scholarly journals HIGH ORDER NONLINEAR WAVE INTERACTIONS FROM DEEP TO FINITE WATER DEPTH WITH BOTTOM TOPOGRAPHY CHANGE

2020 ◽  
pp. 24
Author(s):  
Zuorui Lyu ◽  
Hiroaki Kashima ◽  
Nobuhito Mori
Keyword(s):  
Nonlinear Wave ◽  
Water Depth ◽  
Deep Water ◽  
Modulational Instability ◽  
High Order ◽  
Long Distance ◽  
Freak Wave ◽  
Wave Evolution ◽  
Finite Water Depth ◽  
Skewness And Kurtosis

In recent years, freak wave/rouge wave has become an important problem in science and engineering. Modulational instability is considered to be an important factor leading to freak wave in the wave evolution of deep water, and Janssen (2003) defined Benjamin-Feir index (BFI) to reflect it. Mori and Janssen (2006) gave the occurrence probability of freak waves based on a weakly non-Gaussian theory, and distribution of wave height is determined by skewness and kurtosis of surface elevation to a considerable extent in deep water. According to observational record, freak wave has not only been found in deep water in the ocean, but also been observed in shallow water and coastal areas. In the process of water wave entering continental shelf, water depth is changing with mild slope after a long distance propagation. This study focus on investigating how water depth affect skewness and kurtosis in the high order nonlinear wave evolution from deep water to finite water depth in two-dimension.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/a8LiJvXWRrw

scholarly journals Modulational instability and wave amplification in finite water depth

2014 ◽  
Vol 14 (3) ◽  
pp. 705-711 ◽  
Author(s):  
L. Fernandez ◽  
M. Onorato ◽  
J. Monbaliu ◽  
A. Toffoli
Keyword(s):  
Plane Wave ◽  
Water Depth ◽  
Modulational Instability ◽  
Wave Train ◽  
Rogue Waves ◽  
Side Band ◽  
Sea Floor ◽  
Wave Amplification ◽  
Finite Water Depth ◽  
Wave Induced

Abstract. The modulational instability of a uniform wave train to side band perturbations is one of the most plausible mechanisms for the generation of rogue waves in deep water. In a condition of finite water depth, however, the interaction with the sea floor generates a wave-induced current that subtracts energy from the wave field and consequently attenuates the instability mechanism. As a result, a plane wave remains stable under the influence of collinear side bands for relative depths kh &amp;leq; 1.36 (where k is the wavenumber of the plane wave and h is the water depth), but it can still destabilise due to oblique perturbations. Using direct numerical simulations of the Euler equations, it is here demonstrated that oblique side bands are capable of triggering modulational instability and eventually leading to the formation of rogue waves also for kh &amp;leq; 1.36. Results, nonetheless, indicate that modulational instability cannot sustain a substantial wave growth for kh < 0.8.

scholarly journals Ship waves on uniform shear current at finite depth: wave resistance and critical velocity

2016 ◽  
Vol 791 ◽  
pp. 539-567 ◽  
Author(s):  
Yan Li ◽  
Simen Å Ellingsen
Keyword(s):  
Froude Number ◽  
Critical Velocity ◽  
Water Depth ◽  
Deep Water ◽  
Wave Resistance ◽  
Ship Motion ◽  
Ship Waves ◽  
Lateral Wave ◽  
Shear Current ◽  
Finite Water Depth

We present a comprehensive theory for linear gravity-driven ship waves in the presence of a shear current with uniform vorticity, including the effects of finite water depth. The wave resistance in the presence of shear current is calculated for the first time, containing in general a non-zero lateral component. While formally apparently a straightforward extension of existing deep water theory, the introduction of finite water depth is physically non-trivial, since the surface waves are now affected by a subtle interplay of the effects of the current and the sea bed. This becomes particularly pronounced when considering the phenomenon of critical velocity, the velocity at which transversely propagating waves become unable to keep up with the moving source. The phenomenon is well known for shallow water, and was recently shown to exist also in deep water in the presence of a shear current (Ellingsen, J. Fluid Mech., vol. 742, 2014, R2). We derive the exact criterion for criticality as a function of an intrinsic shear Froude number $S\sqrt{b/g}$ ($S$ is uniform vorticity, $b$ size of source), the water depth and the angle between the shear current and the ship’s motion. Formulae for both the normal and lateral wave resistance forces are derived, and we analyse their dependence on the source velocity (or Froude number $Fr$) for different amounts of shear and different directions of motion. The effect of the shear current is to increase wave resistance for upstream ship motion and decrease it for downstream motion. Also the value of $Fr$ at which $R$ is maximal is lowered for upstream and increased for downstream directions of ship motion. For oblique angles between ship motion and current there is a lateral wave resistance component which can amount to 10–20 % of the normal wave resistance for side-on shear and $S\sqrt{b/g}$ of order unity. The theory is fully laid out and far-field contributions are carefully separated off by means of Cauchy’s integral theorem, exposing potential pitfalls associated with a slightly different method (Sokhotsky–Plemelj) used in several previous works.

Finite-amplitude steady-state wave groups with multiple near-resonances in finite water depth

2019 ◽  
Vol 867 ◽  
pp. 348-373 ◽  
Author(s):  
Z. Liu ◽  
D. Xie
Keyword(s):  
Steady State ◽  
Water Depth ◽  
Deep Water ◽  
High Frequency ◽  
Finite Amplitude ◽  
Wave Groups ◽  
State Wave ◽  
Resonant Interactions ◽  
Frequency Components ◽  
Finite Water Depth

Finite-amplitude wave groups with multiple near-resonances are investigated to extend the existing results due to Liu et al. (J. Fluid Mech., vol. 835, 2018, pp. 624–653) from steady-state wave groups in deep water to steady-state wave groups in finite water depth. The slow convergence rate of the series solution in the homotopy analysis method and extra unpredictable high-frequency components in finite water depth make it hard to obtain finite-amplitude wave groups accurately. To overcome these difficulties, a solution procedure that combines the homotopy analysis method-based analytical approach and Galerkin method-based numerical approaches has been used. For weakly nonlinear wave groups, the continuum of steady-state resonance from deep water to finite water depth is established. As nonlinearity increases, the frequency bands broaden and more steady-state wave groups are obtained. Finite-amplitude wave groups with steepness no less than $0.20$ are obtained and the resonant sets configuration of steady-state wave groups are analysed in different water depths. For waves in deep water, the majority of non-trivial components appear around the primary ones due to four-wave, six-wave, eight-wave or even ten-wave resonant interactions. The dominant role of four-wave resonant interactions for steady-state wave groups in deep water is demonstrated. For waves in finite water depth, additional non-trivial high-frequency components appear in the spectra due to three-wave, four-wave, five-wave or even six-wave resonant interactions with the components around the primary ones. The amplitude of these high-frequency components increases further as the water depth decreases. Resonances composed by components only around the primary ones are suppressed while resonances composed by components around the primary ones and from the high-frequency domain are enhanced. The spectrum of steady-state resonant wave groups changes with the water depth and the significant role of three-wave resonant interactions in finite water depth is demonstrated.

scholarly journals Modulational instability and rogue waves in finite water depth

2013 ◽  
Vol 1 (5) ◽  
pp. 5237-5260
Author(s):  
L. Fernandez ◽  
M. Onorato ◽  
J. Monbaliu ◽  
A. Toffoli
Keyword(s):  
Plane Wave ◽  
Water Depth ◽  
Modulational Instability ◽  
Wave Train ◽  
Rogue Waves ◽  
Side Band ◽  
Sea Floor ◽  
Relative Water ◽  
Finite Water Depth ◽  
Wave Induced

Abstract. The mechanism of side band perturbations to a uniform wave train is known to produce modulational instability and in deep water conditions it is accepted as a plausible cause for rogue wave formation. In a condition of finite water depth, however, the interaction with the sea floor generates a wave-induced current that subtracts energy from the wave field and consequently attenuates this instability mechanism. As a result, a plane wave remains stable under the influence of collinear side bands for relative water depths kh &amp;leq; 1.36 (where k represents the wavenumber of the plane wave and h the water depth), but it can still destabilise due to oblique perturbations. Using direct numerical simulations of the Euler equations, it is here demonstrated that oblique side bands are capable of triggering modulational instability and eventually leading to the formation of rogue waves also for kh &amp;leq; 1.36. Results, nonetheless, indicates that modulational instability cannot sustain a substantial wave growth for kh < 0.8.

Ship Springing Response in Finite Water Depth

2012 ◽  
Vol 56 (02) ◽  
pp. 80-90
Author(s):  
Jelena Vidic-Perunovic
Keyword(s):  
Relative Motion ◽  
Water Depth ◽  
Deep Water ◽  
Bending Moment ◽  
Intermediate Water ◽  
Short Term ◽  
Strip Theory ◽  
Influence Of Water ◽  
Finite Water Depth ◽  
Wave Induced

The influence of water depth on the vertical wave induced bending moment acting on a hull has been studied. The deep-water second-order nonlinear hydroelastic strip theory, which is based on the relative motion concept, has been generalized to account for a finite water depth. Results for an analytical beam and for a tanker ship are presented and discussed. Short-term load predictions that account for a range of different sea states are given for a tanker ship. As seen from the present study, the effect of intermediate water depth may be a significant factor in calculations of ship springing response.

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