non-hydrostatic algorithm for free-surface ocean modelling
Auclair F., Estournel C., Floor J. W., Herrmann M.,
Nguyen C., Marsaleix P.
Ocean Modelling 2011
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 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.