Ship Wakes: Kelvin or Mach Angle?

Rabaud, Marc; Moisy, Frédéric

doi:10.1103/physrevlett.110.214503

Cited by 134 publications

(156 citation statements)

References 15 publications

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“…We plot the Mach angle line 4.52 ⁄ with the coefficient 4.52 adopted from the wave pattern when the particle's velocity is 0.9c. The results show clearly the transition from Kelvin angle of 19.5° at small velocities of the charged particle to the Mach angle at large velocities, being similar to the recent studies in fluid mechanics [26,27].…”

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confidence: 90%

Caustic graphene plasmons with Kelvin angle

et al. 2015

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A century-long argument made by Lord Kelvin that all swimming objects have an effective Mach number of 3, corresponding to the Kelvin angle of 19.5 degree for ship waves, has been recently challenged with the conclusion that the Kelvin angle should gradually transit to the Mach angle as the ship's velocity increases. Here we show that a similar phenomenon can happen for graphene plasmons. By analyzing the caustic wave pattern of graphene plasmons stimulated by a swift charged particle moving uniformly above graphene, we show that at low velocities of the charged particle, the caustics of graphene plasmons form the Kelvin angle. At large velocities of the particle, the caustics disappear and the effective semi-angle of the wave pattern approaches the Mach angle.Our study introduces caustic wave theory to the field of graphene plasmonics, and reveals a novel physical picture of graphene plasmon excitation during electron energy-loss spectroscopy measurement.

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supporting

confidence: 90%

Caustic graphene plasmons with Kelvin angle

et al. 2015

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“…In some surveys manta net was fixed from the stern of the vessel 17,18 , but in that case you have to be sure that the net is out of the wake zone. The distance, on which the trawl is set for sampling, should be determined individually, since the zone of turbulences caused by the vessel varies from the size of the vessel and from the speed of the boat 19,20 . Separation of microplastic particles from the sea surface samples is most often done just by visual identification 21 .…”

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confidence: 99%

Protocol for Microplastics Sampling on the Sea Surface and Sample Analysis

Viršek

Palatinus

Koren

et al. 2016

JoVE

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Microplastic pollution in the marine environment is a scientific topic that has received increasing attention over the last decade. The majority of scientific publications address microplastic pollution of the sea surface. The protocol below describes the methodology for sampling, sample preparation, separation and chemical identification of microplastic particles. A manta net fixed on an »A frame« attached to the side of the vessel was used for sampling. Microplastic particles caught in the cod end of the net were separated from samples by visual identification and use of stereomicroscopes. Particles were analyzed for their size using an image analysis program and for their chemical structure using ATR-FTIR and micro FTIR spectroscopy. The described protocol is in line with recommendations for microplastics monitoring published by the Marine Strategy Framework Directive (MSFD) Technical Subgroup on Marine Litter. This written protocol with video guide will support the work of researchers that deal with microplastics monitoring all over the world.

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“…Recent research (Rabaud & Moisy 2013;Darmon et al 2014) has highlighted the complexity of the ship wake structure and demonstrated that the appearance and properties of even the (formally) Kelvin wake may substantially change at higher Froude numbers. Our analysis shows that remarkable differences of the actual wake patterns from the ideal linear Kelvin wakes exist even at relatively low Froude numbers.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

“…An increase in the ship speed is, most probably, associated with an increase in the proportion of non-stationary components of the wave wake, and consequently, a widening of the frequency spectrum of the wake. A series of recent studies has also been devoted to the investigation of wake patterns for length Froude numbers F L 0.5, for which recent observations have highlighted that the dominant wake wedge angle is 232 T. Torsvik, T. Soomere, I. Didenkulova and A. Sheremet significantly less than the Kelvin angle, and that the angle decreases with increasing ship speed (Rabaud & Moisy 2013). However, these observations are not necessarily in contradiction with linear Kelvin wake theory (Darmon, Benzaquen & Raphael 2014;Noblesse et al 2014), but indicate that the highest waves may not coincide with the cusp line wave system for ships sailing in the high Froude number regime, making it difficult to determine the actual edge of the wake wedge.…”

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confidence: 99%

Identification of ship wake structures by a time–frequency method

et al. 2015

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The wake of a ship that sails at relatively large Froude numbers usually contains a number of components of different nature and with different heights, lengths, timings and propagation directions. We explore the possibilities of the spectrogram representation of one-point measurements of the ship wake to identify these components and to quantify their main properties. This representation, based on the short-time Fourier transform, facilitates a reliable decomposition of the wake into constituent components and makes it possible to quantify their variations in the time-space domain and the energy content of each component, from very low-frequency precursor waves up to high-frequency signals within the frequency range of typical wind-generated waves. A method for estimation of the ship speed and the distance of its sailing line from the measurement site is proposed, which only uses information available within the record of the ship wake surface elevation, but where it is assumed that the wake pattern does not deviate significantly from the classical Kelvin wake structure. The wake decomposition using the spectrogram method allows investigation of the energy content that can be attributed to each individual component of the wake. We demonstrate that the majority (60-80 %) of wake energy from strongly powered large ferries that sail at depth Froude numbers ∼0.7 is concentrated in components that are located near the edge of the wake wedge. Finally, we demonstrate that the spectrogram representation offers a convenient way to identify a specific signature of single types of ships.

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Ship Wakes: Kelvin or Mach Angle?

Cited by 134 publications

References 15 publications

Caustic graphene plasmons with Kelvin angle

Caustic graphene plasmons with Kelvin angle

Protocol for Microplastics Sampling on the Sea Surface and Sample Analysis

Identification of ship wake structures by a time–frequency method

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