Bursting Phenomenon near the Wall in Open-channel Flows and its Simple Mathematical Model

Abstract

In this paper we propose a new evaluation method for the bursting period, on the basis of the phenomenological consideration that the number of the occurrences of interaction-like motions should be removed from those of the ejection or the sweep events in the sorted Reynolds-stress fluctuating signals. Then, it is confirmed by this method that the mean bursting period in open-channel flows may be universally expressed by outer rather than inner parameters, and that its probability distribution becomes log-normal, irrespective of the Reynolds and the Froude numbers, as well as the wall roughness. Next, in order to explain even quantitatively the bursting process or the turbulent structure in the wall region, we propose a simple mathematical model on the basis of the Einstein-Li model and also the knowledge of the bursting-period characteristics obtained above. Though the present model is inherently quasi-two-dimensional and quasi-linear, this model can describe fairly well some distributions of mean-velocity, turbulence intensities and Reynolds stress. In particular, it can satisfactorily explain a sequence of the bursting process.