An optical study of turbulence

Abstract

This paper describes theoretical and experimental work carried out at the Cavendish Laboratory of the University of Cambridge. The main object of the work was to develop a new technique for measuring the structure of fluid turbulence.A parallel beam of light is passed through the turbulent region, containing refractive index fluctuations, and analyzed on exit by gratings of periodic transmissivity. Two forms of analysis yield (a) the spatial power spectrum of the refractive index fluctuations in the turbulence, and (b) the velocity distribution within the beam aperture. The method does not disturb the fluid physically, does not depend on the existence of a mean flow velocity, and works well in liquids.One of the limitations of this single-beam method is that it produces information averaged along the path length of the beam in the turbulence, and to overcome this a cross-beam technique, using two beams intersecting at right-angles, has been developed in theory. This method gives the spatial power spectrum of the refractive index fluctuations, as does the single beam method, but the results are characteristic only of the volume of intersection of the beams.The paper first discusses the theory of the single-beam and crossed-beam techniques, and then experimental results obtained with the single-beam method.The turbulent region investigated was a rectangular tank of water, heated from below and cooled from above, producing convective turbulence of high Rayleigh number (4·1 × 108), a system difficult to analyze by conventional methods of measurement, such as the hot-wire anemometer.Spectral density functions (power spectra) of refractive index, and hence in this case temperature fluctuations, have been measured, as have velocity distributions. Statistical analysis of the results also gives useful information about the Eulerian time scale of the turbulent field.