Oscillatory excitation of Faraday waves on the interface of immiscible fluids in a slotted channel

Recent studies of the oscillatory dynamics of the interface between fluids in Hele-Shaw cells have revealed a new type of instability termed the "oscillatory Saffman instability" in the case of fluids with high-viscosity contrast. The present study is dedicated to the experimental investigation of the dynamics of the interface between low-viscosity fluids of different densities oscillating in a vertical narrow channel. It is discovered that as the amplitude of oscillations increases, a threshold excitation of parametric oscillations of the interface in the form of a standing wave is observed in the plane of the fluid layer. This phenomenon bears a resemblance to Faraday waves, but the dependence of the standing wave wavelength on the oscillation frequency does not align with the classical dispersion relation for low-viscosity fluids. The damping effect of viscous boundary layers near the cell walls and the out-of-plane curvature of the oscillating interface leads to a decrease in the natural frequency of oscillations. The experiments demonstrate a significant role of the dimensionless layer thickness. With its decrease (increase in the dimensionless out-of-plane interface curvature), the threshold oscillation acceleration rises in accordance with a power law. To the best of the authors' knowledge, this type of instability has been discovered and studied for the first time. Another important finding is the excitation of intense time-averaged vortical flows in the channel plane within the supercritical region. The physical mechanism underlying the excitation of the time-averaged vortices is clarified, and the dimensionless parameters that govern their intensity are identified.