Dispersion effects of Shallow Water Gravity Waves

Abstract

Anomalous dispersion was found as a growing of the phase velocity of high-frequency bound components of shoaling gravity waves. The velocities of those components get bigger than that of the primary by up to 25% in the near shore zone, where wave heights are approximately equal to the water depth. The ef-fect thus contradicts the theoretical conception about non-dispersive motion as a limited case of shallow water wave movement depending on water depth only. According to the observations the anomalous dispersion effect (ADE) gets weaker with the water depth decreasing and the motion is found to be non-dispersive for bore-like structures in the surf zone. The effect had been detected by field measurements when deep sea storm waves had a narrow spectrum. In laboratory measurements initially monochromatic waves of periods 2.0 to 5.0 s and heights of 0.14 m shoaled over up-sloping plane bottom. The laboratory experiments do confirm the existence of the ADE. In particular the measure-ments show an increase of the intensity of the ADE with the wave periods also increasing. As a result of both investigations it is found that the ADE represents a nonlinear effect, which appears, however, to be hidden at conditions charac-terized by free components coinciding with bound components in the same spectrum. The anomalous dispersion effect is responsible for the transformation of waves into the so-called „saw-tooth“ form being a typical feature of the surf zone.