Abstract
The modulational instability of nonlinearly interacting spatially incoherent Stokes waves is analyzed. Starting from a pair of nonlinear Schrödinger equations, we derive a coupled set of wave-kinetic equations by using the Wigner transform technique. It is shown that the partial coherence of the interacting waves induces novel effects on the dynamics of crossing sea states.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. Smith, J. Fluid Mech. 77, 417 (1976).
R. G. Dean, Water Wave Kinetics, Ed. by A. Torum and O. T. Gudmestad (Kluwer, Dordrecht, 1990), p. 609.
C. Kharif and E. Pelinovsky, Eur. J. Mech. B 22, 603 (2003).
B. V. Divinsky, B. V. Levin, L. I. Lopatikhin, et al., Dokl. Earth Sci. 395, 438 (2004).
K. B. Dysthe, Proc. R. Soc. London, Ser. A 369, 105 (1979); K. Trulsen and K. B. Dysthe, Wave Motion 24, 281 (1996).
M. Onorato, A. R. Osborne, M. Serio, and S. Bertone, Phys. Rev. Lett. 86, 5831 (2001).
A. A. Kurkin and E. N. Pelinovsky, Freak Waves: Facts, Theory and Modeling (Nizhegor. Gos. Univ., Nizhni Novgorod, 2004) [in Russian].
A. I. Dyachenko and V. E. Zakharov, JETP Lett. 81, 255 (2005).
J. L. Hammack, D. M. Henderson, and H. Segur, J. Fluid Mech. 532, 1 (2005).
V. E. Zakharov, J. Appl. Mech. Tech. Phys. 9, 190 (1968).
F. Fedele, J. Offshore Mech. Arctic Eng. 128, 11 (2006).
T. B. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).
E. R. Tracy and H. H. Chen, Phys. Rev. A 37, 815 (1988).
V. E. Zakharov, F. Dias, and A. N. Pushkarev, Phys. Rep. 398, 1 (2004).
D. R. Crawford, P. G. Saffman, and H. C. Yuen, Wave Motion 2, 1 (1980).
K. B. Dysthe, K. Trulsen, H. E. Krogstad, and H. Socquet-Juglard, J. Fluid Mech. 478, 1 (2003).
M. Onorato, A. R. Osborne, and M. Serio, Phys. Rev. Lett. 96, 014503 (2006).
H. C. Yuen and B. M. Lake, Adv. Appl. Mech. 22, 67 (1982).
E. P. Wigner, Phys. Rev. 40, 749 (1932).
J. E. Moyal, Proc. Cambridge Philos. Soc. 45, 99 (1949).
I. E. Alber, Proc. R. Soc. London, Ser. A 363, 525 (1978).
R. Fedele and D. Anderson, J. Opt. B: Quantum Semiclassic. Opt. 2, 207 (2000).
R. Fedele, D. Anderson, and M. Lisak, Phys. Scr. T 84, 27 (2000).
J. T. Mendonça, Theory of Photon Acceleration (Inst. of Physics, Bristol, 2001).
M. Onorato, A. R. Osborne, R. Fedele, and M. Serio, Phys. Rev. E 67, 046305 (2003).
Yu. L. Klimontovich, The Statistical Theory of Non-Equilibrium Processes in a Plasma (Mosk. Gos. Univ., Moscow, 1964; Pergamon, Oxford, 1967).
R. Loudon, The Quantum Theory of Light, 3rd ed. (Oxford Univ. Press, Oxford, 2000; Mir, Moscow, 1987).
S. V. Vladimirov, L. Stenflo, and M. Y. Yu, Phys. Lett. A 153, 144 (1991).
Author information
Authors and Affiliations
Additional information
The text was submitted by the authors in English.
Rights and permissions
About this article
Cite this article
Shukla, P.K., Marklund, M. & Stenflo, L. Modulational instability of nonlinearly interacting incoherent sea states. Jetp Lett. 84, 645–649 (2007). https://doi.org/10.1134/S0021364006240039
Received:
Issue Date:
DOI: https://doi.org/10.1134/S0021364006240039