Late-Stage Transitional Boundary-Layer Structures. Direct Numerical Simulation and Experiment

Abstract.

This paper is devoted to direct comparisons of related, detailed experimental and numerical studies of the non-linear, late stages of laminar-turbulenttransition in a boundary layer including flow breakdown and the beginning offlow randomization. Preceding non-linear stages of the transition process arealso well documented and compared with previous studies. The experiments wereconducted with the help of a hot-wire anemometer. The numerical study wascarried out by direct numerical simulation (DNS) of the flow employing theso-called spatial approach. Both the experiments and the DNS were performed atcontrolled disturbance conditions with an excitation of instability waves inthe flat-plate boundary layer. In the two cases, the primary disturbanceconsists of a time-harmonic, two-dimensional Tollmien--Schlichting wave thathas a very weak initial spanwise modulation. Despite somewhat differentinitial disturbance conditions used in the experiment and simulation, thesubsequent flow evolution at late non-linear stages is found to be practicallythe same. Detailed qualitative and quantitative comparisons of theinstantaneous velocity and vorticity fields are performed for twocharacteristic stages of the non-linear flow breakdown: (i) “one-spike stage” and (ii) “three-spike stage.” The twoapproaches clearly show in detail the process of development of the Γ-structure, a periodical formation of ring-like vortices, the evolution of the surrounding flow field, and the beginning of flowrandomization. In particular, it is found experimentally and numerically thatthe ring-like vortices (associated with the well-known spikes) induce somerather intensive positive velocity fluctuations (positive spikes) in thenear-wall region which have the same scales as the ring-like vortices and propagate downstream with the same high (almost free-stream) speed. The positive spikes form a new high-shear layer in the near-wall region. In the experiment the induced near-wall perturbationshave a significant irregular low-frequency component. These non-periodicalmotions play an important role in the process of flow randomization and finaltransition to turbulence that starts under the ring-like vortices in thevicinity of the peak position.