Interfacial waves in two liquid layers driven by horizontal oscillation

When a closed vessel containing two stably stratified, immiscible liquids is oscillated in the horizontal direction, the flat interface between the two liquids is known to undergo a symmetry breaking bifurcation to two-dimensional (2-D) 'frozen wave' driven by interfacial shear, similar to the Kelvin-Helmholtz instability. In this thesis we present an experimental study on the dynamics of this interfacial wave as a function of the vibrational Froude number (W, square root of the ratio of vibrational to gravitational forces). The onset of the 'frozen wave' is followed by a nonlinear growth of the wave to large amplitudes, which precedes a secondary instability to three-dimensional (3-D) waves.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Steep capillary-gravity waves in oscillatory shear-driven flows

We study steep capillary-gravity waves that form at the interface between two stably stratified layers of immiscible liquids in a horizontally oscillating vessel. The oscillatory nature of the external forcing prevents the waves from overturning, and thus enables the development of steep waves at large forcing. They arise through a supercritical pitchfork bifurcation, characterized by the square root dependence of the height of the wave on the excess vibrational Froude number (W, square root of the ratio of vibrational to gravitational forces). At a critical value Wc, a transition to a linear variation in W is observed. It is accompanied by sharp qualitative changes in the harmonic content of the wave shape, so that trochoidal waves characterize the weakly nonlinear regime, but ‘finger’-like waves form for W Wc. In this strongly nonlinear regime, the wavelength is a function of the product of amplitude and frequency of forcing, whereas for W <Wc, the wavelength exhibits an explicit dependence on the frequency of forcing that is due to the effect of viscosity. Most significantly, the radius of curvature of the wave crests decreases monotonically with W to reach the capillary length for W =Wc, i.e. the lengthscale for which surface tension forces balance gravitational forces. For W <Wc, gravitational restoring forces dominate, but for W Wc, the wave development is increasingly defined by localized surface tension effects

The influence of viscosity on the frozen wave stability: theory and experiment

We present the results of an experimental and linear stability study of the influence of viscosity on the frozen wave (FW) instability, which arises when a vessel containing stably stratified layers of immiscible liquids is oscillated horizontally. Our linear stability model consists of two superposed fluid layers of arbitrary viscosities and infinite lateral extent, subject to horizontal oscillation. The effect of the endwalls of the experimental vessel is simulated by enforcing the conservation of horizontal volume flux, so that the base flow consists of counterflowing layers. We perform experiments with four pairs of fluids, keeping the viscosity of the lower layer (ν1) constant, and increasing the viscosity of the upper layer (ν2), so that 1.02 × 102 ≤ N1 = ν2/ν1 ≤ 1.21 × 104. We find excellent quantitative agreement between theory and experiment despite the simple model geometry, for both the critical onset parameter and wavenumber of the FW. We show that the model of lyubimov:1987 (Fluid Dyn. vol. 86, 1987, p. 849), which is valid in the limit of inviscid fluids, consistently underestimates the instability threshold for fluids of equal viscosity, but generally overestimates the threshold for fluids of unequal viscosity. We extend the experimental parameter range numerically to viscosity contrasts 1 ≤ N1 ≤ 6 × 104 and identify four regions of N1 where qualitatively different dynamics occur, which are reflected in the non-monotonic dependence of the most unstable wavenumber and the critical amplitude on N1. In particular, we find that increasing the viscosity contrast between the layers leads to destabilization over a wide range of N1, 10 ≤ N1 ≤ 8 × 103. The intricate dependence of the instability on viscosity contrast is due to considerable changes in the time-averaged perturbation vorticity distribution near the interface