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

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 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.

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

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

Experimental Investigation of Trimaran Models in Shallow Water

2014 ◽  
Vol 30 (02) ◽  
pp. 66-78
Author(s):  
Mark Pavkov ◽  
Morabito Morabitob
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Critical Speed ◽  
Water Effect ◽  
Finite Water Depth ◽  
Speed Regime ◽  
Displacement Speed ◽  
Littoral Combat Ship ◽  
Shallow Water Effect ◽  
The U.S

Experiments were conducted at the U.S. Naval Academy's Hydromechanics Laboratory to determine the effect of finite water depth on the resistance, heave, and trim of two different trimaran models. The models were tested at the same length to water depth ratios over a range of Froude numbers in the displacement speed regime. The models were also towed in deep water for comparison. Additionally, the side hulls were adjusted to two different longitudinal positions to investigate possible differences resulting from position. Near critical speed, a large increase in resistance and sinkage was observed, consistent with observations of conventional displacement hulls. The data from the two models are scaled up to a notional 125-m length to illustrate the effects that would be observed for actual ships similar in size to the U.S. Navy's Independence Class Littoral Combat Ship. Faired plots are developed to allow for rapid estimation of shallow water effect on trimaran resistance and under keel clearance. An example is provided.

COMPARISON OF UNSTEADY REYNOLDS-AVERAGED NAVIER-STOKES PREDICTION OF SELF-PROPELLED CONTAINER SHIP SQUAT AGAINST EMPIRICAL METHODS AND BENCHMARK DATA

2021 ◽  
Vol 162 (A2) ◽  
Author(s):  
Z Kok ◽  
J T Duffy ◽  
S Chai ◽  
Y Jin
Keyword(s):  
Water Depth ◽  
High Speed ◽  
Navier Stokes ◽  
Container Ship ◽  
Benchmark Data ◽  
High Speeds ◽  
Port Throughput ◽  
Finite Water Depth ◽  
Urans Cfd ◽  
Effective Wake

The demand to increase port throughput has driven container ships to travel relatively fast in shallow water whilst avoiding grounding and hence, there is need for more accurate high-speed squat predictions. A study has been undertaken to determine the most suitable method to predict container ship squat when travelling at relatively high speeds (Frh ≥ 0.5) in finite water depth (1.1 ≤ h/T ≤ 1.3). The accuracy of two novel self-propelled URANS CFD squat model are compared with that of readily available empirical squat prediction formulae. Comparison of the CFD and empirical predictions with benchmark data demonstrates that for very low water depth (h/T < 1.14) and when Frh < 0.46; Barass II (1979), ICORELS (1980), and Millward’s (1992) formulae have the best correlation with benchmark data for all cases investigated. However, at relatively high speeds (Frh ≥ 0.5) which is achievable in deeper waters (h/T ≥ 1.14), most of the empirical formulae severely underestimated squat (7-49%) whereas the quasi-static CFD model presented has the best correlation. The changes in wave patterns and effective wake fraction with respect to h/T are also presented.

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