Steepness and spectrum of nonlinear deformed shallow water wave

Zahibo, Narcisse; Didenkulova, Ira; Kurkin, A. A.; Pelinovsky, Efim

doi:10.1016/j.oceaneng.2007.07.001

Cited by 31 publications

(33 citation statements)

References 12 publications

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“…At the same time, waves of negative shape in the dataset were more asymmetric in terms of face-back asymmetry than positive and sign-variable waves, confirming the conclusion of the nonlinear shallow water wave theory that wave asymmetry and wave breaking affect the wave trough more than the wave crest (Didenkulova et al, 2007;Zahibo et al, 2008). The back front of the observed negative waves was steeper than the face front; while in the case of positive or sign-variable waves the face front was steeper, as predicted by the theory (Didenkulova et al, 2007;Zahibo et al, 2008). The fact that waves of sign-variable shape have less asymmetry than freak waves of positive or negative shape can be explained by wave nonlinearity.…”

Section: Recorded Freak Waves: Their Typical Propertiessupporting

confidence: 74%

Freak waves of different types in the coastal zone of the Baltic Sea

Didenkulova

Anderson

2010

Nat. Hazards Earth Syst. Sci.

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Abstract. We present a statistical analysis of freak waves 1 measured during the 203 h of observation on sea surface elevation at a location in the coastal zone of the Baltic Sea (2.7 m depth) during June-July 2008. The dataset contains 97 freak waves occurring in both calm and stormy weather conditions. All of the freak waves are solitary waves, 63% of them having positive shape, 17.5% negative shape and 19.5% sign-variable shape. It is suggested that the freak waves can be divided into two groups. Those of the first group, which includes 92% of the freak waves, have an amplification factor (ratio of freak wave height to significant wave height) which does not vary from significant wave height and has values largely within the range of 2.0 to 2.4; while for the second group, which contain the most extreme freak waves, amplification factors depend strongly on significant wave height and can reach 3.1. Analysis based on the Generalised Pareto distribution is used to describe the waves of the first group and lends weight to the identification of the two groups. It is suggested that the probable mechanism of the generation of freak waves in the second group is dispersive focussing. The time-frequency spectra of the freak waves are studied and dispersive tracks, which can be interpreted as dispersive focussing, are demonstrated.

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Section: Recorded Freak Waves: Their Typical Propertiessupporting

confidence: 74%

Freak waves of different types in the coastal zone of the Baltic Sea

Didenkulova

Anderson

2010

Nat. Hazards Earth Syst. Sci.

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“…The Riemann waves of depression always propagate slower than the linear shallow-water wave speed gh and tend to form a skewed shape with characteristic steep rear slope [31,32,37]. A Riemann wave of depression can only propagate over reasonable distances if its trough is not too deep: for |η max | > (5/9)h, the wave would almost instantly break [32,37]. This condition was only met at measurement site B3 located in less than 1 m deep water.…”

Section: Riemann Wavesmentioning

confidence: 99%

“…Differently from several families of weakly nonlinear equations, solution (3) may be a long-living wave of depression. This solution has been often used to analyze the properties of waves produced, for example, by a wavemaker [32,37,38]. Here, ships play the role of a wavemaker.…”

Section: Riemann Wavesmentioning

confidence: 99%

Ship-induced solitary Riemann waves of depression in Venice Lagoon

et al. 2015

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We demonstrate that ships of moderate size, sailing at low depth Froude numbers (0.37-0.5) in a navigation channel surrounded by shallow banks, produce depressions with depths up to 2.5 m. These depressions (Bernoulli wakes) propagate as long-living strongly nonlinear solitary Riemann waves of depression substantial distances into Venice Lagoon. They gradually become strongly asymmetric with the rear of the depression becoming extremely steep, similar to a bore. As they are dynamically similar, air pressure fluctuations moving over variable-depth coastal areas could generate meteorological tsunamis with a leading depression wave followed by a devastating bore-like feature.

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“…The distance where the wave starts to split up can be estimated from the nonlinear shallow water theory as the wave breaking distance X (Didenkulova et al 2006, Zahibo et al 2008 ( )…”

Section: Propagation Of Solitary Wavesmentioning

confidence: 99%