Research output: Contribution to journal › Article › peer-review
Envelope equation for water waves : Soliton turbulence and wavebreaking. / Dyachenko, A. I.; Kachulin, D. I.; Zakharov, V. E.
In: Journal of Ocean Engineering and Marine Energy, Vol. 3, No. 4, 01.11.2017, p. 409-415.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Envelope equation for water waves
T2 - Soliton turbulence and wavebreaking
AU - Dyachenko, A. I.
AU - Kachulin, D. I.
AU - Zakharov, V. E.
N1 - Publisher Copyright: © 2017, Springer International Publishing AG.
PY - 2017/11/1
Y1 - 2017/11/1
N2 - Water waves have long been a subject of attention of both mathematicians and physicists. The formulation of the problem is simple enough to be considered fundamental, but as of yet many questions still remain unanswered and many phenomena associated with wind-driven turbulence remain puzzling. We consider a “unidirectional” motion of weakly nonlinear gravity waves, i.e., we assume that the spectrum of the free surface contains only nonnegative wavenumbers. We use remarkably simple form of the water wave equation that we named “the super compact equation”. This new equation includes a nonlinear wave term (à la NLSE) together with an advection term that can describe the initial stage of wave breaking. This equation has also very important property. It allows to introduce exact envelope for waves without assumption of narrowness bandwidth.
AB - Water waves have long been a subject of attention of both mathematicians and physicists. The formulation of the problem is simple enough to be considered fundamental, but as of yet many questions still remain unanswered and many phenomena associated with wind-driven turbulence remain puzzling. We consider a “unidirectional” motion of weakly nonlinear gravity waves, i.e., we assume that the spectrum of the free surface contains only nonnegative wavenumbers. We use remarkably simple form of the water wave equation that we named “the super compact equation”. This new equation includes a nonlinear wave term (à la NLSE) together with an advection term that can describe the initial stage of wave breaking. This equation has also very important property. It allows to introduce exact envelope for waves without assumption of narrowness bandwidth.
KW - Envelope equation
KW - Hamiltonian formalism
KW - Modulational instability
KW - Wave breaking
UR - http://www.scopus.com/inward/record.url?scp=85032032247&partnerID=8YFLogxK
U2 - 10.1007/s40722-017-0100-z
DO - 10.1007/s40722-017-0100-z
M3 - Article
AN - SCOPUS:85032032247
VL - 3
SP - 409
EP - 415
JO - Journal of Ocean Engineering and Marine Energy
JF - Journal of Ocean Engineering and Marine Energy
SN - 2198-6444
IS - 4
ER -
ID: 9070089