Numerical study of Rogue waves as nonlinear Schrödinger breather solutions under finite water depth

Wave Motion ◽  
2015 ◽  
Vol 52 ◽  
pp. 81-90 ◽  
Author(s):  
Zhe Hu ◽  
Wenyong Tang ◽  
Hongxiang Xue ◽  
Xiaoying Zhang
Keyword(s):  
Water Depth ◽  
Numerical Study ◽  
Rogue Waves ◽  
Nonlinear Schrödinger ◽  
Finite Water Depth

Analytical and Numerical Study of Nearshore Multiple Oscillating Water Columns

2013 ◽  
Author(s):  
Kourosh Rezanejad ◽  
Joydip Bhattacharjee ◽  
C. Guedes Soares
Keyword(s):  
Water Depth ◽  
Numerical Study ◽  
Integral Equation Method ◽  
Wave Theory ◽  
Boundary Integral ◽  
Water Columns ◽  
Finite Water Depth ◽  
Cartesian Coordinate ◽  
Oscillating Water Columns ◽  
Good Agreement

In the present study, the performance of two chamber nearshore oscillating water columns (OWCs) in finite water depth is analyzed based on the linearized water wave theory in the two dimensional Cartesian coordinate systems. The barriers are assumed to be fixed and the turbine characteristics are assumed linear with respect to the fluctuations of volume flux and pressure inside the chamber. The free surface inside the chambers is modeled as a non-plane wave surface. Two different mathematical models are employed to solve the hydrodynamic problem; the semi-analytic method of matched eigenfunction expansion and the numerical scheme of Boundary Integral Equation Method (BIEM). The numerical results are compared with the semi-analytic results and show good agreement. The effects of the distance between the barriers and the length of the barriers on the efficiency of the OWC device are investigated. The results of two chambers OWC are also compared with the results for an equivalent single OWC chamber. Further, the effect of the water depth on the capacity of the wave power absorption is discussed.

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.

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

2013 ◽  
Vol 25 (9) ◽  
pp. 091701 ◽  
Author(s):  
A. Toffoli ◽  
L. Fernandez ◽  
J. Monbaliu ◽  
M. Benoit ◽  
E. Gagnaire-Renou ◽  
...  
Keyword(s):  
Plane Wave ◽  
Experimental Evidence ◽  
Water Depth ◽  
Rogue Waves ◽  
Finite Water Depth

Numerical study of nonlinear Peregrine breather under finite water depth

2015 ◽  
Vol 108 ◽  
pp. 70-80 ◽  
Author(s):  
Zhe Hu ◽  
Hongxiang Xue ◽  
Wenyong Tang ◽  
Xiaoying Zhang
Keyword(s):  
Water Depth ◽  
Numerical Study ◽  
Finite Water Depth ◽  
Peregrine Breather

scholarly journals EVOLUTION OF UNSTABLE WAVE PACKETS OVER VARIABLE BATHYMETRY

2020 ◽  
pp. 8
Author(s):  
Olivier Kimmoun ◽  
H.C Hsu ◽  
Amin Chabchoub
Keyword(s):  
Water Depth ◽  
Wave Train ◽  
Rogue Waves ◽  
Wave Transformation ◽  
Unstable Wave ◽  
Coastal Zones ◽  
Directional Waves ◽  
Transformation Mechanisms ◽  
Finite Water Depth ◽  
Steep Slopes

Several field observations have reported the formation of rogue waves in coastal zones, see Chien et al. (2002) for an example in Taiwanese sea. The mechanisms that lead to the occurrence of rogue waves in finite water depth to shallow water are not well understood yet under the conjecture of modulation instability. Indeed, this theory for uni-directional waves shows that when kh is lower than a threshold of 1.363 in homogeneous water depth conditions, the wave train becomes stable to side-band perturbations. Then if the wave train is stable, the appearance of rogue waves is not possible within this linear stability framework. One explanation may come from the complex wave transformation mechanisms in variable bathymetry, especially, for cases of steep slopes or near the edge between a steep slope and a gentle slope as it is the case of the continental shelf. Very few laboratory experiments have been so far addressing the influence of the bathymetry on extreme wave occurrence (Baldock and Swan (1996), Kashima et al. (2012), Ma et al. (2015)).Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/a5M4PS-Lo4Q

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.

Analytical and Numerical Study of Nearshore Multiple Oscillating Water Columns

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
Kourosh Rezanejad ◽  
Joydip Bhattacharjee ◽  
Carlos Guedes Soares
Keyword(s):  
Water Depth ◽  
Numerical Study ◽  
Integral Equation Method ◽  
Wave Theory ◽  
Boundary Integral ◽  
Water Columns ◽  
Finite Water Depth ◽  
Cartesian Coordinate ◽  
Oscillating Water Columns ◽  
Good Agreement

In the present study, the performance of two chamber nearshore oscillating water columns (OWCs) in finite water depth is analyzed based on the linearized water wave theory in the two-dimensional Cartesian coordinate systems. The barriers are assumed to be fixed and the turbine characteristics are assumed linear with respect to the fluctuations of volume flux and pressure inside the chamber. The free surface inside the chambers is modeled as a nonplane wave surface. Two different mathematical models are employed to solve the hydrodynamic problem: the semi-analytic method of matched eigenfunction expansion and the numerical scheme of boundary integral equation method (BIEM). The numerical results are compared with the semi-analytic results and show good agreement. The effects of the distance between the barriers and the length of the barriers on the efficiency of the OWC device are investigated. The results of two chambers OWC are also compared with the results for an equivalent single OWC chamber. Further, the effect of the water depth on the capacity of the wave power absorption is discussed.

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