The Interaction of a Finite Amplitude Surface Wave with an Internal Wave.

摘要

The conservation equation approach is used to describe the interaction of a large amplitude surface wave with a long wavelength internal wave disturbance,including the effect of surface tension. The character of the equations is found to be dependent on a slope parameter as well as a parameter describing the relative importance of surface tension and gravity,but is independent of the disturbance. Both elliptic and hyperbolic domains exist. The system is parabolic if finite amplitude effects are neglected. The initial value problem for a small disturbance for the more pertinent elliptic case produces exponential time growth. Oscillatory,rather than growing solutions,occur for the hyperbolic case. Linear and quadratic time growth occur for the nonresonant and resonant (C = (C g sub 0)) small amplitude,initial-value problem. Finite amplitude effects remove the singularity present in the small amplitude case at C = (C g sub 0). A steady-state solution is seen to be of limited usefulness. Viscosity severely damps capillary waves. Conditions for which viscous damping can overcome the growth are found for both the capillary and gravity wave cases. (Author)