Experiments on critical Reynolds number and global instability in roughness-induced laminar–turbulent transition

Abstract

The effects of isolated, cylindrical roughness elements on laminar–turbulent transition in a flat-plate boundary layer are investigated in a laminar water channel. Our experiments aim at providing a comparison to global linear stability theory (LST) by means of hot-film anemometry and particle image velocimetry. Although the critical Reynolds number from theory does not match the transition Reynolds number observed in experiments, there are distinct experimental observations indicating a changeover from purely convective to absolute/global instability very close to the critical Reynolds number predicted by theory. Forcing with a vibrating wire reveals the evolution of the system dynamics from an amplifier to a wavemaker when the critical Reynolds number is exceeded. The mode symmetry is varicose for thick roughness elements and a changeover from varicose to sinuous modes is observed at the critical Reynolds number for thin roughness elements. Therefore, most predictions by global LST can be confirmed, but additional observations in the physical flow demonstrate that not all features can be captured adequately by global LST.

Experimental observation of frequency lock-in of roughness-induced instabilities in a laminar boundary layer

“…In contrast to convective instabilities, a global instability is intrinsic and does not depend on external periodic forcing (Huerre & Monkewitz 1990;Theofilis 2003;Chomaz 2005). In the present work, the set-up of Bucci et al (2018) and Puckert & Rist (2018a) is reproduced to investigate the nonlinear interaction between sinuous and varicose modes and to suggest synchronization as an important nonlinear mechanism in boundary layers.…”

“…Boundary-layer thickening in the corners of the test section is reduced by suction through a small gap between the flat plate and the side walls. More details on the flow facility and the fluctuation levels inside the boundary layer can be found in Wiegand (1996) and Puckert & Rist (2018a).…”

“…Recall from the previous section that the aspect ratio is the diameter d of the cylindrical roughness divided by the roughness height k. The choice of η allows for an evaluation of three important configurations which are already known from the 3-D global linear stability analyses of Loiseau et al (2014) and Bucci et al (2018). Parameter studies on the aspect ratio have already been done by Loiseau et al (2014) and Puckert & Rist (2018a). As discussed in the introduction, the first unstable global mode is sinuous for configurations with small aspect ratios (of the order of η 1) and varicose instabilities for configurations with large aspect ratios (of the order of η 3).…”

“…In the present work, we distinguish between the critical Reynolds number (3-D global instability) and the transition (tripping to turbulence) Reynolds number. Puckert & Rist (2018a) showed that the critical Reynolds number from 3-D global LST is typically larger than the transition Reynolds number. Bucci et al (2018) explained the subcritical instability in the experiment as a result of quasi-resonance of a varicose, stable global mode.…”

The Simulation of Vortex Structures Induced by Different Local Vibrations at the Wall in a Flat-Plate Laminar Boundary Layer

“…The effects of isolated, cylindrical roughness elements on laminar-turbulent transition in a flat-plate boundary layer were investigated in a laminar water channel. Most predictions by global linear stability theory could be confirmed, but additional observations in the physical flow demonstrated that not all features could be captured adequately by global linear stability theory [10].…”