TABLE OF CONTENTS The major difficulty in using averaged equations to describe turbulence is the closure problem: finding adequate approximations for the Reynolds stresses etc. Now the above averaged boundary conditions (62), (69) and (70) introduce on their right-hand sides a further range of terms that need to be determined. First, consider the structure of the problem.
The number of boundary conditions for a liquid at a free surface is one greater than that required at a rigid surface since the position of the surface is an extra independent variable that must be determined as part of the problem. Here there are numerous extra variables, of which the major/simpler ones are:
| b: | the position of the base of the layer; |
| d: | the equivalent thickness of the layer; |
| W: | the mass transfer to the layer; |
| ? h b ? U ? dn: | the mass flow in the layer; |
| also | the terms representing momentum flow in the layer; |
| the terms representing phase interaction in the layer, e.g. air drag, capillarity effects, etc.. |
Note that these terms include the mean flow properties of the surface layer, as well as the turbulent fluctuations within the layer.
As usual, we cannot use fundamental conservation concepts for our modelling unless we return to the full equations of motion. Our discussion in Part 1 of the various regimes and flows when turbulence meets a free surface provides the key to developing closures, since for many cases the properties of the turbulence below the...
