SUBHARMONIC RESONANCE OF OBLIQUE INTERFACIAL WAVES BY A PROGRESSIVE SURFACE-WAVE

Experimental and theoretical investigations into the generation of int ernal gravity waves by monochromatic progressive surface waves are pre sented. Using the method of nonlinear resonant interactions, a triad c onsisting of a single surface wave and two oblique internal waves in a two-layer model is considered. A multiple scales analysis is adopted and the boundary value problem is expanded in a power series of the su rface-wave steepness. At the leading order, the linear harmonics are o btained and the conditions for resonance are determined. A second-orde r analysis is then used to derive temporal evolution equations for the internal-wave amplitudes. As a consequence of having a single generat ing train of the sm:face waves, two oblique trains of internal waves o f much shorter wavelength are found to be resonated exponentially in t ime. Both linear and nonlinear bounds on surface-wave frequency, densi ty ratio and interaction angle are found, demonstrating that the insta bility is highly narrow banded. It is found that the internal waves gr ow most rapidly at the linear cut-off values. Experimental evidence is presented and demonstrates good agreement with the theoretical result s. Discussion of an application of the theory to the nonlinear energy transfer between very-low-frequency waves in the deep ocean is then pr ovided.