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Breaking of modulated wave groups: kinematics and energy dissipation processes

Published online by Cambridge University Press:  18 September 2018

Francesco De Vita*
Dipartimento di Ingegneria Industriale, University of Rome ‘Tor Vergata’, Via del Politecnico 1, Rome 00133, Italy CNR-INSEAN, Via di Vallerano 139, Rome 00128, Italy
Roberto Verzicco
Dipartimento di Ingegneria Industriale, University of Rome ‘Tor Vergata’, Via del Politecnico 1, Rome 00133, Italy Physics of Fluids Group and Twente Max Planck Center, Department of Science and Technology, Mesa+ Institute, and J. M. Burgers Center for Fluid Dynamics, University of Twente, 7500 AE Enschede, The Netherlands
Alessandro Iafrati
CNR-INSEAN, Via di Vallerano 139, Rome 00128, Italy
Email address for correspondence:


The two-dimensional flow induced by the breaking of modulated wave trains is numerically investigated using the open source software Gerris (Popinet, J. Comput. Phys., vol. 190, 2003, pp. 572–600; J. Comput. Phys., vol. 228, 2009, pp. 5838–5866. The two-phase flow is modelled by the Navier–Stokes equations for a single fluid with variable density and viscosity, coupled with a volume-of-fluid (VOF) technique for the capturing of the interface dynamics. The breaking is induced through the Benjamin–Feir mechanism, by adding two sideband disturbances to a fundamental wave component. The evolution of the wave system is simulated starting from the initial condition until the end of the breaking process, and the role played by the initial wave steepness is investigated. As already noted in previous studies as well as in field observations, it is found that the breaking is recurrent and several breaking events are needed before the breaking process finally ceases. The down-shifting of the fundamental component to the lower sideband is made irreversible by the breaking. At the end of the breaking process the magnitude of the lower sideband component is approximately 80 % of the initial value of the fundamental one. The time histories of the energy content in water and the energy dissipation are analysed. The whole breaking process dissipates a fraction of between twenty and twenty-five per cent of the pre-breaking energy content, independently of the initial steepness. The energy contents of the different waves of the group are evaluated and it is found that after the breaking, the energy of the most energetic wave of the group decays as $t^{-1}$.

JFM Papers
© 2018 Cambridge University Press 

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