Swirling against the forcing: Evidence of stable counter-directed sloshing waves in orbital-shaken reservoirs

We investigate the response of the free liquid surface in a partially filled circular cylindrical container undergoing a planar elliptic and time-periodic orbit while maintaining fixed its orientation. For small forcing amplitudes and deep liquid layers, we quantify the effect of the orbit’s aspect ratio on the surface dynamics in the vicinity of the fluid system’s lowest natural frequency. We provide experimental evidence of the existence of a frequency range where stable swirling can be either co- or counter-directed with respect to the container’s direction of motion. Our findings are then rationalized by an inviscid weakly nonlinear model, amended with heuristic damping.

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Caption: Free surface snapshots corresponding to an elliptic harmonic forcing of driving frequency $\Omega/\omega_0=1.04$, driving amplitude $a_x=1.5\,\text{mm}$, and ellipticity $\alpha=a_y/a_x=0.50$. Direction of the container motion: left, anticlockwise; right, clockwise (follow the black arrows). The white arrows indicate the direction of the wave rotation: left, co-swirling ; right, counter-swirling. A visual indication of the different wave amplitudes is provided by the black double-sided arrows. Stable counter-swirling displays a lower wave amplitude.