The interaction trapping of internal gravity waves

Abstract

It is shown that as a result of their non-linear interactions, internal gravity waves in an unbounded fluid can be trapped to a layer of finite depth by periodic small variations in either the density gradient or in a weak horizontal steady current. This trapping occurs when the vertical component of the wave-number is half that of the density gradient or of the current variations. The energy density of the wave motion trapped near the ocean surface decreases exponentially with depth over a distance that is inversely proportional to the magnitude of the variations in density gradient or in horizontal current speed.