Bursting phenomenon in turbulent flows

Abstract

The importance of the phenomenon of bursts in turbulent shear layers has been recognised by fluid dynamicists during the past few years. Kline et al. (1967), Corino & Brodkey (1969), and more recently Grass (1971) noticed the ejection of fluid elements in a random fashion from the wall towards the outer region in a turbulent boundary layer, pipe, and channel respectively, and arrived at the conclusion that these eruptions (now generally known as bursts) might be the triggering mechanism for the turbulent production process. These observations were made in liquids using flow visualisation techniques at rather low Reynolds numbers (Re < 2000). The present work was initiated for the investigation of the bursting phenomenon using a hot wire in air. At low Reynolds numbers and at low velocities, the frequent periods of activity, identified as bursts, could be recognised with a little processing such as differentiating and cutting off the lower frequency part of the signal. But at higher Reynolds numbers and particularly at high velocities, the bursts could be identified only after processing the signal through a narrow band-pass filter or a wave analyser. It was noticed that the number of bursts per second was independent of the frequency beyond a certain mid-frequency setting on the wave analyser, and the bursts were always counted under this condition. Using this method for the identification of bursts, the average time between two bursts (T) was measured in a turbulent boundary layer at various distances from the wall and was found to be constant almost all across the boundary layer for a given flow condition. The time interval (T) between bursts follows a log-normal distribution. When non-dimensionalised with the wall variables, the burst rate u?T/?u_* T / \nuu??T/? (where u?u_*u?? is the friction velocity and ?\nu? the kinematic viscosity) showed a large dependence on Reynolds number, whereas the non-dimensional parameter UT/?UT / \deltaUT/? (where UUU is the free stream velocity and ?\delta? the boundary layer thickness) formed with the outer variables showed negligible dependence. Similar studies carried out in two other shear flows, namely the two-dimensional channel and the wake, also indicated that the burst rate correlated with the outer scales such as the free stream velocity and the width of the wake or channel in the same way as in a boundary layer, the appropriate non-dimensional parameter being independent of the Reynolds number. This suggests that the origin of the bursting phenomenon cannot be traced directly either to the wall or to the outer interface. Preliminary work in grid turbulence indicated the presence of bursts even in the absence of the mean shear, but a suitable non-dimensional burst rate appeared to depend strongly on the Reynolds number based on a macro scale, in the range covered in the present experiments. No conclusions can be drawn unless the experiments are made in fully developed high Reynolds number grid turbulence, which is very difficult to get in the laboratory. It is suggested that these bursts are to be identified with the ‘spotting’ of Kolmogorov (1941) and Landau and the high-frequency intermittency observed by Batchelor & Townsend (1949). They also concluded that the dynamics of the energy balance in a turbulent boundary layer can be understood only on the basis of a coupling between the inner and the outer layers.