TY - JOUR

T1 - Interactions of coherent structures on the surface of deep water

AU - Kachulin, Dmitry

AU - Dyachenko, Alexander

AU - Gelash, Andrey

N1 - Publisher Copyright: © 2019 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2019/6/1

Y1 - 2019/6/1

N2 - We numerically investigate pairwise collisions of solitary wave structures on the surface of deep water - breathers. These breathers are spatially localised coherent groups of surface gravity waves which propagate so that their envelopes are stable and demonstrate weak oscillations. We perform numerical simulations of breather mutual collisions by using fully nonlinear equations for the potential flow of ideal incompressible fluid with a free surface written in conformal variables. The breather collisions are inelastic. However, the breathers can still propagate as stable localised wave groups after the interaction. To generate initial conditions in the form of separate breathers we use the reduced model - the Zakharov equation. We present an explicit expression for the four-wave interaction coefficient and third order accuracy formulas to recover physical variables in the Zakharov model. The suggested procedure allows the generation of breathers of controlled phase which propagate stably in the fully nonlinear model, demonstrating only minor radiation of incoherent waves. We perform a detailed study of breather collision dynamics depending on their relative phase. In 2018 Kachulin and Gelash predicted new effects of breather interactions using the Dyachenko-Zakharov equation. Here we show that all these effects can be observed in the fully nonlinear model. Namely, we report that the relative phase controls the process of energy exchange between breathers, level of energy loses, and space positions of breathers after the collision.

AB - We numerically investigate pairwise collisions of solitary wave structures on the surface of deep water - breathers. These breathers are spatially localised coherent groups of surface gravity waves which propagate so that their envelopes are stable and demonstrate weak oscillations. We perform numerical simulations of breather mutual collisions by using fully nonlinear equations for the potential flow of ideal incompressible fluid with a free surface written in conformal variables. The breather collisions are inelastic. However, the breathers can still propagate as stable localised wave groups after the interaction. To generate initial conditions in the form of separate breathers we use the reduced model - the Zakharov equation. We present an explicit expression for the four-wave interaction coefficient and third order accuracy formulas to recover physical variables in the Zakharov model. The suggested procedure allows the generation of breathers of controlled phase which propagate stably in the fully nonlinear model, demonstrating only minor radiation of incoherent waves. We perform a detailed study of breather collision dynamics depending on their relative phase. In 2018 Kachulin and Gelash predicted new effects of breather interactions using the Dyachenko-Zakharov equation. Here we show that all these effects can be observed in the fully nonlinear model. Namely, we report that the relative phase controls the process of energy exchange between breathers, level of energy loses, and space positions of breathers after the collision.

KW - Breathers

KW - Dyachenko equations

KW - Freak waves

KW - Nonlinear waves

KW - Solitons

KW - Surface gravity waves

KW - Zakharov equation

KW - breathers

KW - surface gravity waves

KW - freak waves

KW - GRAVITY

KW - COMPACT EQUATION

KW - IDEAL FLUID

KW - nonlinear waves

KW - DYNAMICS

KW - FREAK WAVES

KW - solitons

UR - http://www.scopus.com/inward/record.url?scp=85069761237&partnerID=8YFLogxK

U2 - 10.3390/fluids4020083

DO - 10.3390/fluids4020083

M3 - Article

AN - SCOPUS:85069761237

VL - 4

JO - Experiments in Fluids

JF - Experiments in Fluids

SN - 0723-4864

IS - 2

M1 - 83

ER -