A
non-hydrostatic algorithm for free-surface ocean modelling
Auclair F., Estournel C., Floor J. W., Herrmann
M., Nguyen C., Marsaleix P.
Ocean Modelling 2011
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 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.
http://dx.doi.org/10.1016/j.ocemod.2010.09.006
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