As discussed above, the use of a lateral friction coefficient is a general requirement for modeling all hydrodynamic processes that have strong nonlinearities, and as such it becomes a necessary part of ocean models as well. As mentioned above, such friction is necessary both for physical and numerical reasons. The size of such a coefficient can be estimated from various arguments, as we present below.
It has been found during the long history of numerical simulation of nonlinear flows that the size of this friction coefficient A is determined by a constraint laid on the so-called mesh-box Reynolds number, defined as , where is the mesh size and U is the magnitude of the velocity in that mesh box. This number is constrained generally to take on values in nonlinear flow simulations, as discussed by Roache . Though the barotropic flow modeled here has actually an almost linear behavior, the presence of a sharp topography can be shown to cause effects similar to those of nonlinearity. From Equations (1), (2), and (3) we can derive a wave equation of the form
We note that the second term has the form of an advection term, and in particular that represents a ``velocity'' by dimension, namely the speed of fast surface gravity waves in an ocean of depth . Inserting this ``velocity'' into the formula for the critical sub-mesh Reynolds number gives . Thus ; for a bottom-slope rise of 100 m in 25 km, a value of implies a lateral friction value of m/s, and for a rise of m a value of m/s.