Computation of Nonlinear Free-Surface Flows

Tsai, Wu‐ting; Yue, Dick K. P.

doi:10.1146/annurev.fl.28.010196.001341

Cited by 202 publications

(118 citation statements)

References 48 publications

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“…The full set of non-linear equations, albeit in a different coordinate system, can be found in Wehousen & Laitone (1960) and in a more concise manner in, for example, Tsai & Yue (1996) and Sarpkaya (1996). As mentioned in chapter 1, the governing equations for the fluid motion are the continuity equation (for an incompressible flow):…”

Section: Boundary Conditions At a Free Surfacementioning

confidence: 99%

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Experiments on free-surface turbulence

Savelsberg

Water

2009

J. Fluid Mech.

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We study the free surface of a turbulent flow, in particular the relation between the statistical properties of the wrinkled surface and those of the velocity field beneath it. Channel flow turbulence is generated using an active grid. Through a judicial choice of the stirring protocol the anisotropy of the subsurface turbulence can be controlled. The largest Taylor Reynolds number obtained is Reλ = 258. We characterize the homogeneity and isotropy of the flow and discuss Taylor's frozen turbulence hypothesis, which applies to the subsurface turbulence but not to the surface. The surface gradient field is measured using a novel laser-scanning device. Simultaneously, the velocity field in planes just below the surface is measured using particle image velocimetry (PIV). Several intuitively appealing relations between the surface gradient field and functionals of the subsurface velocity field are tested. For an irregular flow shed off a vertical cylinder, we find that surface indentations are strongly correlated with both vortical and strain events in the velocity field. For fully developed turbulence this correlation is dramatically reduced. This is because the large eddies of the subsurface turbulent flow excite random capillary–gravity waves that travel in all directions across the surface. Therefore, the turbulent surface has dynamics of its own. Nonetheless, it does inherit both the integral scale, which determines the predominant wavelength of the capillary–gravity surface waves, and the (an)isotropy from the subsurface turbulence. The kinematical aspects of the surface–turbulence connection are illustrated by a simple model in which the surface is described in terms of waves originating from Gaussian wave sources that are randomly sprinkled on the moving surface.

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Section: Boundary Conditions At a Free Surfacementioning

confidence: 99%

“…The normal stress in the water is balanced by the pressure in the air and the surface tension. These conditions can be combined in the following equation (Tsai & Yue, 1996):…”

Section: Boundary Conditions At a Free Surfacementioning

confidence: 99%

Experiments on free-surface turbulence

Savelsberg

Water

2009

J. Fluid Mech.

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“…For large-amplitude (and arbitrary) body motions, the general nonlinear problem must be solved numerically in the time domain, and three-dimensional results are still quite limited (see e.g. Tsai & Yue 1996 for a review). The other problem is that of a cable in arbitrary motion wherein both transverse and longitudinal motions are important as well as the effect of bending stiffness when tension in the cable becomes zero or negative.…”

Section: Introductionmentioning

confidence: 99%

Mechanics of nonlinear short-wave generation by a moored near-surface buoy

et al. 1999

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We consider the nonlinear interaction problem of surface waves with a tethered near-surface buoy. Our objective is to investigate mechanisms for nonlinear short surface wave generation in this complete coupled wave-buoy-cable dynamical system. We develop an effective numerical simulation capability coupling an efficient and high-resolution high-order spectral method for the nonlinear wave-buoy interaction problem with a robust implicit finite-difference method for the cable-buoy dynamics. The numerical scheme accounts for nonlinear wave-wave and wave-body interactions up to an arbitrary high order in the wave steepness and is able to treat extreme motions of the cable including conditions of negative cable tension. Systematic simulations show that beyond a small threshold value of the incident wave amplitude, the buoy performs chaotic motions, characterized by the snapping of the cable. The root cause of the chaotic response is the interplay between the snapping of the cable and the generation of surface waves, which provides a source of strong (radiation) damping. As a result of this interaction, the chaotic buoy motion switches between two competing modes of snapping response: one with larger average peak amplitude and lower characteristic frequency, and the other with smaller amplitude and higher frequency. The generated high-harmonic/short surface waves are greatly amplified once the chaotic motion sets in. Analyses of the radiated wave spectra show significant energy at higher frequencies which is orders of magnitude larger than can be expected from nonlinear generation under regular motion.

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“…The numerical confirmation of the theory for gravity waves propagating on a surface has not been an easy task (for capillary waves see [14], for one dimensional wave turbulence see [15,16]), basically because of the intrinsic difficulties of the computation of the boundary conditions. Different numerical approaches have been used for integrating the fully nonlinear surface gravity waves equations (see [17] for a review). The numerical methods based on volume formulations show very interesting results, in particular they are capable of modeling in a quite appropriate way wave breaking.…”

mentioning

confidence: 99%

Freely Decaying Weak Turbulence for Sea Surface Gravity Waves

et al. 2002

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We study numerically the generation of power laws in the framework of weak turbulence theory for surface gravity waves in deep water. Starting from a random wave field, we let the system evolve numerically according to the nonlinear Euler equations for gravity waves in infinitely deep water. In agreement with the theory of Zakharov and Filonenko, we find the formation of a power spectrum characterized by a power law of the form of |k| −2.5 .

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Computation of Nonlinear Free-Surface Flows

Cited by 202 publications

References 48 publications

Experiments on free-surface turbulence

Experiments on free-surface turbulence

Mechanics of nonlinear short-wave generation by a moored near-surface buoy

Freely Decaying Weak Turbulence for Sea Surface Gravity Waves

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