Observations of low-frequency surface waves in a vertically oscillating elastic container
Date/Time: 16:00 07-Aug-2014
An initial goal of our experiment was to study mechanisms of the inverse cascade in surface wave turbulence using a well-controlled laboratory set-up with energy pumping scale in gravitational range. For this we used an open rectangular cell with the horizontal sizes 42 x 42 cm and the height 30 cm. The cell was filled with water to a depth 15-20 cm and the surface waves were generated parametrically by vertical vibrations of the whole cell. We checked all possible range of vibration frequencies corresponding to the parametric wave wavelengths from 2 to 10 cm and used different types of excitation with single or multi frequencies, but we did not observe any waves with the frequency below than the lowest parametrically forced mode has. Nevertheless, when we move to the higher frequencies corresponding to the parametric waves in capillary range, we found a narrow excitation frequency interval around 82 Hz, where the low frequency modes of large amplitudes appeared as a result of the single frequency excitation. The frequencies of these stationary waves are 2.3 and 2.7 Hz and their $k$-vectors are oriented along the diagonals and the side walls of the cell correspondingly. Our further studies showed that these low frequency waves are coupled with bending oscillations of the cell side walls which resonate at the frequency about 82 Hz. The amplitude of bending side walls vibrations in the open cell is minimum (zero) at the cell bottom and corners were the walls are fixed and is maximum at the middle and the top of the side wall. The forcing is provided by the oscillating hydrostatic pressure. Above some critical vibration amplitude, in addition to Faraday waves, the oscillating walls produce the cross waves at a half excitation frequency with the wave vector parallel to the wall. Further increase of the vertical vibration amplitude leads to a significant growth of the cross wave amplitude. And finally, after the amplitude of cell vibrations exceeds the next threshold the slow modes arise.
We characterized the observed wave configurations using a profilometry technique allowing us to measure time evolutions of the 2D surface wave elevations $\eta(x,y,t)$. We show that the slow mode appears as the result of an instability and present $k$- and $\omega$-spectra for the stationary wave field regimes. We draw a parallel between our observations and the ?dragon wash? phenomenon and discuss possible mechanisms responsible for the low frequency mode instability.
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