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Published on: February 13, 2018
Nonlinear dynamics of flexural wave turbulence
Benjamin Miquel1, Nicolas Mordant
1Laboratoire de Physique Statistique, Ecole Normale Supérieure, Université Pierre et Marie Curie, CNRS, 24 rue Lhomond, F-75005 Paris, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 7, 2012
Summary
Direct measurements reveal that the Kolmogorov-Zakharov spectrum is not observed in flexural wave turbulence due to finite size effects. A crossover from continuous to discrete turbulence alters the energy cascade.
Area of Science:
- Fluid Dynamics and Wave Phenomena
- Condensed Matter Physics
- Nonlinear Dynamics
Background:
- Weak turbulence theory predicts a Kolmogorov-Zakharov spectrum for energy transfer in wave turbulence.
- This spectrum has been elusive in experimental studies of flexural waves on thin elastic plates.
- Understanding energy transfer mechanisms in such systems is crucial for various physical applications.
Purpose of the Study:
- To directly measure the nonlinear time scale (T(NL)) in flexural wave turbulence.
- To investigate the validity of the time scale separation hypothesis (T(d) >> T(NL) >> T) in this system.
- To identify the reasons for the discrepancy between theoretical predictions and experimental observations.
Main Methods:
- Space-time measurements of plate deformation were conducted.
- Wavelet coefficients of the turbulent field were analyzed to extract the nonlinear time scale.
- Comparison of experimental results with weak turbulence theory, considering finite size effects.
Main Results:
- The time scale separation hypothesis was confirmed to be valid for the studied system.
- Discrete modes, arising from finite size effects, were identified as a key factor for theoretical deviations.
- A crossover from continuous weak turbulence to discrete turbulence was observed when T(NL) approached the frequency separation of discrete modes.
Conclusions:
- Finite size effects and discrete modes significantly alter the expected Kolmogorov-Zakharov energy cascade in flexural wave turbulence.
- The energy cascade is modified and effectively 'frozen' before reaching the dissipative regime due to these effects.
- This study highlights the importance of considering discrete effects in wave turbulence phenomena on finite systems.
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