scattering problems which contain both a free surface and a sharp interface, in which case energy can be transferred between internal and free surface waves. Presumably a similar analysis could be performed for the finite pycnocline situation and this would have an effect on the calculated results which may bring the experimental and theoretical results closer together.
Another aspect of Linton and McIver’s work was the systematic derivation, from Green’s theorem, of identities connecting the various hydrodynamic quantities which arise, such as reflection and transmission coefficients and exciting forces, and which are analogous to those that exist in standard linear water-wave theory. Presumably similar results exist for a finite pycnocline, both with the free surface approximated by a rigid lid and with the linear free-surface boundary condition applied. Such relations are of intrinsic theoretical importance and can also be used as a check on results obtained from any numerical procedure.
We agree that the theoretical analysis can be performed with consideration the free surface on the upper boundary. Effect of the free surface on scattering of the internal waves in the two-layer fluid was studied by Sturova . In the experiments described in the present paper the density variation over depth was very small what implies that the transfer of energy from internal modes to surface motion at free surface has been observed in experiments.
Indeed, the identities connecting the various hydrodynamic quantities exist for a finite pycnocline and are obtained by Sturova .
1. Sturova, I.V., “Scattering of Surface and Internal Waves on Submerged Body,” Computational technology, Vol. 2, No. 4, ICT SD RAS, Novosibirsk, 1993, pp. 30–45 (in Russian).
2. Sturova, I.V., “Diffraction and Radiation Problems for the Circular Cylinder in Stratified Fluid,” (submitted to Fluid Dynamics).