scholarly journals Lagrangian transport for two-dimensional deep-water surface gravity wave groups

2016 ◽  
Vol 472 (2192) ◽  
pp. 20160159 ◽  
Author(s):  
T. S. van den Bremer ◽  
P. H. Taylor
Keyword(s):  
Gravity Wave ◽  
Frequency Dispersion ◽  
Wave Theory ◽  
Stokes Drift ◽  
Surface Gravity ◽  
Return Flow ◽  
Surface Gravity Wave ◽  
Wave Groups ◽  
Lagrangian Transport ◽  
Separation Of Scales

The Lagrangian trajectories of neutrally buoyant particles underneath surface gravity wave groups are dictated by two physical phenomena: the Stokes drift results in a net displacement of particles in the direction of propagation of the group, whereas the Eulerian return flow, as described by the multi-chromatic wave theory of Longuet-Higgins & Stewart (1962 J. Fluid Mech. 13 , 481–504. ( doi:10.1017/S0022112062000877 )), transports such particles in the opposite direction. By pursuing a separation of scales expansion, we develop simple closed-form expressions for the net Lagrangian displacement of particles. By comparing the results from the separation of scales expansion at different orders in bandwidth, we study the effect of frequency dispersion on the local Lagrangian transport, which we show can be ignored for realistic sea states.

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.

scholarly journals The set-down and set-up of directionally spread and crossing surface gravity wave groups

2017 ◽  
Vol 835 ◽  
pp. 131-169 ◽  
Author(s):  
M. L. McAllister ◽  
T. A. A. Adcock ◽  
P. H. Taylor ◽  
T. S. van den Bremer
Keyword(s):  
Free Surface ◽  
Gravity Wave ◽  
Standing Wave ◽  
Wave Pattern ◽  
Surface Gravity ◽  
Linear Wave ◽  
Surface Gravity Wave ◽  
Wave Groups ◽  
Single Wave ◽  
Set Up

For sufficiently directionally spread surface gravity wave groups, the set-down of the wave-averaged free surface, first described by Longuet-Higgins and Stewart (J. Fluid Mech. vol. 13, 1962, pp. 481–504), can turn into a set-up. Using a multiple-scale expansion for two crossing wave groups, we examine the structure and magnitude of this wave-averaged set-up, which is part of a crossing wave pattern that behaves as a modulated partial standing wave: in space, it consists of a rapidly varying standing-wave pattern slowly modulated by the product of the envelopes of the two groups; in time, it grows and decays on the slow time scale associated with the translation of the groups. Whether this crossing wave pattern actually enhances the surface elevation at the point of focus depends on the phases of the linear wave groups, unlike the set-down, which is always negative and inherits the spatial structure of the underlying envelope(s). We present detailed laboratory measurements of the wave-averaged free surface, examining both single wave groups, varying the degree of spreading from small to very large, and the interaction between two wave groups, varying both the degree of spreading and the crossing angle between the groups. In both cases, we find good agreement between the experiments, our simple expressions for the set-down and set-up, and existing second-order theory based on the component-by-component interaction of individual waves with different frequencies and directions. We predict and observe a set-up for wave groups with a Gaussian angular amplitude distribution with standard deviations of above $30{-}40^{\circ }$ ($21{-}28^{\circ }$ for energy spectra), which is relatively large for realistic sea states, and for crossing sea states with angles of separation of $50{-}70^{\circ }$ and above, which are known to occur in the ocean.

scholarly journals Surface gravity wave effects on submesoscale currents in the open ocean

2021 ◽  
Author(s):  
Delphine Hypolite ◽  
Leonel Romero ◽  
James C. McWilliams ◽  
Daniel P. Dauhajre
Keyword(s):  
Gravity Wave ◽  
Wave Spectrum ◽  
Open Ocean ◽  
Stokes Drift ◽  
Vertical Shear ◽  
Surface Gravity ◽  
Minor Effect ◽  
Surface Gravity Wave ◽  
Wave Effects ◽  
Forced Waves

AbstractA set of realistic coastal simulations in California allows for the exploration of surface gravity wave effects on currents (WEC) in an active submesoscale current regime. We use a new method that takes into account the full surface gravity wave spectrum and produces larger Stokes drift than the monochromatic peak-wave approximation. We investigate two high wave events lasting several days — one from a remotely generated swell and another associated with local wind-generated waves — and perform a systematic comparison between solutions with and without WEC at two submesoscale-resolving horizontal grid resolutions (dx = 270 m and 100 m). WEC results in the enhancement of open-ocean surface density and velocity gradients when the averaged significant wave height HS is relatively large (> 4.2m). For smaller waves, WEC is a minor effect overall. For the remote swell (strong waves and weak winds), WEC maintains submesoscale structures and accentuates the cyclonic vorticity and horizontal convergence skewness of submesoscale fronts and filaments. The vertical enstrophy ζ2 budget in cyclonic regions (ζ/f > 2) reveals enhanced vertical shear and enstrophy production via vortex tilting and stretching. Wind-forced waves also enhance surface gradients, up to the point where they generate a small-submesoscale roll-cell pattern with high vorticity and divergence that extends vertically through the entire mixed layer. The emergence of these roll-cells results in a buoyancy gradient sink near the surface that causes a modest reduction in the typically large submesoscale density gradients.

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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