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T. Torsvik
specify a no-slip boundary condition
u b = v b = w b = 0 at z = −H (x, y).
In either case, additional parameterization terms are usually needed to account for
the influence of the bottom friction and the bottom boundary layer on the general
circulation. The simplest parameterization is the linear bottom stress formula
τ
B
= r b u b ,
which enters as an additional term in the momentum equation for the bottom velocity. A typical value for the bottom resistance coefficient r b is 0.0002 m/s. A more
realistic treatment is provided by the quadratic stress formula
τ
B
= −c B u b
u 2
b + v 2
b ,
where the non-dimensional quadratic bottom stress coefficient c B usually is set to a
constant value between 0.001 and 0.003.
The simplest boundary condition for the sea surface interface is the rigid lid
approximation, where we specify
w = 0 at z = 0,
which is usually used in combination with z-coordinate models. When terrainfollowing vertical coordinates are used, it is more common to use the kinematic
boundary condition
w =
∂η
∂t
+ u
∂η
∂x
+ v
∂η
∂y
at z = η(x, y, t).
To simplify the calculation of the kinematic boundary condition it is often assumed
that the sea surface displacement is small and therefore that the condition can be
computed for z = 0 instead of for z = η. The wind stress acting on the free surface interface can be accounted for in a similar manner as the bottom friction term.
A typical wind stress parameterization is provided by the quadratic stress formula
τ w = ρ a c D |U 10 |U 10 ,
where ρ a is the density of the air and U 10 is the wind speed 10 meters above the
sea surface (so-called 10 m wind). A typical value for the non-dimensional drag
coefficient c D is 0.003.
The wind stress depends on wind velocity data that is not provided by the ocean
model itself. Wind data from a climatological dataset is required to perform this
calculation. Atlases of climatological data have been built based on observations
from weather stations and satellites, and by using output from global or large scale
weather or climate models. Meteorological reanalysis is a data assimilation technique where numerical weather models are fitted to historical data. Notable examples include the European Centre for Medium-Range Weather Forecasts (ECMWF)
T. Torsvik
specify a no-slip boundary condition
u b = v b = w b = 0 at z = −H (x, y).
In either case, additional parameterization terms are usually needed to account for
the influence of the bottom friction and the bottom boundary layer on the general
circulation. The simplest parameterization is the linear bottom stress formula
τ
B
= r b u b ,
which enters as an additional term in the momentum equation for the bottom velocity. A typical value for the bottom resistance coefficient r b is 0.0002 m/s. A more
realistic treatment is provided by the quadratic stress formula
τ
B
= −c B u b
u 2
b + v 2
b ,
where the non-dimensional quadratic bottom stress coefficient c B usually is set to a
constant value between 0.001 and 0.003.
The simplest boundary condition for the sea surface interface is the rigid lid
approximation, where we specify
w = 0 at z = 0,
which is usually used in combination with z-coordinate models. When terrainfollowing vertical coordinates are used, it is more common to use the kinematic
boundary condition
w =
∂η
∂t
+ u
∂η
∂x
+ v
∂η
∂y
at z = η(x, y, t).
To simplify the calculation of the kinematic boundary condition it is often assumed
that the sea surface displacement is small and therefore that the condition can be
computed for z = 0 instead of for z = η. The wind stress acting on the free surface interface can be accounted for in a similar manner as the bottom friction term.
A typical wind stress parameterization is provided by the quadratic stress formula
τ w = ρ a c D |U 10 |U 10 ,
where ρ a is the density of the air and U 10 is the wind speed 10 meters above the
sea surface (so-called 10 m wind). A typical value for the non-dimensional drag
coefficient c D is 0.003.
The wind stress depends on wind velocity data that is not provided by the ocean
model itself. Wind data from a climatological dataset is required to perform this
calculation. Atlases of climatological data have been built based on observations
from weather stations and satellites, and by using output from global or large scale
weather or climate models. Meteorological reanalysis is a data assimilation technique where numerical weather models are fitted to historical data. Notable examples include the European Centre for Medium-Range Weather Forecasts (ECMWF)