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Statistics of surface gravity wave turbulence in the space and time domains

Published online by Cambridge University Press:  09 December 2009

SERGEY NAZARENKO ,
SERGEI LUKASCHUK ,
STUART McLELLAND  and
PETR DENISSENKO
SERGEY NAZARENKO
Affiliation:
Mathematics Institute, Warwick University, Coventry CV4 7AL, UK
SERGEI LUKASCHUK*
Affiliation:
Department of Engineering, Hull University, Hull HU6 7RX, UK
STUART McLELLAND
Affiliation:
Department of Geography, Hull University, Hull HU6 7RX, UK
PETR DENISSENKO
Affiliation:
School of Engineering, Warwick University, Coventry CV4 7AL, UK
*
†Email address for correspondence: [email protected]
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Abstract

We present experimental results on simultaneous space–time measurements for the gravity wave turbulence in a large laboratory flume. We compare these results with predictions of the weak turbulence theory (WTT) based on random waves, as well as with predictions based on the coherent singular wave crests. We see that the both wavenumber and frequency spectra are not universal and dependent on the wave strength, with some evidence in favour of the WTT at larger wave intensities when the finite-flume effects are minimal. We present further theoretical analysis of the role of the random and coherent waves in the wave probability density function (p.d.f.) and the structure functions (SFs). Analysing our experimental data we found that the random waves and the coherent structures/breaks coexist: the former show themselves in a quasi-Gaussian p.d.f. core and the low-order SFs and the latter in the p.d.f. tails and the high-order SFs. It appears that the x-space signal is more intermittent than the t-space signal, and the x-space SFs capture more singular coherent structures than the t-space SFs do. We outline an approach treating the interactions of these random and coherent components as a turbulence cycle characterized by the turbulence fluxes in both the wavenumber and the amplitude spaces.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Wave breaking
Type
Papers
Information
Journal of Fluid Mechanics , Volume 642 , 10 January 2010 , pp. 395 - 420
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Belcher, S. E. & Vassilicos, J. C. 1997 Breaking waves and the equilibrium range of wind-wave spectra. J. Fluid Mech. 342, 377–401.CrossRefGoogle Scholar
Choi, Y., Lvov, Y., Nazarenko, S. & Pokorni, B. 2005 Anomalous probability of large amplitudes in wave turbulence. Phys. Lett. A 339, 361–369.CrossRefGoogle Scholar
Connaughton, C., Nazarenko, S. & Newell, A. C. 2003 Dimensional analysis and weak turbulence. Physica D 184, 86–97.CrossRefGoogle Scholar
Cooker, M. J. & Peregrine, D. H. 1991 Violent water motion at breaking-wave impact. In Proceedings of the 22nd International Conference on Coastal Engineering (ICCE22, Delft, The Netherlands, July '90) (ed. Banner, M. L. & Grimshaw, R. H. J.), vol. 1, pp. 164–176. Springer.Google Scholar
Denissenko, P., Lukaschuk, S. & Nazarenko, S. 2007 Gravity wave turbulence in a laboratory flume. Phys. Rev. Lett. 99, 014501.CrossRefGoogle Scholar
Dyachenko, S., Newell, A. C., Pushkarev, A. & Zakharov, V. E. 1992 Optical turbulence: weak turbulence, condensates and collapsing filaments in the nonlinear Schrödinger equation. Physica D 57, 96–160.CrossRefGoogle Scholar
Falcon, E., Laroche, C. & Fauve, S. 2007 Observation of gravity–capillary wave turbulence. Phys. Rev. Lett. 98, 094503.CrossRefGoogle ScholarPubMed
Hasselman, K. 1962 Anomalous probability of large amplitudes in wave turbulence. J. Fluid Mech. 12, 481.Google Scholar
Janssen, P. A. E. M. 2004 The Interaction of Ocean Waves and Wind. Cambridge University Press.CrossRefGoogle Scholar
Kadomtsev, B. B. 1965 Plasma Turbulence. Academic.Google Scholar
Kartashova, E. A. 1991 On properties of weakly nonlinear wave interactions in resonators. Physica D 54, 125–134.CrossRefGoogle Scholar
Kartashova, E. A. 1998 Wave resonances in systems with discrete spectra. Nonlinear Waves and Weak Turbulence – Advances in the Mathematical Sciences (ed. by Zakharov, V. E.), pp. 95–129. Am. Math. Soc.CrossRefGoogle Scholar
Kitaigorodskii, S. A. 1962 Application of the theory of similarity to the analysis of wind-generated wave motion as a stochastic process. Bull. Acad. Sci. USSR Ser. Geophys. 1, 105–117.Google Scholar
Krasitskii, V. P. 1994 On reduced equations in the hamiltonian theory of weakly nonlinear surface-waves. J. Fluid Mech. 272, 1–20.CrossRefGoogle Scholar
Kudryavtsev, V., Hauser, D., Caudal, G. & Chapron, G. 2003 A semiempirical model of the normalized radar cross-section of the sea surface. J. Geophys. Res 108 (C3), 8054.Google Scholar
Kuznetsov, E. A. 2004 Turbulence spectra generated by singularities. JETP Lett. 80, 83–89.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1993 Highly accelerated, free-surface flows. J. Fluid Mech 248, 449–475.CrossRefGoogle Scholar
Mukto, M. A., Atmane, M. A. & Loewen, M. R. 2007 A particle-image based wave profile measurement technique. Exp. Fluids 42, 131–142.CrossRefGoogle Scholar
Nazarenko, S. V. 2006 Sandpile behaviour in discrete water-wave turbulence. J. Stat. Mech., 2, 11–18, L02002.Google Scholar
Newell, A. C., Nazarenko, S. & Biven, L. 2001 Wave turbulence and intermittency. Physica D 152–53, 520–550.CrossRefGoogle Scholar
Newell, A. C. & Zakharov, V. E. 2008 The role of the generalized Phillips' spectrum in wave turbulence. Phys. Lett. A 372, 4230–4233.CrossRefGoogle Scholar
Onorato, M., Cavaleri, L., Fouques, S., Gramstad, O., Janssen, P. A. E. M., Monmaliu, J., Osborne, A. R., Pakozdi, C., Serio, M., Stansberg, C. T., Toeffoli, A. & Trulsen, K. 2009 Statistical properties of mechanically generated surface gravity waves: a laboratory experiment in a three-dimensional wave basin. J. Fluid Mech. 627, 235–257.CrossRefGoogle Scholar
Onorato, M., Osborne, A., Serio, M., Cavaleri, L., Brandini, C. & Stansberg, C. T. 2006b Extreme waves, modulational instability and second order theory: wave flume experiments on irregular waves. Eur. J. Mech. B 25, 586–601.CrossRefGoogle Scholar
Pelinovsky, E. & Kharif, C. 2009 Extreme Ocean Waves. Springer.Google Scholar
Phillips, O. M. 1958 The equilibrium range in the spectrum of wind generated waves. J. Fluid Mech. 4, 426–434.CrossRefGoogle Scholar
Socquet-Juglard, H., Dysthe, K., Trulsen, K., Krogstad, H. E. & Liu, J. 2005 Distribution of surface gravity waves during spectral changes. J. Fluid Mech. 542, 195–216.CrossRefGoogle Scholar
Tayfun, M. A. 1980 Distribution of surface gravity waves during spectral changes. J. Geophys. Res. 85 (C3), 1548–1552.CrossRefGoogle Scholar
Tayfun, M. A. & Fedele, F. 2007 Wave-height distributions and nonlinear effects. Ocean Engng 34, 1631–1649.CrossRefGoogle Scholar
Toba, Y. 1973 Local balance in the air-sea boundary process. J. Oceanogr. Soc. Jpn 29, 209–220.CrossRefGoogle Scholar
Zakharov, V. E. & Filonenko, N. N. 1967 Weak turbulence of capillary waves. J. Appl. Mech. Tech. Phys. 4, 506–515.Google Scholar
Zakharov, V. E., Lvov, V. S. & Falkovich, G. G. 1992 Kolmogorov Spectra of Turbulence. Springer.CrossRefGoogle Scholar