that the ratio o^/£is somewhat smaller than one (see Christof fersen, 

 1980, in preparation, 1983). At least one accurate laboratory experi- 

 ment is needed to settle this problem. 



Another matter is that for small values of wave particle amplitude 

 over roughness, a constant eddy viscosity in the wave boundary layer is 

 more likely than a linearly varying one. Using this concept, a simpler 

 set of formulas emerges for friction factors, etc. (see the above 

 references) . 



Coastal Engineering Significance. This is a serious attempt to 

 determine the bottom shear stress and the current profile in a three- 

 dimensional current wave motion. It gives detailed instructions for the 

 calculation procedure. Analytically it is quite complicated, involving 

 Kelvin functions and iterations. For many cases of practical interest, 

 however, the near-bed current speed is small compared with the orbital 

 speed and this allows approximations which greatly simplify the calcula- 

 tions, (in the above-mentioned references it is shown that the Grant/ 

 Madsen friction factor formula, which involves Kelvin functions, 

 generally can be approximated by a logarithmic friction factor expres- 

 sion. This is formally analogous to Jonsson's friction factor formula, 

 adjusted to take the current into account.) Some of the major assump- 

 tions are open to discussion, but the model can explain some of the very 

 large (apparent) roughnesses found in field experiments by other inves- 

 tigators. 



18. HASHIZUME, Y., "Interaction Between Short Surface Waves and Long 

 Internal Waves," Journal of the Physical Society of Japan, Vol. 48, 

 No. 2, Feb. 1980, pp. 631-638. 



Keywords. Interactions, Internal Waves; Theory; Wave Effect on Current. 



Discussion. The problem is treated theoretically starting with 

 Laplace's equation for a liquid of two layers of different density and 

 the exact inviscid boundary conditions. A perturbation solution for the 

 combination of surface waves and internal waves is sought for two 

 different cases. The group velocity of the surface waves is assumed to 

 be close to the phase velocity of the long internal wave in order that 

 there be resonant interaction. 



The first case considered is where the particle velocities due to 

 surface waves are much greater than those due to the internal wave. 

 Then modulation of the surface waves induces a mean flow which affects 

 the internal wave. Interaction equations are derived, and solutions 

 which propagate unchanged are derived. 



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