Physics

For example, the surface slopes
and
representing the barotropic pressure-gradients may
be determined by means of local observations or results from
three-dimensional numerical models. It is also possible to prescribe a
time series of the near-bed velocity components for reconstructing the
barotropic pressure gradient, see Burchard (1999). The
implementation of these options for the external pressure gradient is
carried out in `extpressure.F90`, described in
section 3.2.8. The internal pressure-gradient, which results
from horizontal density gradients, can be prescribed from observations
of horizontal gradients of and or from three-dimensional
model results (see `intpressure.F90` in section 3.2.9).
These gradients may also be used for horizontally advecting
and (see section 3.2.11 and section 3.2.12).

Another option in GOTM for parameterising the advection of and is to relax the model results to observations. Evidently, this raises questions about the physical consistency of the model, but it might help to provide a more realistic density field for studies of turbulence dynamics. Nudging is also possible for the horizontal velocity components. This makes sense in order to initialise inertial oscillations from observed velocity profiles, see section 3.2.6 and section 3.2.7. In the momentum equations, advection and horizontal diffusion terms are neglected.

In hydrostatic ocean models, the vertical velocity is calculated by
means of the continuity equation, where the horizontal gradients of
and are needed. Since these are not available or set to zero,
the assumption of zero vertical velocity would be consistent. In many
applications however, a non-zero vertical velocity is needed in order
to reflect the vertical adiabatic motion of e.g. a thermocline. In
GOTM, we have thus included the option of prescribing a vertical
velocity time series at one height level which might be vertically
moving. Vertical velocities at the surface and at the bottom are
prescribed according to the kinematic boundary conditions ( at
the bottom and
at the surface), and between these
locations and the prescribed vertical velocity at a certain height,
linear interpolation is applied, see `updategrid.F90` in
section 3.2.4. This vertical velocity is then used for the
vertical advection of all prognostic quantities.

Standard relations according to the law of the wall are used for
deriving bottom boundary conditions for the momentum equations (see
`friction.F90` in section 3.2.10). At the sea surface, they
have to be prescribed or calculated from meteorological observations
with the aid of bulk formulae using the simulated or observed sea
surface temperature (see section 5.2). In `stratification.F90` described in section 3.2.15, the
buoyancy as defined in equation (33) is calculated by
means of the UNESCO equation of state (Fofonoff and Millard (1983))
or its linearised version. In
special cases, the buoyancy may also be calculated from a simple
transport equation. `stratification.F90` is also used for
calculating the Brunt-Väisälä frequency, .

The turbulent fluxes are calculated by means of various different
turbulence closure models described in great detail in the `turbulence` module, see section 4.7. As a simplifying
alternative, mixing can be computed according to the so-called
`convective adjustment' algorithm, see section 3.2.16.

Furthermore, the vertical grid is also defined in the meanflow module
(see `updategrid.F90` in section 3.2.4). Choices for the
numerical grid are so-called -coordinates with layers heights
having a fixed portion of the water depth throughout the
simulation. Equidistant and non-equidistant grids are possible.

Karsten Bolding 2012-01-24