2007 The influence of viscosity on the frozen wave instability: 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 × 102N1 = 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 & Cherepanov (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 exten