Effect of Local Periodic Disturbance on Mixing Layer Downstream of Two-Dimensional Jet (Spatial Structure and Quantitative Representation of Laminar-Turbulent Transition Process)

Abstract

The laminar-turbulent transition of a mixing layer induced by oscillating flat plates at an exit of a two-dimensional nozzle was experimentally investigated. The mixing layer was formed between the jet, which issued from the nozzle and the surrounding quiescent fluid. The plates oscillated vertically in relation to the mean flow. The oscillation frequency was two orders of magnitude smaller than the fundamental frequency of the velocity fluctuation. Mean and fluctuating velocity components in the streamwise and normal directions were measured by hot-wire anemometers. In the oscillating state, the same phenomenon as in the natural transition process appeared more upstream. In the early stage within the nonlinear region, the growth of fluctuating velocity attenuated and the Reynolds shear stress component decreased. The decrease in their production rate due to the expansion of the mixing layer contributed to the attenuation and decrease. The probability of the streamwise and normal fluctuating velocity components taking the same sign, increased or decreased in accordance with the increase and decrease of the Reynolds shear stress component. The randomness factor, which had been proposed by Sato, appeared to be a reasonable indicator of the present transition process, especially in the process in which the periodic velocity fluctuation became irregular. However, this factor certainly indicated the same value at two streamwise positions.

Randomness Representation in Turbulent Flows with Kolmogorov Complexity (In Mixing Layer)

“…6, the contour map of the randomness factor, z, in the x-y plane is shown. The randomness factor was also shown in the range of x/h ≦ 14 in the previous report (1) , but is shown here in x/h ≦ 20. As a guide of the region where the mean velocity gradient -∂U /∂ y exits, positions where U/U m equals 0.99 near the centerline (y/(h/2) = 0) and 0.05 in the outer (large y) region are drawn as white solid lines, where U m is the velocity on the local centerline.…”

“…For irregularities from the transition process to developed turbulence of the mixing layer, one of the authors (1) pointed out the effectiveness and disadvantage of the randomness factor (2) based on the distribution of the power spectrum of the turbulence. The present study follows a previous study and examines the problem in the irregularities from the viewpoint of "Kolmogorov complexity" (3) about an object, which recently has been studied in various fields.…”

“…We measured the distributions of the mean and fluctuating velocities, spreading of the jet, production, convection and dissipation rates of the fluctuating energy (49) . We also revealed the progression of the laminar-turbulent transition process in the flow-normal direction, and obtained the randomness factor (1) which was proposed by Sato (2) as an indicator of the transition progress, then examined its validity in the transition process.…”

“…As described in the previous section, Sato et al proposed a randomness factor defined as the ratio of the energy of the continuous spectrum to the total energy in the power spectrum distribution of the velocity fluctuations (2) . In the previous report, the power spectrum and the probability density function of the velocity fluctuation were obtained, and the applicability of the randomness factor to the transition progress was examined (1) . As a result, the process appeared first where the line spectral region increased gradually and the periodical fluctuation became dominant.…”

“…Such upstream regularity is due to the smallness of the velocity fluctuation. Details of the transition progress including the fact that the flow just behind the nozzle exit is still laminar were given in the previous report (1) (49) .…”