3 Introduction to Computational Fluid Dynamics and Ocean Modelling
99
reanalysis projects, ERA-40 and ERA-Interim, and the National Centres for Environmental Prediction and for Atmospheric Research (NCEP/NCAR) reanalysis,
which provide data for the state of the Earth’s atmosphere from mid-20th century
until present time. In addition to wind data, ocean models require data for atmospheric temperature in order to prescribe a realistic heat flux at the free surface
interface.
The lateral boundary conditions are determined by the specific application. If the
sidewall of the domain can be considered as a solid wall, as is the case when the
sidewall is located on dry land, we can use the no-flux condition
u · n = 0,
where n is the outward normal vector for the sidewall. In many applications at least
some of the lateral boundaries will intersect sea areas. In the case of global models, where the lateral boundary may be located along a line of longitude, periodic
boundary conditions can be used at the east and west boundaries. The location of
Antarctica at the South Pole allows the use of a no-flux wall condition, but the Arctic Ocean is difficult to represent in such a model. One solution to this problem is
to model the Arctic Ocean and North Atlantic with a separate model using a rotated
grid with poles at the equator, as is done in the OCCAM (Ocean Circulation and
Climate Advanced Modelling Project) global ocean model. An alternative method
is to apply a non-spherical coordinate system where polar singularities are hidden
over land.
The sea intersecting lateral boundary condition becomes more complicated for
regional models which should allow flow exchange with sea areas not covered by
the numerical model. Such open boundary conditions should be able to eliminate
any reflection from waves and currents leaving the computational domain, and allow inflow of water masses according to parameters describing conditions in the
exterior sea areas. The parameters for exterior sea areas may reflect transport due to
major ocean currents and seasonal variability in average temperature and salinity, or
may be extracted from a global ocean model in a similar way as the atmospheric climatology datasets. There is no universally accepted ‘correct’ way to prescribe such
open boundary conditions, and a single model may use a combination of several
methods (zero gradient, radiation conditions, flow relaxation) to achieve the desired
result.
Climatological datasets, including hydrographic data for potential temperature
and salinity, are important for the initialization of ocean models. If a global ocean
model is initiated with a homogeneous state, it will take thousands of simulated
years for diffusive processes to generate realistic deep ocean water masses. Even if
the model is initialized with hydrographic data close to the long term equilibrium
state, the model will usually require some spin-up time before a realistic circulation pattern emerges. At the start of a simulation the initial density field is adjusted
towards an equilibrium state. For a global circulation model it takes from a few
weeks to a few months to set up the barotropic wind generated currents, whereas
the baroclinic response is set up after a few years, and the thermohaline circulation
99
reanalysis projects, ERA-40 and ERA-Interim, and the National Centres for Environmental Prediction and for Atmospheric Research (NCEP/NCAR) reanalysis,
which provide data for the state of the Earth’s atmosphere from mid-20th century
until present time. In addition to wind data, ocean models require data for atmospheric temperature in order to prescribe a realistic heat flux at the free surface
interface.
The lateral boundary conditions are determined by the specific application. If the
sidewall of the domain can be considered as a solid wall, as is the case when the
sidewall is located on dry land, we can use the no-flux condition
u · n = 0,
where n is the outward normal vector for the sidewall. In many applications at least
some of the lateral boundaries will intersect sea areas. In the case of global models, where the lateral boundary may be located along a line of longitude, periodic
boundary conditions can be used at the east and west boundaries. The location of
Antarctica at the South Pole allows the use of a no-flux wall condition, but the Arctic Ocean is difficult to represent in such a model. One solution to this problem is
to model the Arctic Ocean and North Atlantic with a separate model using a rotated
grid with poles at the equator, as is done in the OCCAM (Ocean Circulation and
Climate Advanced Modelling Project) global ocean model. An alternative method
is to apply a non-spherical coordinate system where polar singularities are hidden
over land.
The sea intersecting lateral boundary condition becomes more complicated for
regional models which should allow flow exchange with sea areas not covered by
the numerical model. Such open boundary conditions should be able to eliminate
any reflection from waves and currents leaving the computational domain, and allow inflow of water masses according to parameters describing conditions in the
exterior sea areas. The parameters for exterior sea areas may reflect transport due to
major ocean currents and seasonal variability in average temperature and salinity, or
may be extracted from a global ocean model in a similar way as the atmospheric climatology datasets. There is no universally accepted ‘correct’ way to prescribe such
open boundary conditions, and a single model may use a combination of several
methods (zero gradient, radiation conditions, flow relaxation) to achieve the desired
result.
Climatological datasets, including hydrographic data for potential temperature
and salinity, are important for the initialization of ocean models. If a global ocean
model is initiated with a homogeneous state, it will take thousands of simulated
years for diffusive processes to generate realistic deep ocean water masses. Even if
the model is initialized with hydrographic data close to the long term equilibrium
state, the model will usually require some spin-up time before a realistic circulation pattern emerges. At the start of a simulation the initial density field is adjusted
towards an equilibrium state. For a global circulation model it takes from a few
weeks to a few months to set up the barotropic wind generated currents, whereas
the baroclinic response is set up after a few years, and the thermohaline circulation