On the chance of freak waves at sea

White, Bebo; Fornberg, Bengt

doi:10.1017/s0022112097007751

Cited by 199 publications

(152 citation statements)

References 34 publications

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“…Indeed, such currents may reach velocities up to 1.5 meter per second and for a group velocity corresponding to waves of period equal to 10 second (a typical condition during storms), the ratio ∆U/c g is of the order of 0.2, large enough to trigger a dangerous rogue wave. We underline that this is completely different process from the development of a caustic, a pure linear mechanism [25][26][27]. From a physical point of view, the mechanism of formation of rogue waves can be summarized as follows: an initial wave whose perturbation is stable in terms of the modulational instability may become unstable in the presence of a current because of the a shift of the modulational instability band.…”

Section: Index (Bfi)mentioning

confidence: 96%

Triggering Rogue Waves in Opposing Currents

2011

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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, U0, and the wave group velocity, cg. 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 Schrodinger equation with non constant coefficient is applicable. In particular, nonlinear optics laboratory experiments are natural candidates for verifying experimentally our results. PACS numbers:In the ocean, rogue waves are often observed in regions characterized by strong currents like the Gulf Stream, Agulhas Current and the Kuroshio Current [1, 2]. Several ship accidents have been reported in these regions as being due to the impact with very large waves. One of these occurred in February 1986 to the SS Spray, which was travelling along the East coast of the USA. The ship was hit by a wave with a height of approximately 17 m (estimated by eyes from the deck of the ship), which was the second of a system of three consecutive large waves, commonly known as the three sisters. This particular wave system is usually observed in the nonlinear stages of the modulational instability process. Such instability was discovered in the late sixties independently by Zakharov [3] and Benjamin and Feir [4] (an interesting and stimulating review on the subject can be found in [5]). The theory is based on the linear stability analysis of a plane wave and predicts that a small perturbation may grow exponentially when εN > 1/ √ 2, where ε = k 0 A 0 is the steepness of the plane wave, with k 0 its wave number and A 0 its amplitude; N = ω 0 /∆Ω is the number of waves under the modulation, with ω 0 the angular frequency corresponding to the wave number k 0 and ∆Ω the angular frequency of the modulation.

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Section: Index (Bfi)mentioning

confidence: 96%

Triggering Rogue Waves in Opposing Currents

2011

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“…Another topic of practical interest in wave-current interaction problems is the appearance of large transient or freak waves with great amplitude and steepness owing to the focusing mechanism (e.g., Peregrine, 1976;Lavrenov, 1998;White and Fornberg, 1998;Kharif and Pelinovsky, 2006;Janssen and Herbers, 2009;Ruban, 2012;Osborne, 2001). Both nonlinear instability and refractive focusing have been identified as mechanisms for extreme-wave generation and these processes are generally concomitant in oceans and potentially act together to create giant waves.…”

Section: V Shugan Et Al: An Analytical Model Of the Evolution Ofmentioning

confidence: 99%

An analytical model of the evolution of a Stokes wave and its two Benjamin–Feir sidebands on nonuniform unidirectional current

Shugan

Hwung

Yang

2015

Nonlin. Processes Geophys.

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Abstract. An analytical weakly nonlinear model of the Benjamin-Feir instability of a Stokes wave on nonuniform unidirectional current is presented. The model describes evolution of a Stokes wave and its two main sidebands propagating on a slowly varying steady current. In contrast to the models based on versions of the cubic Schrödinger equation, the current variations could be strong, which allows us to examine the blockage and consider substantial variations of the wave numbers and frequencies of interacting waves. The spatial scale of the current variation is assumed to have the same order as the spatial scale of the Benjamin-Feir (BF) instability. The model includes wave action conservation law and nonlinear dispersion relation for each of the wave's triad. The effect of nonuniform current, apart from linear transformation, is in the detuning of the resonant interactions, which strongly affects the nonlinear evolution of the system.The modulation instability of Stokes waves in nonuniform moving media has special properties. Interaction with countercurrent accelerates the growth of sideband modes on a short spatial scale. An increase in initial wave steepness intensifies the wave energy exchange accompanied by wave breaking dissipation, resulting in asymmetry of sideband modes and a frequency downshift with an energy transfer jump to the lower sideband mode, and depresses the higher sideband and carrier wave. Nonlinear waves may even overpass the blocking barrier produced by strong adverse current. The frequency downshift of the energy peak is permanent and the system does not revert to its initial state. We find reasonable correspondence between the results of model simulations and available experimental results for wave interaction with blocking opposing current. Large transient or freak waves with amplitude and steepness several times those of normal waves may form during temporal nonlinear focusing of the waves accompanied by energy income from sufficiently strong opposing current. We employ the model for the estimation of the maximum amplification of wave amplitudes as a function of opposing current value and compare the result obtained with recently published experimental results and modeling results obtained with the nonlinear Schrödinger equation.

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“…Freak waves on the ocean surface are known for sinking the largest ships (White and Fornberg, 1998). Whether any similar waves occur in the atmosphere is uncertain.…”

Section: Freak Wavementioning

confidence: 99%

All-weather volume imaging of the boundary layer and troposphere using the MU radar

Worthington

2004

Ann. Geophys.

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Abstract. This paper shows the first volume-imaging radar that can run in any weather, revealing the turbulent threedimensional structure and airflow of convective cells, rain clouds, breaking waves and deep convection as they evolve and move. Precipitation and clear air can be volume-imaged independently. Birds are detected as small high-power echoes moving near horizontal, at different speeds and directions from background wind. The volume-imaging method could be used to create a real-time virtual-reality view of the atmosphere, in effect making the invisible atmosphere visible in any weather.

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On the chance of freak waves at sea

Cited by 199 publications

References 34 publications

Triggering Rogue Waves in Opposing Currents

Triggering Rogue Waves in Opposing Currents

An analytical model of the evolution of a Stokes wave and its two Benjamin–Feir sidebands on nonuniform unidirectional current

All-weather volume imaging of the boundary layer and troposphere using the MU radar

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