The Mechanism Of Breakdown In Laminar-turbulent Transition And The Characteristics Of Turbulence In An Incompressible Boundary Layer On A Flat Plate

Temporal mode direction numerical simulation (DNS) has been done for the process of laminar-turbulent transition and the fully developed turbulence in an incompressible boundary layer on a flat plate. Then studies of the essential mechanism of breakdown in laminar-turbulent transition and important characteristics of the fully developed turbulence have been carried on. The effects of different initial disturbances were discussed on the duration of transition and turbulent boundary-layer thickness. Analytical results obtained include:1. When the amplitudes of the disturbances in laminar flow become larger, such that the mean flow profiles is modified to such an extent that the unstable zone encircled by neutral curves is appreciably enlarged and the maximum amplification rate also becomes appreciably larger, many more harmonics will be quickly excited, and their amplitudes will also increase quickly. The direct consequence is that the Reynolds-stresses and their corresponding normal-wise gradients both become large, which in turn further modifies the mean flow profile, in a much faster pace, leading to the breakdown of the laminar flow with a catastrophic nature.2. If the oblique waves in the initial disturbances did not form symmetrical pairs, the subsequent span-wise mean velocities would, in general, be nonzero due to non-linear interaction. It can have a great effect on the linear stability characteristics. The phenomenon may not occur in experiments, because the boundary conditions in the experiment may prohibit it to happen, which is different from those in direction numerical simulation, in which different span-wise boundary condition is applied. The non-zero span-wise mean velocity in direction numerical simulation is apparently not random, which implies that turbulence determined by direct numerical simulation is not a random process.3. Under a given computational domain, the durations of transition induced by different initial disturbances are comparatively closed. However, under different computational domains, they are different with one another. On the other hand, under a given computational domain, if the initial disturbances were dissymmetrical in span-wise direction, the ratio of the time-averaged boundary-layer thickness after transition to the boundary-layer thickness of the beginning of breakdown process in the transition,δ_e/δ_b, shows the same growth rate with respect to time, which is independent of the initial disturbances. Comparatively, if the initial disturbances were symmetric in span-wise direction, theirδ_e/δ_b with respect to time show the similar growth rate. However, compared to the initial symmetric disturbances, the dissymmetrical initial disturbances will induce the different growth trend.4. The normal-wise distribution of several statistical mean values of disturbances of a fully developed turbulence, such as the mean flow profile, the non-dimensional mean velocity defect, and the root mean square of the fluctuating velocity, as well as the Reynolds stresses, bore similarity in nature, which might be used to simplify the computation of turbulent flows. However, from the end of transition to the fully developed state of turbulence, there was a transient period, during which the similarity did not hold. The coherent structures, which are characterized by the quasi-stream-wise vortexes or vortex pairs, were found to exist in the wall region of a turbulent boundary layer.