Even in multi-level ocean models where there is an attempt to model in great detail the vertical structure, the effort to resolve boundary layers is usually confined to the surface mixed layers (see section 4 ``Mixed-Layer Models''), paying little attention to the so-called ``benthic'' or bottom boundary layer (i.e. the turbulent frictional layer along the ocean bottom). Generally, most ocean models resort to the application of some sort of drag law in the lowest layer to represent the turbulent frictional processes there. The use of lateral (i.e. horizontal) friction, on the other hand, is an almost universal constraint imposed on all hydrodynamic numerical models by their inability to follow the nonlinear cascade of energy below scales of the mesh size. This friction effectively prevents the pileup of energy in a numerical simulation in the wavelength range corresponding to the mesh size (the nonlinear terms in 3-D turbulence cause an energy cascade down toward high wave numbers or short length scales). The form of the bottom friction term can take either a linear or nonlinear form; both formulations have been used in the past in ocean models of various types.
a. The linear approach: This has
been used by several modelers utilizing layered-type ocean models.
Nowlin
[48],
during an investigation of the energy transfers in a
two layer model, has also derived some magnitudes for the value of
from spindown considerations, where the wind is turned off
suddenly and the flow decelerates due to bottom friction (with
minimum lateral friction) in this case. His recommended value of
is in the range 1-5
/sec.
Creegan
[6]
has utilized the linear drag
law in a study of the wind-driven circulation in the GIN
Sea and
used a value of 
/sec.
b. The non-linear approach: Many of the modeling efforts in the North Sea have employed a nonlinear bottom stress of the form
with the value of the drag
coefficient 
taken to be either .0025 or .0050, depending on the
author. Many studies
[62],
[1],
[12],
[13],
and
[9]
have used
, whereas
[8]
and
[17]
have used a value of 
.
These values were generally determined during computation of
tides, from their transient behavior. In considering an
application of these values for the barotropic experiments carried
out here, we must consider whether the nature of the benthic
boundary layer processes in the North Sea are really very
different from the ones at the bottom of the GIN Sea. To really
answer this question one would need to know the typical benthic
boundary layer thicknesses, interior flow speeds and the size of
the turbulent eddies. On first approximation it doesn't appear
that these processes would be very different at a depth of 500m
from those at, say 2500m, and hence the use of drag coefficients
with the same magnitude appears to be warranted.
