Skip to Main Content

Access Provided by Xinjiang University

Physical Review E

Access by Xinjiang University

Generation of intermittent gravitocapillary waves via parametric forcing

Gustavo Castillo^*

Claudio Falcón

Instituto de Ciencias de la Ingeniería, Universidad de O'Higgins, Av. Libertador Bernardo O'Higgins 611, Rancagua, Chile

Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Avenida Blanco Encalada 2008, Santiago, Chile

^*gustavo.castillo@uoh.cl

Phys. Rev. E 97, 043101 – Published 3 April, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.043101

Abstract

We report on the generation of an intermittent wave field driven by a horizontally moving wave maker interacting with Faraday waves. The spectrum of the local gravitocapillary surface wave fluctuations displays a power law in frequency for a wide range of forcing parameters. We compute the probability density function of the local surface height increments, which show that they change strongly across time scales. The structure functions of these increments are shown to display power laws as a function of the time lag, with exponents that are nonlinear functions of the order of the structure function. We argue that the origin of this scale-invariant intermittent spectrum is the Faraday wave pattern breakup due to its advection by the propagating gravity waves. Finally, some interpretations are proposed to explain the appearance of this intermittent spectrum.

Physics Subject Headings (PhySH)

Article Text

References (46)

V. E. Zakharov, V. S. L'vov, and G. Falkovich, Kolmogorov Spectra of Turbulence I, Wave Turbulence, Springer Series in Nonlinear Dynamics (Springer, Berlin, 1992); S. Nazarenko, Wave Turbulence, Lecture Notes in Physics (Springer, Berlin, 2011); A. C. Newell and B. Rumpf, Annu. Rev. Fluid Mech. 43, 59 (2011).
K. Hasselmann, J. Fluid Mech. 12, 481 (1962); 15, 273 (1963).
M. Onorato, A. R. Osborne, M. Serio, D. Resio, A. Pushkarev, V. E. Zakharov, and C. Brandini, Phys. Rev. Lett. 89, 144501 (2002); A. Pushkarev, D. Resio, and V. Zakharov, Physica (Amsterdam) D 184, 29 (2003); A. I. Dyachenko, A. O. Korotkevich, and V. E. Zakharov, Phys. Rev. Lett. 92, 134501 (2004).
Y. Toba, J. Oceanogr. Soc. Jpn. 29, 209 (1973); K. K. Kahma, J. Phys. Oceanogr. 11, 1503 (1981).
E. Falcon, C. Laroche, and S. Fauve, Phys. Rev. Lett. 98, 094503 (2007).
V. E. Zakharov and N. N. Filonenko, J. Appl. Mech. Tech. Phys. 8, 37 (1967).
A. N. Pushkarev and V. E. Zakharov, Phys. Rev. Lett. 76, 3320 (1996); L. Deike, D. Fuster, M. Berhanu, and E. Falcon, ibid. 112, 234501 (2014).
W. B. Wright, R. Budakian, and S. J. Putterman, Phys. Rev. Lett. 76, 4528 (1996); M. Lommer and M. T. Levinsen, J. Fluoresc. 12, 45 (2002); E. Henry, P. Alstrøm, and M. T. Levinsen, Europhys. Lett. 52, 27 (2000); C. Falcon, E. Falcon, U. Bortolozzo, and S. Fauve, ibid. 86, 14002 (2009).
G. Düring, C. Josserand, and S. Rica, Phys. Rev. Lett. 97, 025503 (2006).
N. Mordant, Phys. Rev. Lett. 100, 234505 (2008); A. Boudaoud, O. Cadot, B. Odille, and C. Touzé, ibid. 100, 234504 (2008).
S. Dyachenko, A. Newell, A. Pushkarev, and V. Zakharov, Physica D 57, 96 (1992); C. Connaughton et al., Phys. Rev. Lett. 95, 263901 (2005).
U. Bortolozzo, J. Laurie, S. Nazarenko, and S. Residori, J. Opt. Soc. Am B 26, 2280 (2009).
L. Biven, S. V. Nazarenko, and A. C. Newell, Phys. Lett. A 280, 28 (2001).
G. Düring, A. Picozzi, and S. Rica, Physica D 238, 1524 (2009).
O. M. Phillips, J. Fluid Mech. 4, 426 (1958).
H. Mitsuyasu and T. Honda, J. Oceanogr. Soc. Jpn. 30, 185 (1974).
L. Romero, W. K. Melville, and J. M. Kleiss, J. Phys. Oceanogr. 42, 1421 (2012).
S. Nazarenko, S. Lukaschuk, S. McLelland, and P. Denissenko, J. Fluid Mech. 642, 395 (2010).
A. C. Newell and V. E. Zakharov, Phys. Lett. A 372, 4230 (2008).
A. C. Newell and V. E. Zakharov, Phys. Rev. Lett. 69, 1149 (1992).
B. Miquel, A. Alexakis, C. Josserand, and N. Mordant, Phys. Rev. Lett. 111, 054302(R) (2013); S. Chibaro and C. Josserand, Phys. Rev. E 94, 011101(R) (2013).
E. A. Kuznetsov, JETP Lett. 80, 83 (2004).
J. Laurie, V. S. L'vov, S. Nazarenko, and O. Rudenko, Phys. Rev. B 81, 104526 (2010).
V. S. L'vov and S. Nazarenko, JETP (Pis'ma Zh. Eksp. Teor. Fiz.) 91, 464 (2010).
A. M. Balk, S. V. Nazarenko, and V. E. Zakharov, Phys. Lett. A 146, 217 (1990).
S. V. Nazarenko, Pis'ma Zh. Eksp. Teor. Fiz. 53, 604 (1991).
C. Connaughton, S. Nazarenko, and B. Quinn, Europhys. Lett. 96, 25001 (2011).
Y. Mehtar-Tani, Nucl. Phys. A 966, 241 (2017).
M. Faraday, Philos. Trans. R. Soc. London 121, 299 (1831).
L. Gordillo et al., Eur. Phys. J. D 62, 39 (2011).
C. L. Goodridge, H. G. E. Hentschel, and D. P. Lathrop, Phys. Rev. Lett. 82, 3062 (1999).
C. Falcón and S. Fauve, Int. J. Bifurcat. Chaos 19, 3553 (2009).
V. E. Zakharov et al., JETP 82, 487 (2005).
Y. V. Lvov, S. Nazarenko, and B. Pokorni, Physica D 218, 24 (2006).
S. Nazarenko, J. Stat. Mech. (2006) L02002.
P. Denissenko, S. Lukaschuk, and S. Nazarenko, Phys. Rev. Lett. 99, 014501 (2007).
L. Deike, M. Berhanu, and E. Falcon, Phys. Rev. E 85, 066311 (2012).
L. Deike, J.-C. Bacri, and E. Falcon, J. Fluid Mech. 733, 394 (2013).
L. Deike et al., J. Fluid Mech. 781, 196 (2015).
A. Chaigne and C. Lambourg, JASA 109, 1422 (2001).
B. Miquel and N. Mordant, Phys. Rev. Lett. 107, 034501 (2011).
T. Humbert et al., Europhys. Lett. 102, 30002 (2013).
L. Deike, M. Berhanu, and E. Falcon, Phys. Rev. E 89, 023003 (2014).
B. Miquel, A. Alexakis, and N. Mordant, Phys. Rev. E 89, 062925 (2014).
J. Laurie, U. Bortolozzo, S. Nazarenko, and S. Residori, Phys. Rep. 514, 121 (2012).
E. Falcon, S. G. Roux, and B. Audit, Europhys. Lett. 90, 50007 (2010).