scholarly journals Potential flow simulations of Peregrine-type deep water surface gravity wave packets

PAMM ◽  
2015 ◽  
Vol 15 (1) ◽  
pp. 537-538
Author(s):  
Arne Wenzel ◽  
Dennis Bünte ◽  
Norbert P. Hoffmann
Keyword(s):  
Gravity Wave ◽  
Deep Water ◽  
Potential Flow ◽  
Water Surface ◽  
Wave Packets ◽  
Surface Gravity ◽  
Surface Gravity Wave ◽  
Flow Simulations

Focusing deep-water surface gravity wave packets: wave breaking criterion in a simplified model

2019 ◽  
Vol 873 ◽  
pp. 238-259 ◽  
Author(s):  
Nick Pizzo ◽  
W. Kendall Melville
Keyword(s):  
Gravity Wave ◽  
Deep Water ◽  
Wave Breaking ◽  
Water Surface ◽  
Dynamic Properties ◽  
Wave Packets ◽  
Surface Gravity ◽  
Simplified Model ◽  
Surface Gravity Wave ◽  
Maximum Slope

Geometric, kinematic and dynamic properties of focusing deep-water surface gravity wave packets are examined in a simplified model with the intent of deriving a wave breaking threshold parameter. The model is based on the spatial modified nonlinear Schrödinger equation of Dysthe (Proc. R. Soc. Lond. A, vol. 369 (1736), 1979, pp. 105–114). The evolution of initially narrow-banded and weakly nonlinear chirped Gaussian wave packets are examined, by means of a trial function and a variational procedure, yielding analytic solutions describing the approximate evolution of the packet width, amplitude, asymmetry and phase during focusing. A model for the maximum free surface gradient, as a function of $\unicode[STIX]{x1D716}$ and $\unicode[STIX]{x1D6E5}$, for $\unicode[STIX]{x1D716}$ the linear prediction of the maximum slope at focusing and $\unicode[STIX]{x1D6E5}$ the non-dimensional packet bandwidth, is proposed and numerically examined, indicating a quasi-self-similarity of these focusing events. The equations of motion for the fully nonlinear potential flow equations are then integrated to further investigate these predictions. It is found that a model of this form can characterize the bulk partitioning of $\unicode[STIX]{x1D716}-\unicode[STIX]{x1D6E5}$ phase space, between non-breaking and breaking waves, serving as a breaking criterion. Application of this result to better understanding air–sea interaction processes is discussed.

scholarly journals Experimental study of particle trajectories below deep-water surface gravity wave groups

2019 ◽  
Vol 879 ◽  
pp. 168-186 ◽  
Author(s):  
T. S. van den Bremer ◽  
C. Whittaker ◽  
R. Calvert ◽  
A. Raby ◽  
P. H. Taylor
Keyword(s):  
Gravity Wave ◽  
Deep Water ◽  
Water Waves ◽  
Wave Equations ◽  
Stokes Drift ◽  
Surface Gravity ◽  
Return Flow ◽  
Surface Gravity Wave ◽  
Wave Groups ◽  
Wave Induced

Owing to the interplay between the forward Stokes drift and the backward wave-induced Eulerian return flow, Lagrangian particles underneath surface gravity wave groups can follow different trajectories depending on their initial depth below the surface. The motion of particles near the free surface is dominated by the waves and their Stokes drift, whereas particles at large depths follow horseshoe-shaped trajectories dominated by the Eulerian return flow. For unidirectional wave groups, a small net displacement in the direction of travel of the group results near the surface, and is accompanied by a net particle displacement in the opposite direction at depth. For deep-water waves, we study these trajectories experimentally by means of particle tracking velocimetry in a two-dimensional flume. In doing so, we provide visual illustration of Lagrangian trajectories under groups, including the contributions of both the Stokes drift and the Eulerian return flow to both the horizontal and the vertical Lagrangian displacements. We compare our experimental results to leading-order solutions of the irrotational water wave equations, finding good agreement.

Non-stationary regimes of surface gravity wave turbulence

JETP Letters ◽  
2013 ◽  
Vol 97 (8) ◽  
pp. 459-465 ◽  
Author(s):  
R. Bedard ◽  
S. Lukaschuk ◽  
S. Nazarenko
Keyword(s):  
Gravity Wave ◽  
Surface Gravity ◽  
Wave Turbulence ◽  
Surface Gravity Wave
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