Interfacial solitary waves in a two-fluid medium

Abstract

Solitary waves are generated on the interface between two immiscible liquids with free upper surface; their behavior is generally consistent with that predicted by the Korteweg-de Vries equation. Inviscid theory expanded to include capillary effects predicts unchanged wave speed and narrowed wave shape to first order in amplitude regardless of upper boundary condition; but measured speeds are down 8% and narrowing is substantially greater at very small amplitudes. The speed difference appears consistent with an interfacial viscous boundary layer. The critical depth ratio separating the elevation and depression modes of the stable gravity solitary wave agrees with prediction in the inviscid limit. The design of a programmed, variable flux wave maker for efficiently generating interfacial waves is discussed.