Particle trajectories of nonlinear gravity waves in deep water

Chang, Han; Chen, Yangyi; Liou, Jin Cheng

doi:10.1016/j.oceaneng.2008.12.007

Cited by 12 publications

(9 citation statements)

References 32 publications

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“…Equation (30) also confirms that the Lagrangian mean level is higher than the Eulerian mean level (Longuet-Higgins 1986). Unlike Longuet-Higgins (1986, 1987 and Chang et al (2009) who used the Euler-Lagrange transformation to derive this result, the theory presented here is perfectly constructed in the Lagrangian framework for all particles from the free surface to the bottom.…”

Section: Second-order Approximationsupporting

confidence: 71%

“…Clamond (2007) obtained a third-order Lagrangian solution for gravity waves in finite-depth water and a seventh-order solution for deep water waves; moreover, Henry (2009) studied the steady periodic flow induced by the Korteweg and de Vries equation. Longuet-Higgins (1986, 1987 and Chang et al (2009) found that the Lagrangian period of particle motion is different from the Eulerian wave period, with a higher Lagrangian mean level than the Eulerian mean level at the free surface in deep water.…”

Section: Introductionmentioning

confidence: 99%

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Lagrangian experiment and solution for irrotational finite-amplitude progressive gravity waves at uniform depth

2010

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This study investigates the theory for predicting Lagrangian properties including particle orbit, Lagrangian mean level, Lagrangian wave frequency, mass transport velocity, wave profile, velocity distribution and wave pressure in progressive gravity water waves at uniform depth. A series of laboratory experiments are performed to measure the trajectories of particles and the wave pressure. Asymptotic solutions up to fifth order that describe irrotational finite amplitude progressive gravity water waves are derived in completely Lagrangian coordinates. The analytical Lagrangian solution that is uniformly valid satisfies the irrotational condition, the dynamic boundary condition and the zero pressure at the free surface. The explicit fifth-order parametric solution highlights the trajectory of a water particle and the wave kinematics above the mean water level and within a vertical water column, which were calculated previously by an approximation method using an Eulerian approach. Mass transport up to fourth order associated with a particle displacement can now be obtained directly in Lagrangian form. In particular, the Lagrangian wave frequency and the Lagrangian mean level of particle motion can also be obtained, which are different from those in an Eulerian description. By comparing the present fifth-order asymptotic solution with data from laboratory experiments, it is found that theoretical results show good agreement with experimental data.

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Section: Second-order Approximationsupporting

confidence: 71%

Section: Introductionmentioning

confidence: 99%

Lagrangian experiment and solution for irrotational finite-amplitude progressive gravity waves at uniform depth

2010

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“…That said, there is also other work on these matters, most of it in the physical and fluid-dynamics literature. The interested reader may for example consult [3,4,47]. While those investigations are in line with the analytical results, some of the recent mathematical findings cover cases which are new, or at least not well-investigated, from a more applied point of view.…”

Section: Introductionmentioning

confidence: 70%

Recent progress on particle trajectories in steady water waves

Ehrnström¹,

Villari²

2009

Discrete &Amp; Continuous Dynamical Systems - B

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“…Longuet-Higgins 1986) and observed in numerical simulation (see e.g. Chang, Chen & Liou 2009). Note that T is the time it takes for a fixed spatial position to experience the same wave phase again, whereas T L is for a particle that is convected downstream with the Stokes drift and is thus longer than T. Lagrangian fluctuation is defined by…”

Section: Appendix a Average Operatormentioning

confidence: 99%

Numerical study of the effect of surface waves on turbulence underneath. Part 1. Mean flow and turbulence vorticity

Guo

Shen

2013

J. Fluid Mech.

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Direct numerical simulation is performed to study the effect of progressive gravity waves on turbulence underneath. The Navier-Stokes equations subject to fully nonlinear kinematic and dynamic free-surface boundary conditions are simulated on a surface-following mapped grid using a fractional-step scheme with a pseudo-spectral method in the horizontal directions and a finite-difference method in the vertical direction. To facilitate a mechanistic study that focuses on the fundamental physics of wave-turbulence interaction, the wave and turbulence fields are set up precisely in the simulation: a pressure-forcing method is used to generate and maintain the progressive wave being investigated and to suppress other wave components, and a random forcing method is used to produce statistically steady, homogeneous turbulence in the bulk flow beneath the surface wave. Cases with various moderate-to-large turbulenceto-wave time ratios and wave steepnesses are considered. Study of the turbulence velocity spectrum shows that the turbulence is dynamically forced by the surface wave. Mean flow and turbulence vorticity are studied in both the Eulerian and Lagrangian frames of the wave. In the Eulerian frame, statistics of the underlying turbulence field indicates that the magnitude of turbulence vorticity and the inclination angle of vortices are dependent on the wave phase. In the Lagrangian frame, wave properties and the accumulative effect on turbulence vorticity are studied. It is shown that vertical vortices are tilted in the wave propagation direction due to the cumulative effects of both the Stokes drift velocity and the correlation between turbulence fluctuations and wave strain rate, whereas for streamwise vortices, these two factors offset each other and result in a negligible tilting effect.

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Particle trajectories of nonlinear gravity waves in deep water

Cited by 12 publications

References 32 publications

Lagrangian experiment and solution for irrotational finite-amplitude progressive gravity waves at uniform depth

Lagrangian experiment and solution for irrotational finite-amplitude progressive gravity waves at uniform depth

Recent progress on particle trajectories in steady water waves

Numerical study of the effect of surface waves on turbulence underneath. Part 1. Mean flow and turbulence vorticity

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