Is Tollmien-Schlichting wave necessary for transition of zero pressure gradient boundary layer flow?

Abstract

Comprehensive understanding of the routes of instability and transition for many flows is not complete yet. For a zero pressure gradient (ZPG) boundary layer, linear spatial theory predicted Tollmien-Schlichting (TS) waves, which have been experimentally verified by vortically exciting the flow by a monochromatic source. This is the well-known frequency response of dynamical system theory. Natural transition in real flows occurs due to polychromatic excitation, and to simulate such transition, the ZPG boundary layer has been excited via an impulse response in some of our recent direct numerical simulations. Such impulse responses cause transition even when TS waves are not excited. In the present exercise, we show the theoretical basis of natural transition by spatiotemporal stability analysis, as used in the work of Sengupta et al. [“Spatiotemporal growing wave fronts in spatially stable boundary layers,” Phys. Rev. Lett. 96(22), 224504 (2006)], by invoking finite start-up of the frequency response to wall excitation. There appear to be different instability mechanisms active for the frequency and the impulse responses to localized wall excitation. Here, we show that in both the frequency and impulse responses, the spatiotemporal wave-front (STWF) is the common element. Additionally, we also consider cases, where following different start-ups, the wall excitation remains constant, which also show the presence of the STWF. The presented results for the ZPG boundary layer show that the TS wave is not necessary for transition to turbulence and help us to re-evaluate our understanding of the transition mechanism for this canonical flow.

Nonmodal nonlinear route of transition to two-dimensional turbulence

“…The initial STWF transforms into a turbulent spot creating additional STWFs, which merge downstream to create the turbulent flow. The free-stream excitation case considered here is distinctly different from the wall-excitation case [35], as the local solution and the STWF continually interact for the former, while for the latter, these two components do not interact after the onset of STWF. As a consequence, the linear and nonlinear solutions are completely different for the free-stream excitation case.…”

“…[11,19,23,24]. Recently, it has been shown that the STWF is the definitive causal mechanism for the onset of transition to turbulence, irrespective of the nature of the imposed wall excitation [35]. For the same equilibrium flow in Refs.…”

“…It has been shown in Ref. [35] that transition can occur without the modal component. In the same way, here we show transition without TS waves for free-stream excitation by highly accurate computing, treating this as a global receptivity problem for an aperiodic vortex.…”

Combined effects of amplitude, frequency and bandwidth on wavepackets in laminar turbulent transition

“…Bhaumik et al (2017) and Sharma et al (2018) found that the modulation characteristics and consequently the features of the wavepacket change when one shifts from an impulsive monochromatic onset of excitation to a gradual monochromatic excitation. In the case of switching the exciter on and off (finite onset and termination of the exciter), it would result in the evolution of two subsequently phase-shifted and time-delayed spatio-temporal wavepackets as noted in Bhaumik (2013) and Sundaram et al (2019) for 2D disturbances -one wavepacket when the exciter is switched on, and another when the exciter is switched off, while the spatial Tollmien-Schlichting (TS) wavepacket/wavetrain recedes back.…”

Prediction of Roughness Effects on Wind Turbine Aerodynamics

“…Surface roughness has a rather complex influence on airfoil aerodynamics, since it can also effect the transition behavior. For a smooth surface, the boundary layer transition usually occurs with involvement of the Tollmein-Schlichting waves as the primary instabilities [4]. It is known that surface roughness alters the transition behavior due to the changes in the underlying mechanism and can also trigger an earlier transition, the modes of which being strongly dependent on the type of roughness.…”