Towing Experiment of a Hydro-Structural Container Ship Model in Bow-Quartering Modulated Wave Trains

We experimentally investigated the influence of the geometries of a modulated wave train on the vertical-bending and torsional moments acting on a container ship in bow-quartering sea conditions. We conducted a towing experiment with a hydro-structural container ship model in the Actual Sea Model Basin (ASMB) (80 m deep, 40 m wide, and 4.5 m deep) at the National Maritime Research Institute. The ship model is made of urethane foam and was designed to have similar vertical bending and torsional vibration mode shapes to an actual ship. A modulated wave train was generated in the ASMB by the higher-order spectral-method wave generation (HOSM-WG) method such that the maxim crest appeared at the center of the basin. The ship model was towed in the modulated wave train with a relative heading angle of 120 degrees. A series of tests was performed by varying the encounter timing of the ship model and the maximum crest of the modulated wave train. In the experiment, fiber-Bragg-grating strain gauges successfully measured whipping vibrations of the ship model due to a slamming impact. The experimental results revealed that the rear wave height Hr and the ratio of the rear and front wave heights Hr/Hf were the dominant parameters governing the maximum sagging and torsional moments of a ship in bow-quartering modulated wave trains.

David J. Benney: Nonlinear Wave and Instability Processes in Fluid Flows

David J. Benney (1930–2015) was an applied mathematician and fluid dynamicist whose highly original work has shaped our understanding of nonlinear wave and instability processes in fluid flows. This article discusses the new paradigm he pioneered in the study of nonlinear phenomena, which transcends fluid mechanics, and it highlights the common threads of his research contributions, namely, resonant nonlinear wave interactions; the derivation of nonlinear evolution equations, including the celebrated nonlinear Schrödinger equation for modulated wave trains; and the significance of three-dimensional disturbances in shear flow instability and transition.

Analysis of the Momentum Transfer Operated by the Breaking in Modulated Wave Trains in Wind and No-Wind Conditions

An analysis of the flow and of the vertical transfer of the horizontal momentum induced by the breaking of modulated wave trains in wind and no-wind conditions is presented. The study is based on the results of two-dimensional numerical simulation of the Navier-Stokes equations for two-phase flow. The open source Gerris flow solver has been used, which employs a Volume of Fluid technique to capture the air-water interface. The breaking is induced through the Benjamin-Feir instability mechanism. The numerical simulations cover the entire range from the initial development of the instability, the breaking phase and the post-breaking evolution. In order to investigate the role played by the wind, a uniform wind profile, twice the phase speed, is initialized in the air phase and it is left to evolve while interacting with the wave system. Results in terms of averaged horizontal velocity and vertical flux of horizontal momentum are presented. It is shown that in the wind case the backward stresses induced at the wave troughs as a consequence of the flow separation at the crest influence significantly the flow in the upper water layer, particularly in the pre-breaking phase. No substantial differences are found between the wind and no-wind solutions in terms of the vertical transfer of horizontal momentum in the lower water layer. The vertical flux of horizontal momentum in air is consistent with the velocity reduction occurring in the wind case in the early stage.

PREDICTING THE BREAKING STRENGTH OF GRAVITY WATER WAVES FROM DEEP TO SHALLOW WATER

We revisit the classical but as yet unresolved problem of predicting the breaking strength of 2-D and 3-D gravity water waves.Our goal is to find a robust and local parameterization to predict the breaking strength of 2-D and 3-D gravity water waves. We use a LES/VOF model described by Derakhti & Kirby (2014) to simulate nonlinear wave evolution, breaking onset and post-breaking behavior for representative cases of focused wave packets or modulated wave trains. Using these numerical results, we investigate the relationship between the breaking strength parameter b and the breaking onset parameter B proposed by Barthelemy et al. (2018). While the results are potentially applicable more generally, in this paper we concentrate on breaking events due to focusing or modulational instability in wave packets over flat bottom topography and for conditions ranging from deep to intermediate depth, with depth to wavelength ratios ranging from 0.68 to 0.13.

Optical solitary waves and conservation laws to the (2 + 1)-dimensional hyperbolic nonlinear Schrödinger equation

This work studies the hyperbolic nonlinear Schrödinger equation (H-NLSE) in (2 + 1)-dimensions. The model describes the evolution of the elevation of water wave surface for slowly modulated wave trains in deep water in hydrodynamics, and also governs the propagation of electromagnetic fields in self-focusing and normally dispersive planar wave guides in optics. A class of gray and black optical solitary wave solutions of the H-NLSE are reported by adopting an appropriate solitary wave ansatz solution. Moreover, classification of conservation laws (Cls) to the H-NLSE is implemented using the multipliers approach. Some physical interpretations and analysis of the results obtained are also presented.

Breaking of modulated wave groups: kinematics and energy dissipation processes

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 $t^{-1}$ .