Abstract
Gyres are prominent surface structures in the global ocean circulation
that often interact with the sea floor in a complex manner. Diagnostic
methods, such as the depth-integrated vorticity budget, are needed to
assess exactly how such model circulations interact with the bathymetry.
Terms in the vorticity budget can be integrated over the area enclosed
by streamlines to identify forces that spin gyres up and down. In this
article we diagnose the depth-integrated vorticity budgets of both
idealized gyres and the Weddell Gyre in a realistic global model. It is
shown that spurious forces play a significant role in the dynamics of
all gyres presented and that they are a direct consequence of the
Arakawa C-grid discretization and the z-coordinate representation of the
sea floor. The spurious forces include a numerical beta effect and
interactions with the sea floor which originate from the discrete
Coriolis force when calculated with the following schemes: the energy
conserving scheme (ENE); the enstrophy conserving scheme (ENS); and the
energy and enstrophy conserving scheme (EEN). Previous studies have
shown that bottom pressure torques provide the main interaction between
the depth-integrated flow and the sea floor. Bottom pressure torques are
significant, but spurious interactions with bottom topography are
similar in size. Possible methods for reducing the identified spurious
topographic forces are discussed. Spurious topographic forces can be
alleviated by using either a B-grid in the horizontal plane or a
terrain-following vertical coordinate.