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 -