Abstract: In isopycnal coordinate ocean
models, diapycnal diffusion must be expressed as a nonlinear difference
equation. This nonlinear equation is not amenable to traditional
implicit methods of solution, but explicit methods typically have a time
step limit of order  t
h2/
(where t
is the time step, h is the isopycnal layer thickness, and
is the diapycnal diffusivity), which cannot generally be satisfied since
the layers could be arbitrarily thin. It is especially important
that the diffusion time integration scheme have no such limit if the
diapycnal diffusivity is determined by the local Richardson
number. An iterative, implicit time integration scheme of
diapycnal diffusion in isopycnal layers is suggested. This scheme
is demonstrated to have qualitatively correct behavior in the limit of
arbitrarily thin initial layer thickness, is highly accurate in the
limit of well-resolved layers, and is not significantly more expensive
than existing schemes. This approach is also shown to be
compatible with an implicit Richardson number-dependent mixing
parameterization, and to give a plausible simulation of an entraining
gravity current with parameters like the Mediterranean Water overflow
through the Straits of Gibraltar. |