On gravity‐capillary waves due to interface disturbance

Abstract

The generation of gravity‐capillary waves at the interface between two superposed fluids due to interface disturbance is considered, assuming linear theory. Fourier and Laplace transform techniques are employed in the mathematical analysis and the form of the interface depression is obtained as an infinite integral involving oscillatory functions when the disturbance is concentrated at the origin. The method of stationary phase is then employed to evaluate this infinite integral asymptotically. The asymptotic form of the interface depression is presented graphically and compared with the non‐capillary case. It is observed that the interface capillarity has some significant effect on the wave motion.