2. Water waves

Water waves may in fact be the most complex of all; out at sea, the water surface is a summation of an ever-changing mix of waves of many sizes, speeds, and directions, thanks largely to the fact that some waves can last for weeks, and in that time they can travel thousands of kilometres. Until recently, many wave parameters were hard to measure, but accurate measurements can now be made by a number of techniques including dual frequency radar altimetry. ‘Water waves’ describes many different waves and how they build, including capillary waves, breakers, edge waves, harbour resonance, seiches, tides, and tsunamis.

Harbour excitations by incident wave groups

By using the multiple-scales perturbation method, analytical solutions are obtained for the second-order low-frequency oscillations inside a rectangular harbour excited by incident wave groups. The water depth is a constant. The width of the harbour entrance is of the same order of magnitude as the wavelength of incident carrier (short) waves, but small in comparison with the wavelength of the wave envelope. Because of the modulations in the wave envelope, a second-order long wave is locked in with the wave envelope and propagates with the speed of the group velocity. Outside the harbour, locked long waves also exist in the reflected wave groups, but not in the radiated wave groups. Inside the harbour, the analytical expressions for the locked long waves are obtained. Owing to the discontinuity of the locked long waves across the harbour mouth, second-order free long waves are generated. The free long waves propagate with a speed of (gh)½ inside and outside the harbour. The free long waves inside the harbour may be resonated in a low-frequency range which is relevant to the harbour resonance.

AN EXPERIMENTAL STUDY OF HARBOUR RESONANCE PHENOMENA

An extensive series of experiments has been carried out at the laboratory in order to study rectangular harbour oscillation excited by incident long waves. Attention is focused on the effect of head loss entrance on resonant response attenuation. A "gross" quadratic hydraulic head loss coefficient is defined and information about it, resulting from tests, is provided. Experimental conditions used in this piece of work seem to be realistic under suitable scaling for Northern Spain harbours.