June  2010, 13(4): 819-840. doi: 10.3934/dcdsb.2010.13.819

Laboratory experiments on wave turbulence

1. 

Laboratoire Matière et Systèmes Complexes (MSC), Université Paris Diderot, CNRS (UMR 7057), 10 rue A. Domon & L. Duquet, 75 013 Paris, France

Received  March 2009 Revised  June 2009 Published  March 2010

This review paper is devoted to a presentation of recent progress in wave turbulence. I first present the context and state of the art of this field of research both experimentally and theoretically. I then focus on the case of wave turbulence on the surface of a fluid, and I discuss the main results obtained by our group: caracterization of the gravity and capillary wave turbulence regimes, the first observation of intermittency in wave turbulence, the occurrence of strong fluctuations of injected power in the fluid, the observation of a pure capillary wave turbulence in low gravity environment and the observation of magnetic wave turbulence on the surface of a ferrofluid. Finally, open questions in wave turbulence are discussed.
Citation: Eric Falcon. Laboratory experiments on wave turbulence. Discrete & Continuous Dynamical Systems - B, 2010, 13 (4) : 819-840. doi: 10.3934/dcdsb.2010.13.819
[1]

Mark Jones. The bifurcation of interfacial capillary-gravity waves under O(2) symmetry. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1183-1204. doi: 10.3934/cpaa.2011.10.1183

[2]

Kristoffer Varholm. Solitary gravity-capillary water waves with point vortices. Discrete & Continuous Dynamical Systems - A, 2016, 36 (7) : 3927-3959. doi: 10.3934/dcds.2016.36.3927

[3]

Frédéric Rousset, Nikolay Tzvetkov. On the transverse instability of one dimensional capillary-gravity waves. Discrete & Continuous Dynamical Systems - B, 2010, 13 (4) : 859-872. doi: 10.3934/dcdsb.2010.13.859

[4]

Shu-Ming Sun. Existence theory of capillary-gravity waves on water of finite depth. Mathematical Control & Related Fields, 2014, 4 (3) : 315-363. doi: 10.3934/mcrf.2014.4.315

[5]

Samuel Walsh. Steady stratified periodic gravity waves with surface tension II: Global bifurcation. Discrete & Continuous Dynamical Systems - A, 2014, 34 (8) : 3287-3315. doi: 10.3934/dcds.2014.34.3287

[6]

Samuel Walsh. Steady stratified periodic gravity waves with surface tension I: Local bifurcation. Discrete & Continuous Dynamical Systems - A, 2014, 34 (8) : 3241-3285. doi: 10.3934/dcds.2014.34.3241

[7]

José Raúl Quintero, Juan Carlos Muñoz Grajales. Solitary waves for an internal wave model. Discrete & Continuous Dynamical Systems - A, 2016, 36 (10) : 5721-5741. doi: 10.3934/dcds.2016051

[8]

Kenta Ohi, Tatsuo Iguchi. A two-phase problem for capillary-gravity waves and the Benjamin-Ono equation. Discrete & Continuous Dynamical Systems - A, 2009, 23 (4) : 1205-1240. doi: 10.3934/dcds.2009.23.1205

[9]

Calin Iulian Martin. A Hamiltonian approach for nonlinear rotational capillary-gravity water waves in stratified flows. Discrete & Continuous Dynamical Systems - A, 2017, 37 (1) : 387-404. doi: 10.3934/dcds.2017016

[10]

Ademir Pastor. On three-wave interaction Schrödinger systems with quadratic nonlinearities: Global well-posedness and standing waves. Communications on Pure & Applied Analysis, 2019, 18 (5) : 2217-2242. doi: 10.3934/cpaa.2019100

[11]

Lili Fan, Hongxia Liu, Huijiang Zhao, Qingyang Zou. Global stability of stationary waves for damped wave equations. Kinetic & Related Models, 2013, 6 (4) : 729-760. doi: 10.3934/krm.2013.6.729

[12]

Vera Mikyoung Hur. On the formation of singularities for surface water waves. Communications on Pure & Applied Analysis, 2012, 11 (4) : 1465-1474. doi: 10.3934/cpaa.2012.11.1465

[13]

Eleftherios Gkioulekas, Ka Kit Tung. Is the subdominant part of the energy spectrum due to downscale energy cascade hidden in quasi-geostrophic turbulence?. Discrete & Continuous Dynamical Systems - B, 2007, 7 (2) : 293-314. doi: 10.3934/dcdsb.2007.7.293

[14]

Martina Chirilus-Bruckner, Guido Schneider. Interaction of oscillatory packets of water waves. Conference Publications, 2015, 2015 (special) : 267-275. doi: 10.3934/proc.2015.0267

[15]

Jeongwhan Choi, Tao Lin, Shu-Ming Sun, Sungim Whang. Supercritical surface waves generated by negative or oscillatory forcing. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1313-1335. doi: 10.3934/dcdsb.2010.14.1313

[16]

Xiao-Biao Lin, Stephen Schecter. Traveling waves and shock waves. Discrete & Continuous Dynamical Systems - A, 2004, 10 (4) : i-ii. doi: 10.3934/dcds.2004.10.4i

[17]

Peter R. Kramer, Joseph A. Biello, Yuri Lvov. Application of weak turbulence theory to FPU model. Conference Publications, 2003, 2003 (Special) : 482-491. doi: 10.3934/proc.2003.2003.482

[18]

José Raúl Quintero, Juan Carlos Muñoz Grajales. On the existence and computation of periodic travelling waves for a 2D water wave model. Communications on Pure & Applied Analysis, 2018, 17 (2) : 557-578. doi: 10.3934/cpaa.2018030

[19]

Feng Xie. Nonlinear stability of combination of viscous contact wave with rarefaction waves for a 1D radiation hydrodynamics model. Discrete & Continuous Dynamical Systems - B, 2012, 17 (3) : 1075-1100. doi: 10.3934/dcdsb.2012.17.1075

[20]

Hiroaki Kikuchi. Remarks on the orbital instability of standing waves for the wave-Schrödinger system in higher dimensions. Communications on Pure & Applied Analysis, 2010, 9 (2) : 351-364. doi: 10.3934/cpaa.2010.9.351

2017 Impact Factor: 0.972

Metrics

  • PDF downloads (8)
  • HTML views (0)
  • Cited by (22)

Other articles
by authors

[Back to Top]