Inverse transition from turbulent to laminar flow in a two-dimensional channel

Abstract

An experimental investigation on inverse transition from turbulent to laminar flow in a two-dimensional channel was carried out. The experiments were conducted in the inverse transition region at Reynolds numbers of 525, 865, 980, and 1250, based on half the channel height and the averaged mean velocity. At all these Reynolds numbers, the initially turbulent mean velocity profiles slowly tend to become laminar. The velocity fluctuations — u′2‾\overline{u'^2}u′2 and v′2‾\overline{v'^2}v′2 averaged over the height of the channel decrease exponentially with distance downstream. However, u′v′‾\overline{u'v'}u′v′ does not decay exponentially and seems to become zero at a reasonably well-defined point. During inverse transition, the velocity correlation u′u′′v′v′‾\overline{u'u''v'v'}u′u′′v′v′ also decreases as the flow moves downstream, and Lissajous figures taken with u' and v' signals show qualitatively a change in phase between these two quantities. There is approximate similarity between u′2‾\overline{u'^2}u′2 profiles if the location and the value of u′2‾\overline{u'^2}u′2 at the maximum are taken as the basic parameters. The turbulent energy balance in the integrated form (across the height of the channel) shows that there is some kind of equilibrium in the flow during the decay process, and this is supported to some extent by the spectrum measurements. The spectrum of u′2‾\overline{u'^2}u′2 is roughly similar at all stations, and the non-dimensional spectrum is exponential in wave number. All the turbulent quantities, when plotted in proper coordinates, indicate that there is a definite critical Reynolds number of 1400 ± 50 for inverse transition in the channel.