows for incompressible inviscid fluids
76B55 Internal waves for incompressible inviscid fluids
76B70 Stratification effects in inviscid fluids
76M20 Finite difference methods applied to problems in fluid mechanics
86A05 Hydrology, hydrography, oceanography

Software:

MUDPACK-2; MUDPACK
PDFBibTeX XMLCite
Full Text: DOI

References:

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