Abstract
An original implementation of a non-hydrostatic, free-surface algorithm based on a pressure correction method is proposed for ocean modelling. The free surface is implemented through an explicit scheme combined with a mode-spitting method but the depth-averaged velocity and the position of the free surface are updated at each non-hydrostatic iteration. The vertical momentum equation is also integrated up to the surface enabling a natural and accurate treatment of the surface layer. The consistent specification of the numerical schemes provides balanced transfers of potential and kinetic energy. This algorithm is well-suited for implementation as a non-hydrostatic kernel on originally hydrostatic free-surface ocean models such as Symphonie ( http://poc.obs-mip.fr/pages/research_topics/modelling/symphonie/symphonie.htm) for which it has originally been developed. Energy balances associated with the propagation of short surface waves and solitary waves are presented for two dedicated well-documented configurations over closed domains. The buoyancy flux, the work rate of the pressure force together with the power of the advective terms are evaluated and discussed for the generation and the propagation of these two types of waves. The dissipation rate is in particular shown to be several orders of magnitude smaller than the work rates of the hydrostatic and non-hydrostatic pressure forces confirming the necessity for the exchanges of energy to be numerically balanced. The algorithm is subsequently applied to the complex generation of non-linear solitary internal waves by surface tides over Georges Bank, in the Gulf of Maine. The generation and the propagation of the observed non-linear and non-hydrostatic features in this region are correctly reproduced.
Highlights
The present algorithm tackles the problem of the removal of the hydrostatic assumption in ocean free-surface models
The vertical velocity that is computed diagnostically under the hydrostatic assumption transforms into a prognostic variable with its own momentum equation and it must at the same time satisfies kinematic conditions at the surface and at the bottom
This algorithm is designed to be implemented as a nonhydrostatic kernel for originally hydrostatic ocean models
Summary
The present algorithm tackles the problem of the removal of the hydrostatic assumption in ocean free-surface models. The apparent simplicity of treatment of the surface and bottom boundary conditions in r-coordinates should not hide some recurrent difficulties associated with their use in regions cumulating steep topography gradients and steep density stratification These configurations can lead to rather large truncation errors in the horizontal pressure gradient (Mellor et al, 1994) and Auclair et al (2000) and Marsaleix et al (2009) recently proposed adapted algorithms and numerical schemes that result in a drastic reduction of these errors. A non-hydrostatic correction of the free surface elevation is deduced from the adjustment of the non-hydrostatic pressure component but a mode-spitting approach enables the treatment of the free surface dynamics at affordable computational costs in the present algorithm. The algorithm is eventually used to model the generation of non-linear internal waves by surface tides in the region of Georges Bank in Section 4 and the transfers of energy more associated with both surface and internal solitary waves are studied on dedicated closed configurations
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
