Bragg Reflection of Water Waves in a Rectanglar Channel

摘要

A series of corrugations on the bottom of a layer of water of otherwise uniform depth can have a cooperative effect on incident water waves. The phenomenon is well-known, called Bragg reflection or Bragg resonance. These effects on the normal modes of oscillation in a rectangular tank with corrugated bottom are studied using an asymptotic theory, and by developing an exact theory. The exact theory confirms the essential correctness of the asymptotic results for the slowly varying aspects of the motions. The rapidly varying components are, however, important to the flow near the boundaries. Higher order Bragg resonance, i.e. when the spacing of corrugations is an integer (greater than 1) multiple of half the water wavelength, is examined and the solution regimes (resonance tongues) are constructed using the exact theory.