ABSTRACT
We consider the oscillatory flow between time-periodically corotating cylinders, in the case of a two-frequency forcing. The angular velocity Omega(t) of the cylinders is the sum of a low-frequency omega(1) oscillation plus a harmonic frequency omega(2) oscillation at a lower amplitude, Omega(t)=Omega(1) cos(omega(1)t)+Omega(2) cos(omega(2)t). The temporal behavior of the secondary flow is characterized by ultrasound Doppler velocimetry. For a single-frequency forcing at omega(1), above a critical amplitude Omega(1), within one cycle, the secondary flow measurements exhibit a spikelike behavior with several successive growths, dampings, and periods of quietness. The effect of the superimposed omega(2) frequency is the following, although if alone it would be stable: to sharpen the spikes, restabilizing the flow for some intervals that exhibit secondary flow for the single forcing at omega(1); and to induce further secondary flow spikes during what is a quiescent stage in the single omega(1) frequency forcing case. Numerical calculations for the finite-gap quasisteady linear stability analysis are presented and provide a good prediction of the times of growth and damping of the secondary flow observed experimentally during a flow period.
ABSTRACT
We report experimental results for the Kelvin-Helmholtz instability between two immiscible fluids in parallel flow in a Hele-Shaw cell. We focus our interest on the influence of the gap size between the walls on the instability characteristics. Experimental results show that the instability threshold, the critical wavelength, the phase velocity, and the spatial growth rate depend on this gap size. These results are compared to both the previous two-dimensional analysis of Gondret and Rabaud [Phys. Fluids 9, 3267 (1997)] and the three-dimensional analysis recently derived by Plouraboué and Hinch [Phys. Fluids (to be published)], showing that the agreement is still not complete especially when gap size increases.
