No abstract

The Authors state that using values of C, and C,, which are functions of the KeuleganCarpenter number, to calculate the forces on circular cylinders in waves results in good agreement with experiment except near Keulegan-Carpenter numbers of 1 6 1 5 . However, for some applications it may be necessary to consider C, and CM not as variables but as constants. For instance, Fig. 9 shows the root mean square force F o n a circular cylinder of diameter D in a unidirectional sinusoidal flow generated in a U tube, the

The Authors present some remarkable experimental measurements of velocities and accelerations beneath a breaking wave. As a theoretical model of this process, a regular wave theory-such as the stream function theory used in the Paper-is a poor substitute for a time-dependent solution which reproduces the unsteady nature of the flow. As the Authors note, however, it has the advantages of familiarity and relative simplicity.42. In modelling the flow beneath a breaking wave, presumably the best that can be done with a theory for regular waves, without violating the conditions on which it is based, is to solve the wave which has the desired period and mean water depth but is of limiting height, since this is in many respects the most severe condition. Near the crest the physical process may be very different, thus necessitating the type of empirical corrections proposed. It is known that at its crest, the regular wave of limiting height must have a downwards particle acceleration of This is about 4% less than the wave height H used in the example, and is therefore outside the range of conditions for which one may hope for an analytical solution to the regular wave problem. This probably makes little difference to the outcome, but any results computed in this region must consequently reflect those errors in the model which permit a solution to be reached; in the case of series-type expansions, such as stream function theory, these come from series truncation and incomplete convergence. I would suggest that these considerations render the Paper's conclusions on the performance of stream function theory rather subjective; with other stream function programs (taken to different orders, or with different formulations), other results can be obtained.