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Measurements of Waves in a Wind-wave Tank Under Steady and Time-varying Wind Forcing

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Space-time resolved wave turbulence in a vibrating plate.

Pablo Cobelli¹, Philippe Petitjeans, Agnès Maurel

¹Physique et Mécanique des Milieux Hétérogènes, ESPCI & CNRS, 10 rue Vauquelin, 75005 Paris, France.

Physical Review Letters

|April 7, 2010

Summary

This study experimentally investigates wave turbulence in thin elastic plates. Researchers found that energy concentrates on a nonlinear dispersion relation, validating common experimental methods and revealing weak nonlinear effects.

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Area of Science:

Physics
Fluid Dynamics
Nonlinear Dynamics

Background:

Wave turbulence is a complex phenomenon observed in nonlinear systems.
Experimental investigation of wave turbulence in elastic plates is crucial for understanding energy dissipation and transfer.
Previous studies often rely on approximations for wave-vector-frequency relationships.

Purpose of the Study:

To experimentally investigate wave turbulence in a thin elastic plate.
To measure the space-time deformation field and compute its Fourier spectrum.
To analyze the energy distribution in the wave-vector-frequency space and its relation to dispersion.

Main Methods:

Utilized Fourier transform profilometry for simultaneous space-time measurement of plate surface deformation.
Computed the full space-time deformation velocity's wave-vector-frequency (k, omega) Fourier spectrum.
Analyzed the energy concentration in the 3D (k, omega) space.

Main Results:

Observed energy concentration on a 2D surface representing a nonlinear dispersion relation in (k, omega) space.
The nonlinear dispersion relation closely approximates the linear dispersion relation.
Deviations from linear dispersion increase with input forcing power, attributed to weak nonlinear effects.

Conclusions:

The experimental technique validates the use of wave-number-frequency transformations in wave turbulence studies.
Weak nonlinear effects are responsible for the observed deviations from linear dispersion.
The developed method enables extensive quantitative comparisons between wave turbulence theory and experiments.