Alessandro Toffoli

Statistical properties of mechanically generated surface gravity waves: a laboratory experiment in a three-dimensional wave basin

A wave basin experiment has been performed in the MARINTEK laboratories, in one of the largest existing three-dimensional wave tanks in the world. The aim of the experiment is to investigate the effects of directional energy distribution on the statistical properties of surface gravity waves. Different degrees of directionality have been considered, starting from long-crested waves up to directional distributions with a spread of ±30° at the spectral peak. Particular attention is given to the tails of the distribution function of the surface elevation, wave heights and wave crests. Comparison with a simplified model based on second-order theory is reported. The results show that for long-crested, steep and narrow-banded waves, the second-order theory underestimates the probability of occurrence of large waves. As directional effects are included, the departure from second-order theory becomes less accentuated and the surface elevation is characterized by weak deviations from Gaussian statistics.

Triggering Rogue Waves in Opposing Currents

We show that rogue waves can be triggered naturally when a stable wave train enters a region of an opposing current flow. We demonstrate that the maximum amplitude of the rogue wave depends on the ratio between the current velocity U(0) and the wave group velocity c(g). We also reveal that an opposing current can force the development of rogue waves in random wave fields, resulting in a substantial change of the statistical properties of the surface elevation. The present results can be directly adopted in any field of physics in which the focusing nonlinear Schrödinger equation with nonconstant coefficient is applicable. In particular, nonlinear optics laboratory experiments are natural candidates for verifying experimentally our results.

Excitation of rogue waves in a variable medium:An experimental study on the interaction of water waves and currents

We show experimentally that a stable wave propagating into a region characterized by an opposite current may become modulationally unstable. Experiments have been performed in two independent wave tank facilities; both of them are equipped with a wavemaker and a pump for generating a current propagating in the opposite direction with respect to the waves. The experimental results support a recent conjecture based on a current-modified nonlinear Schrödinger equation which establishes that rogue waves can be triggered by a nonhomogeneous current characterized by a negative horizontal velocity gradient.

Second-Order Theory and Setup in Surface Gravity Waves: A Comparison with Experimental Data

Abstract The second-order, three-dimensional, finite-depth wave theory is here used to investigate the statistical properties of the surface elevation and wave crests of field data from Lake George, Australia. A direct comparison of experimental and numerical data shows that, as long as the nonlinearity is small, the second-order model describes the statistical properties of field data very accurately. By low-pass filtering the Lake George time series, there is evidence that some energetic wave groups are accompanied by a setup instead of a setdown. A numerical study of the coupling coefficient of the second-order model reveals that such an experimental result is consistent with the second-order theory, provided directional spreading is included in the wave spectrum. In particular, the coupling coefficient of the second-order difference contribution predicts a setup as a result of the interaction of two waves with the same frequency but with different directions. This result is also confirmed by numerical...

Wave Breaking in Directional Fields

Abstract Wave breaking is observed in a laboratory experiment with waves of realistic average steepness and directional spread. It is shown that a modulational-instability mechanism is active in such circumstances and can lead to the breaking. Experiments were conducted in the directional wave tank of the University of Tokyo, and the mechanically generated wave fields consisted of a primary wave with sidebands in the frequency domain, with continuous directional distribution in the angular domain. Initial steepness of the primary wave and sidebands, as well as the width of directional distributions varied in a broad range to determine the combination of steepness/directional-spread properties that separates modulational-instability breaking from the linear-focusing breaking.

Experimental evidence of the modulation of a plane wave to oblique perturbations and generation of rogue waves in finite water depth

We present a laboratory experiment in a large directional wave basin to discuss the instability of a plane wave to oblique side band perturbations in finite water depth. Experimental observations, with the support of numerical simulations, confirm that a carrier wave becomes modulationally unstable even for relative water depths k0h < 1.36 (with k the wavenumber of the plane wave and h the water depth), when it is perturbed by appropriate oblique disturbances. Results corroborate that the underlying mechanism is still a plausible explanation for the generation of rogue waves in finite water depth.

An idealised experimental model of ocean surface wave transmission by an ice floe

Abstract An experimental model of transmission of ocean waves by an ice floe is presented. Thin plastic plates with different material properties and thicknesses are used to model the floe. Regular incident waves with different periods and steepnesses are used, ranging from gently-sloping to storm-like conditions. A wave gauge is used to measure the water surface elevation in the lee of the floe. The depth of wave overwash on the floe is measured by a gauge in the centre of the floe’s upper surface. Results show transmitted waves are regular for gently-sloping incident waves but irregular for storm-like incident waves. The proportion of the incident wave transmitted is shown to decrease as incident wave steepness increases, and to be at its minimum for an incident wavelength equal to the floe length. Further, a trend is noted for transmission to decrease as the mean wave height in the overwash region increases.

Occurrence of rogue sea states and consequences for marine structures

The frequency of occurrence of combined wave systems like wind sea and swell may increase in some ocean areas due to the observed change of storm tracks. These combined sea states, when crossing at a particular angle, may lead to more frequent occurrence of rogue events. The present study addresses these rogue-wave-prone sea states and their probabilities of occurrence. The analysis is based on hindcast data from the North Atlantic, the North Sea, the Norwegian Sea, Nigeria and Australia and supported by numerical simulations performed by the Higher Order Spectral Method (HOSM, West et al. J Geophys Res 92:11803–11824, 1987). The hindcast data have been generated by the wave model WAM. Long-term probabilistic description of significant wave height and spectral peak period is established for the selected locations and probability of occurrence of crossing rogue-wave-prone sea states is indicated. Further, the occurrence of individual rogue waves in low, intermediate and high sea states is also evaluated. The results are discussed from the perspective of design and operations of ships and offshore structures.

Sea ice floes dissipate the energy of steep ocean waves

A laboratory experimental model of an incident ocean wave interacting with an ice floe is used to validate the canonical, solitary floe version of contemporary theoretical models of wave attenuation in the ice-covered ocean. Amplitudes of waves transmitted by the floe are presented as functions of incident wave steepness for different incident wavelengths. The model is shown to predict the transmitted amplitudes accurately for low incident steepness but to overpredict the amplitudes by an increasing amount, as the incident wave becomes steeper. The proportion of incident wave energy dissipated by the floe in the experiments is shown to correlate with the agreement between the theoretical model and the experimental data, thus implying that wave-floe interactions increasingly dissipate wave energy as the incident wave becomes steeper.

Wind generated rogue waves in an annular wave flume

We investigate experimentally the statistical properties of a wind-generated wave field and the spontaneous formation of rogue waves in an annular flume. Unlike many experiments on rogue waves where waves are mechanically generated, here the wave field is forced naturally by wind as it is in the ocean. What is unique about the present experiment is that the annular geometry of the tank makes waves propagating circularly in an unlimited-fetch condition. Within this peculiar framework, we discuss the temporal evolution of the statistical properties of the surface elevation. We show that rogue waves and heavy-tail statistics may develop naturally during the growth of the waves just before the wave height reaches a stationary condition. Our results shed new light on the formation of rogue waves in a natural environment.