Interaction houle-courant : mesure de la relation de dispersion

Abstract

Résumé :Nous présentons des mesures originales de la relation de dispersion des vagues linéaires en présence d'un courant constant uniforme selon la direction verticale et spatialement homogène dans la direction de contre-propagation. Pour cela, nous utilisons un canal hydraulique SANS batteur à houle : en effet, le bruit spontanément généré par l'installation hydraulique permet de déduire la relation de dispersion des modes excités grâce à la détection sub-pixel de l'interface. Celle-ci est illuminée par une nappe laser qui est absorbée par un colorant fluorescent dans le liquide et est simplement observée à travers la paroi latérale transparente du canal. Nous montrons l'évolution de la relation de dispersion en fonction du débit et de la hauteur d'eau dans le canal avec une concordance excellente avec la théorie. Dans certaines conditions, les modes transverses du canal sont aussi observés. Nous concluons sur la généralisation de nos résultats pour un courant variant dans la direction de propagation longitudinale par exemple en immergeant un obstacle de fond.

Correlations on weakly time-dependent transcritical white-hole flows

“…The Matlab script processes the interface with a subpixel detection method applied to the side meniscus (see Refs. [3,4,[15][16][17][18] for details). The meniscus shows a maximum intensity on the reconstituted image.…”

Classical hydrodynamics for analogue space–times: open channel flows and thin films

“…When looking to steady open channel flows in Classical Hydrodynamics like in the experimental set-ups of figure 3, where a streamlined obstacle is placed in the flume to create a spatially varying current [5,26,29,30,32–34,36,37,41,42,46,47,50,51,57,58], the dispersion relation of gravito-capillary waves in the flowing fluid (say water) is ( ω − U.k ) 2 = ( gk + ( γ / ρ ) k 3 )tanh ( kh ), where h is the mean water depth, g the acceleration due to gravity, γ the surface tension, ρ the fluid density. The ‘acoustic’ dispersion relation is recovered for the shallow water limit when kh ≪ 1 for an infinitesimal wave camber ka ≪ 1 (no harmonics generation or wave breaking [26,42]) with a the wave amplitude and for negligible surface tension effect kl c ≪ 1, where lc=γ/(ρg) is the capillary length [5,29].…”

“…Note the negative relative frequency for the negative gravity waves k N and negative capillary waves k NC [5,29].

Figure 3( a ) Experimental set-ups for Analogue Gravity in Classical Hydrodynamics [, 5, ,, 26, ,, 29, ,, 30, ,, 32, –, 34, ,, 36, ,, 37, , , , , 41, ,, 42, ,, 46, ,, 47, ,, 50, ,, 51, ,, 57, ,, 58]: the water channel of the Institut Pprime with a laser sheet which illuminates the water column coloured by a fluorescent dye; the flow goes over an obstacle and waves may be stimulated at the other end of the channel by an oscillating weir. ( b ) Dispersion relation of pure gravity waves f=ω/2π=(boldU.k±gktanh⁡(kh))/2π (measured in absence of an obstacle for a turbulent flow current) featuring both positive and negative energy branches with the transverse modes akin to massive particles in astrophysics [18] or jumping salmons exploring another dimension in real rivers (the even (red dots) and odd (green dots) modes are theoretically represented but only the even modes are measured with a central laser sheet) [30,34].

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“…The noise due to the bulk turbulent flow (for which the Reynolds number Re = Uh / ν is large, with ν the fluid viscosity) induces a wave turbulence noise on the free surface, which is analogous to the quantum noise in space–time: this noise is easily measured and leads to the dispersion relation of the system for flat analogue space–times (figure 3 and [30,34,36,46,51]). Hence, one can look to the ‘spontaneous’ amplification (non-stimulated by a wave-maker) by the flow velocity gradient at the horizon (the analogue of Hawking temperature) of the noise, which is what the analogue gravity community defined as the analogue Hawking Radiation.…”

Classical Hydrodynamics for Analogue Spacetimes: Open Channel Flows and Thin Films

“…The noise due to the bulk turbulent flow (for which the Reynolds number Re = U h/ν is large with ν the fluid viscosity) induces a wave turbulence noise on the free surface, which is analogous to the quantum noise in space-time: this noise is easily measured and leads to the dispersion relation of the system for flat analogue space-times (see Fig. 3 and [30,34,36,46,51]). Hence, one can look to the "spontaneous" amplification (non-stimulated by a wave-maker) by the flow velocity gradient at the horizon (the analogue of Hawking temperature) of the noise, which is what the analogue gravity community defined as the analogue Hawking Radiation.…”