Experiments on free-surface turbulence

Abstract

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.

Frequency-wavenumber spectrum of the free surface of shallow turbulent flows over a rough boundary

“…8-10), the maxima of the frequency-wavenumber spectra lie near k x = ±k 0 , showing that the stationary waves represented the dominant pattern on the free surface. Patterns of waves which propagate radially in all directions, resembling the model of concentric gravity waves being shed by vertical vortices suggested by Savelsberg and van de Water, 11 were also observed. In the measurements reported here, the scale of the pattern was governed by the wavelength of the stationary waves rather than by the scale of the attached vortices.…”

“…With respect to the experiments of Savelsberg and van de Water, 11 which focused on grid-generated turbulence and relatively short waves, the dispersion relation has been determined near the largest scales where the interaction with the bed manifests itself more clearly. The measurements have been compared with the dispersion relation of gravity-capillary waves in a flow with a 1/3 power function velocity profile and with the standard irrotational theory of gravity-capillary waves.…”

“…9,10 In shallow open channel turbulent flows the effect of gravity is dominating, but the turbulence can effectively disturb the free surface to the point of breaking. 6 The correlation between the free surface elevation and the flow vorticity or turbulent velocities is high in numerical simulations, 10 but generally much lower in experiments, 11,12 where it is difficult to obtain high quality data near the surface, and dispersive waves can affect the correlation locally.…”

“…There has been a very limited number of numerical 21,22 or experimental 11 studies that tried to quantify the frequency-wavenumber spectrum of the waves on a free surface turbulent flow. The numerical simulations 21,22 show patterns of forced waves similar to the ones predicted by the model of Teixeira and Belcher,20 in which the frequency is governed by the turbulent forcing, as well as shorter freely propagating patterns following the dispersion relation of gravity-capillary waves.…”

“…The numerical simulations 21,22 show patterns of forced waves similar to the ones predicted by the model of Teixeira and Belcher,20 in which the frequency is governed by the turbulent forcing, as well as shorter freely propagating patterns following the dispersion relation of gravity-capillary waves. The measurements reported by Savelsberg and van de Water 11 are the only known experimental results that describe the dispersion of the surface patterns on shallow turbulent flows in three-dimensions, but they are focused on grid-generated turbulence which is not representative of the turbulence in open channel shallow flows. The spectral resolution of their spectra was limited.…”