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HGWW (High-Gravity Water Waves) Probing Wave Turbulence at High Gravity

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What might look like jelly being stirred is actually water subjected to 20 times normal Earth gravity within ESA's LDC (Large Diameter Centrifuge) at ESTEC – as part of an experiment giving new insight into the behavior of wave turbulence. 1)

Figure 1: A wave experiment in a centrifuge reveals how the size of the fluid container strongly influences turbulent behavior (image credit: ESA, High-gravity Research Team)

Wave turbulence occurs anywhere where a set of random waves interact with each other – from the ocean to the atmosphere, or in plasmas – but the exact mechanisms behind it are only dimly understood. For surface waves on a liquid, gravity dominates the behavior at low frequencies, while ‘capillary action' based on surface tension becomes more important at high frequencies.

To increase the range of frequencies where waves are dominated by gravity, the researchers conducted their experiment in the ESA's LDC (Large Diameter Centrifuge) where they can create effective gravity levels up to 20 times that of Earth's gravity.

Within this extended range, the result was a surprise: the typical timescales of wave interactions and dissipation did not depend of the wave frequency, as predicted theoretically.

Instead these timescales are set by the longest available wavelength within the system – namely the size of the container the waves occur within, an effect that current wave turbulence theories does not take into account.

Prof. Falcon explains: "This result suggests that ‘container' size needs to be considered in studies of water waves within an ocean—as well as atmospheric waves on Earth and magnetically confined plasma waves as in fusion experiments.

"Notably, this experiment serves to complete the scientific picture of how gravity has an impact on surface wave turbulence, because tuning the gravity level to an opposing low value has already been performed in experiments in zero-G parabolic flights in 2009 and more recently aboard the International Space Station in 2019. This has allowed us to successfully observe pure capillary wave turbulence with no contribution from gravity."

Operating within a sci-fi style white dome, the LDC is an 8-m diameter four-arm centrifuge that gives researchers access to a range of hypergravity up to 20 times Earth gravity for weeks or months at a time. At its fastest, the centrifuge rotates at up to 67 revolutions per minute, with its six gondolas placed at different points along its arms weighing in at 130 kg, and each capable of accommodating 80 kg of payload.

The LDC was made available for this experiment through the Continuously Open Research Announcement of the SciSpace Program, supported by ESA's Directorate of Human and Robotic Exploration.

 


 

This research, led by Stéphane Dorbolo of University of Liège and Eric Falcon of CNRS and University of Paris, has been published in the prestigious Physical Review Letters. 2)

The research team reports on the observation of gravity-capillary wave turbulence on the surface of a fluid in a high-gravity environment. By using a large-diameter centrifuge, the effective gravity acceleration is tuned up to 20 times Earth's gravity. The transition frequency between the gravity and capillary regimes is thus increased up to one decade as predicted theoretically. A frequency power-law wave spectrum is observed in each regime and is found to be independent of the gravity level and of the wave steepness. While the timescale separation required by weak turbulence is well verified experimentally regardless of the gravity level, the nonlinear and dissipation timescales are found to be independent of the scale, as a result of the finite size effects of the system (large-scale container modes) that are not taken currently into account theoretically.

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Figure 2: Experimental setup. Top: schema of the large diameter centrifuge showing the generation of an apparent gravity normal to the fluid surface. Bottom: experimental setup inside the gondola (image credit: High-gravity Research Team)

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Figure 3: PSD (Power Spectrum Density) of the wave height η (t) for 1 g and 19.4 g. Dashed lines display best power law fits for (blue) gravity and (red) capillary regimes (image credit: High-gravity Research Team)

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Figure 4: Transition frequency fgc between gravity and capillary wave turbulence regimes versus g*. Vibration amplitude: σΑ = 3.7 (open circles) and 15.5 mm (solid diamonds). Solid line is the prediction of Eq. (1), image credit: High-gravity Research Team

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Figure 5: Temporal decay of the wave spectrum S (f,t) for 15 g (image credit: High-gravity Research Team)

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Figure 6: Wave turbulence timescale separation for g*=15 g. Solid line: linear timescale τ lin = 1/f (image credit: High-gravity Research Team)

 

Synopsis: Probing Wave Turbulence at High Gravity 3)

Wave turbulence pops up wherever large numbers of waves bump into each other and interact, like in the ocean. But even though the phenomenon is ubiquitous, our understanding of it is incomplete. In a new centrifuge-based experiment, a team led by Eric Falcon of CNRS and Paris Diderot University cranked up the "gravity" acting on a basin of water to about 20 times that of Earth's, allowing them to study gravity-dominated wave turbulence in a regime that previous experiments have been unable to reach. They found that the turbulent wave behavior was dependent on the size of the fluid's container—a factor that current wave-turbulence theories usually don't take into account.

For surface waves on a liquid, gravity dominates the behavior at low frequencies, while capillary action is more important at high frequencies. In Earth's gravity, the transition between these regimes occurs at around 13 Hz, which means lab experiments typically have a limited range (from about 1 to 13 Hz) for studying gravity-dominated waves. But by increasing the effective gravitational acceleration, Falcon and colleagues were able to investigate gravity-dominated waves up to frequencies of 130 Hz.

At the European Space Agency's Large-Diameter Centrifuge in the Netherlands, the team used a wavemaker to create turbulent waves in their water basin. From the recorded wave spectrum, they found that—contrary to what theory predicted—the timescales of wave interactions and of dissipation didn't depend on wave frequency. Instead, this turbulent wave behavior was dictated by the longest available wavelength mode, whose frequency is set by the diameter of the basin. The findings suggest that "container" size needs to be considered in studies of water waves in an ocean—as well as atmospheric waves on Earth and plasma waves in magnetic confinement fusion experiments.

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Figure 7: A wave experiment in a centrifuge reveals how the size of the fluid container strongly influences turbulent behavior (image credit: ESA, A. Le Floc'h)



1) "High-gravity water waves," ESA / Enabling & Support, 15 January 2020, URL: http://www.esa.int/ESA_Multimedia/Images/2020/01/High-gravity_water_waves

2) A. Cazaubiel, S. Mawet, A. Darras, G. Grosjean, J. J. W. A. van Loon, S. Dorbolo, and E. Falcon, "Wave Turbulence on the Surface of a Fluid in a High-Gravity Environment," Physical Review Letters, Volume 123, Issue 244501, Published: 10 December 2019, https://doi.org/10.1103/PhysRevLett.123.244501

3) Erika K. Carlson, "Synopsis: Probing Wave Turbulence at High Gravity," Physics, 10 December 2019, URL: https://physics.aps.org/synopsis-for/10.1103/PhysRevLett.123.244501
 


The information compiled and edited in this article was provided by Herbert J. Kramer from his documentation of: "Observation of the Earth and Its Environment: Survey of Missions and Sensors" (Springer Verlag) as well as many other sources after the publication of the 4th edition in 2002. - Comments and corrections to this article are always welcome for further updates (herb.kramer@gmx.net).

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