Ground Experiments in the Fluids Lab: Surface Waves
Most experiments in the lab are performed using open containers of DC200 silicone oil or water. The container can be vibrated horizontally, vertically, or with any combination of the two, and at frequencies up to 100 Hz or more. Measurements of the surface wave patterns are obtained using a free surface synthetic Schlieren technique (Moisy et al. Exp. Fluids 46, 1021-1036, 2009).
Asymmetric surface wave pattern with combined horizontal and vertical forcing at 50Hz
One basic experimental observation is the preference for obliquely oriented (rotated) cross-wave patterns with horizontally forcing . The angle of these patterns depends somewhat on boundary conditions and other experimental parameters, but seems to be a very general and robust characteristic of subharmonic waves in large-aspect-ratio systems driven by moderate to high frequencies like those used here (30-100 Hz). Another interesting result with horizontally forced systems is the appearance of modulated (quasiperiodic) solutions  related to the interaction of the waves emanating from each endwall, which have a π/2 phase shift. The slowly modulated solutions alternate between one-sided and two-sided patterns and are very sensitive to the strength of the interaction (length of container, damping, detuning). With combined horizontal and vertical forcing, a variety of interesting new patterns and modulated solutions can be obtained and controlled with the forcing parameters.
An essential feature of any applicable theory in this regime is the distributed parametric forcing mechanism concentrated near each endwall. Previous cross-wave theory considered this mechanism to be sufficiently localized to be treated simply as a boundary condition on the slow spatial scale characteristic of streamwise variation. Without this assumption we obtain a nonlinear Schrodinger equation with spatially distributed forcing that is in reasonably good agreement with experimentally measured thresholds . Other interesting features arising from the presence of distributed forcing include families of “cross-wave” modes (modulated or not) with the same crosswise mode number but separated by the number of oscillations experienced within the (supercritical) forced region and, when interaction is strong, additional branches of modulated solutions with distinct frequencies . Much of the phenomenology can be understood in the context of simplified models that include essential features (like distributed forcing) and in terms of symmetry-breaking.
In addition, a horizontally vibrated container of fluid with sufficiently localized wave fields at each endwall (wavemaker) can be considered as an example of weakly coupled parametrically forced oscillators . In the relevant case of two antisymmetrically forced oscillators, the primary instability is a Hopf bifurcation producing modulated solutions, like those observed in experiments . Furthermore, the destruction of these modulated states via a saddle-node heteroclinic bifurcation in the model is consistent with numerical simulations of the Navier-Stokes equations.
To understand how the various surface wave instabilities investigated in the laboratory are altered in microgravity, extensive numerical simulations are done. These have revealed that the surface wave dynamics may affect the average surface shape (vibroequilibria) despite the apparent difference in timescales. Coupling is particularly strong when slowly modulated subharmonic surface waves are present, as these tend to drive an odd sloshing mode that can, in some cases, reach sufficient amplitude to completely destroy the underlying vibroequilibria state .
Control of Fluids in Microgravity with Vibrations (CFVib)
Microgravity experiments have recently been conducted as part of the 2016 Fly you Thesis! programme sponsored by the ESA Education Office . These experiments were designed to test numerical and theoretical results related to vibroequilibria. The experimental set-up was organized around 12 containers (6 cuboids and 6 cylinders) having different liquid-air and liquid-liquid mixtures. Half were subjected to vibrations using a piezoelectric bender beam assembly (excited samples) while the other half (reference samples) were left to respond to the ambient inertial forces (g-jitter).
The main scientific objectives of the CFVib experiment are:
- Determine the feasibility of managing fluids using small amplitude vibrations in microgravity.
- Investigate the vibroequilibria effect in microgravity using different representative fluid configurations and forcing frequencies, including both hydrodynamic and acoustic regimes.
The experiment flew successfully in the 65th ESA Parabolic Flight campaign. In addition to providing very valuable experience in the design, construction and execution of a microgravity experiment, and an unforgettable experience for the participants, a large amount of promising accelerometer and video data was collected.
Snapshot of the first parabolic flight.
Initial results indicate good qualitative agreement between experiment observations and the predictions of vibroequilibria theory and simulations. The expected dependence on the applied voltage to the piezoelectric device is observed in the videos. We expect this microgravity data to be very useful in the continued development and testing of theoretical models, and hope to continue with extensions of this microgravity research — perhaps in upcoming parabolic flight campaigns or aboard the ISS.