Effect of depth ratio on frozen wave instability in immiscible liquids

In the present experimental work, a two-liquid system with comparable densities (density ratio = 0.543) undergoing lateral sinusoidal oscillation [along the length (L) of the container] has been considered. Under high forcing frequency condition (ω≫ν/L2), frozen waves appear at the interface of two-liquid system. Different depth ratios (hr) (or filling levels of liquid-1 and liquid-2) have been used to investigate the variations in the instability thresholds, wave amplitudes, wavelengths, and wave profiles of the frozen waves. Instability threshold of frozen waves shows unidirectional nature with varying depth ratios. A coefficient of relative velocity (c1) has been used to non-dimesionalize the variation of threshold amplitude (Aoc) and wave amplitude (Ar) with respect to depth ratios. Variation of normalized wave amplitude with modified Froude number shows existence of two regimes viz. gravity and surface tension dominated beyond which waves become three dimensional. A significant variation in wave profiles has been observed at high amplitude of forcing and reported in terms of radius of curvature. The three-dimensional frozen waves with temporally and spatially periodic doubling have been discussed.