Fourier transform profilometry for water waves: how to achieve clean water attenuation with diffusive reflection at the water surface?

Przadka, A.; Cabane, Bernard; Pagneux, Vincent; Maurel, Agnès; Petitjeans, Philippe

doi:10.1007/s00348-011-1240-x

Cited by 57 publications

(68 citation statements)

References 19 publications

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“…Typical value of the attenuation part of the wave number used to t our resonance curves is 1.5 m −1 . This value is in good agreement with careful measurements of the attenuation in our experiments [11].…”

Section: Experimental Setup Ftp Measurementssupporting

confidence: 80%

“…7. As previously said, the attenuation in our experiments has been carefully characterized [11] and we found α ≃ 3 m −1 for ω = 38.51 s −1 , three times smaller than the one that we have to take in the numerics to reproduce the experimental measurements. The enhancement of the apparent attenuation produced by the dynamics associated with moving contact lines has been studied in detail, see [22] and reference therein.…”

Section: Experimental Setup Ftp Measurementsmentioning

confidence: 79%

“…The experimental setup consists of a tank lled with water in which dierent contexts of wave propagation are produced ( We proposed recently signicant improvements of the technique (1) by developing a lter free demodulation method [10] and (2) by analyzing carefully the properties of the diusive liquid to nd suspensions that allow to make high diusivity with, when needed, the same properties as clean water, namely weak attenuation of the gravity-capillary waves [11]. As it is now, the method permits us to measure the 2D eld with: (1) the spatial and temporal resolutions of the camera (in our case, a v9 phantom high speed camera with up to more than 1000 fps) and (2) with an accuracy in the measured height given by the periodicity of the projected fringes (in our experiments, up to 10 µm accuracy has been obtained [9]).…”

Section: Experimental Setup Ftp Measurementsmentioning

confidence: 99%

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Space-Time Resolved Experiments for Water Waves

et al. 2011

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An overview of recent works on water wave propagation using a full time-space resolved method is given. The experimental method allows us to precisely measure the surface elevation eld with spatial and temporal resolutions given by the pixel size and frequency acquisition of a high speed camera. Two typical problems are regarded: (i) the propagation of water waves through surface piercing obstacles with trapped modes or directional emission, a problem of interest notably for its practical applications to the protection of oating structures and to the canalization of the water wave energy, (ii) a study of water wave turbulence is also reported, exhibiting the interest to measure the joint space-time power spectrum to study which hypothesis of weak turbulence theory survives in laboratory experiments.

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Section: Experimental Setup Ftp Measurementssupporting

confidence: 80%

Section: Experimental Setup Ftp Measurementsmentioning

confidence: 79%

Section: Experimental Setup Ftp Measurementsmentioning

confidence: 99%

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Space-Time Resolved Experiments for Water Waves

et al. 2011

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“…We used filtered softened water and thoroughly washed the tank. Similarly to Przadka et al [16] we use anatase titanium dioxide particles (Kronos 1001) that do not alter the measured water surface …”

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confidence: 99%

Nonlocal Resonances in Weak Turbulence of Gravity-Capillary Waves

Aubourg

Mordant

2015

Phys. Rev. Lett.

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We report a laboratory investigation of weak turbulence of water surface waves in the gravitycapillary crossover. By using time-space resolved profilometry and a bicoherence analysis, we observe that the nonlinear processes involve 3-wave resonant interactions. By studying the solutions of the resonance conditions we show that the nonlinear interaction is dominantly 1D and involves collinear wave vectors. Furthermore taking into account the spectral widening due to weak nonlinearity explains that nonlocal interactions are possible between a gravity wave and high frequency capillary ones. We observe also that nonlinear 3-wave coupling is possible among gravity waves and we raise the question of the relevance of this mechanism for oceanic waves.A large ensemble of nonlinear waves can exchange energy and develop a turbulent state. The statistic properties of such wave turbulence have been described theoretically for weak nonlinearity in the framework of the Weak Turbulence Theory (WTT). In this theory, only resonant waves are able to exchange significant amounts of energy over long times due to the weak nonlinear coupling. The predicted phenomenology of the stationary statistical states resembles that of fluid turbulence: energy is injected at large scales and cascades down scale to wavelengths at which dissipation takes over and absorbs energy into heat. A major difference with fluid turbulence is that analytical predictions for the stationary spectra (and other statistical quantities) can be derived for weak wave turbulence For isotropic systems, the predicted energy spectrum E(k) has the following expressionwhere k = |k| is the wavenumber, P the energy flux, C a dimensional constant that can be calculated and α the spectral exponent. N is the number of waves taking part in the resonances. Usually N − 1 corresponds to the order of the nonlinear coupling term of the wave equation (N = 3 for quadratic nonlinearities, N = 4 for cubic ones,...). The waves have then to satisfy the resonance conditions such as k 1 = k 2 + k 3 and ω 1 = ω 2 + ω 3 (for 3-wave interaction). In some cases, these resonances conditions do not have solutions. This is the case in particular for gravity waves at the surface of water. The dispersion relation (for infinite depth) is ω = √ gk and its negative curvature does not allow for solutions of the resonance conditions for 3 waves. Thus the resonances are expected to involve 4 waves. At small wavelengths, water waves are capillary waves for which the dispersion relation is ω = γ ρ 1/2 k 3/2 whose curvature allows for 3-wave resonances (γ is the surface tension and ρ the density). The predicted spectra for water waves are thus expected to be E(k) ∝ P 1/2 k −7/4 for capillary waves and E(k) ∝ P 1/3 k −5/2 [2] for gravity waves. Laboratory experiments largely fail to reproduce this predictions, in particular for the gravity waves. In large or small waves tanks, the spectral exponent of the gravity waves is seen to vary strongly with the forcing intensity and to be close to the WTT predictions a...

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“…The surface height deformation h(x, y, t) is obtained with high temporal cadence and high spatial resolution using a fringe projection profilometry technique [16,17]. Titanium dioxide is added to the water as dye, in order to render the free surface light diffusive without changing significatively its rheological properties [47] and be able to project onto it a controlled pattern by means of a highresolution, high-contrast projector. A fast speed camera, with a resolution of 1024×1024 px 2 and inspecting an area of (41.6 × 41.6) cm 2 , is then used to capture deformations of the pattern as the result of the surface deformation.…”

Section: Gravity-capillary Wavesmentioning

confidence: 99%

The spatio-temporal spectrum of turbulent flows

2015

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Abstract. Identification and extraction of vortical structures and of waves in a disorganised flow is a mayor challenge in the study of turbulence. We present a study of the spatio-temporal behavior of turbulent flows in the presence of different restitutive forces. We show how to compute and analyse the spatio-temporal spectrum from data stemming from numerical simulations and from laboratory experiments. Four cases are considered: homogeneous and isotropic turbulence, rotating turbulence, stratified turbulence, and water wave turbulence. For homogeneous and isotropic turbulence, the spectrum allows identification of sweeping by the large scale flow. For rotating and for stratified turbulence, the spectrum allows identification of the waves, precise quantification of the energy in the waves and in the turbulent eddies, and identification of physical mechanisms such as Doppler shift and wave absorption in critical layers. Finally, in water wave turbulence the spectrum shows a transition from gravity-capillary waves to bound waves as the amplitude of the forcing is increased.

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Fourier transform profilometry for water waves: how to achieve clean water attenuation with diffusive reflection at the water surface?

Cited by 57 publications

References 19 publications

Space-Time Resolved Experiments for Water Waves

Space-Time Resolved Experiments for Water Waves

Nonlocal Resonances in Weak Turbulence of Gravity-Capillary Waves

The spatio-temporal spectrum of turbulent flows

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