Direct simulation of transition in an oscillatory boundary layer

Quantitative results for the linear stability of planar Stokes layers subject to small, high frequency perturbations are obtained for both a narrow channel and a flow approximating the classical semi-infinite Stokes layer. Previous theoretical and experimental predictions of the critical Reynolds number for the classical flat Stokes layer have differed widely with the former exceeding the latter by a factor of two or three. Here it is demonstrated that only a one percent perturbation, at an appropriate frequency, to the nominal sinusoidal wall motion is enough to result in a reduction of the theoretical critical Reynolds number of as much as 60%, bringing the theoretical conditions much more in line with the experimentally reported values. Furthermore, within the various experimental observations there is a wide variation in reported critical conditions and the results presented here may provide a new explanation for this behaviour.

Section: Introductionmentioning

confidence: 95%

The linear stability of a Stokes layer subjected to high-frequency perturbations

Thomas

Blennerhassett²,

Bassom³

et al. 2014

“…Transition to turbulence has been investigated by direct numerical simulations of the Stokes boundary layer by Vittori & Verzicco (1998), Costamagna et al (2003) and Ozdemir et al (2014). Tuzi & Blondeaux (2008) have addressed the intermittent turbulent regime observed in a pulsating pipe.…”

Section: Literature Reviewmentioning

confidence: 99%

Linear and nonlinear dynamics of pulsatile channel flow

Pier

Schmid

2017

The dynamics of small-amplitude perturbations as well as the regime of fully developed nonlinear propagating waves is investigated for pulsatile channel flows. The timeperiodic base flows are known analytically and completely determined by the Reynolds number Re (based on the mean flowrate), the Womersley number Wo (a dimensionless expression of the frequency) and the flowrate waveform. This paper considers pulsatile flows with a single oscillating component and hence only three non-dimensional control parameters are present. Linear stability characteristics are obtained both by Floquet analyses and by linearized direct numerical simulations. In particular, the long-term growth or decay rates and the intracyclic modulation amplitudes are systematically computed. At large frequencies (mainly Wo 14), increasing the amplitude of the oscillating component is found to have a stabilizing effect, while it is destabilizing at lower frequencies; strongest destabilization is found for Wo ≃ 7. Whether stable or unstable, perturbations may undergo large-amplitude intracyclic modulations; these intracyclic modulation amplitudes reach huge values at low pulsation frequencies. For linearly unstable configurations, the resulting saturated fully developed finite-amplitude solutions are computed by direct numerical simulations of the complete Navier-Stokes equations. Essentially two types of nonlinear dynamics have been identified: "cruising" regimes for which nonlinearities are sustained throughout the entire pulsation cycle and which may be interpreted as modulated Tollmien-Schlichting waves, and "ballistic" regimes that are propelled into a nonlinear phase before subsiding again to small amplitudes within every pulsation cycle. Cruising regimes are found to prevail for weak baseflow pulsation amplitudes, while ballistic regimes are selected at larger pulsation amplitudes; at larger pulsation frequencies, however, the ballistic regime may be bypassed due to the stabilizing effect of the base-flow pulsating component. By investigating extended regions of a multi-dimensional parameter space and considering both two-dimensional and threedimensional perturbations, the linear and nonlinear dynamics are systematically explored and characterized.

“…Consequently, the idealised analytical flow has quite different stability properties from those seen in practice. For example, the perturbation growth can be amplified by wall roughness (Blondeaux & Vittori 1994;Vittori & Verzicco 1998) or a base flow variation (Thomas et al 2015).…”

Section: Introductionmentioning

confidence: 99%

Transient growth of perturbations in Stokes oscillatory flows

Biau

2016

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Oscillatory Stokes flows, with zero mean, are subjected to subcritical transition to turbulence. The maximal energy growth of perturbations is computed in the subcritical regime through an optimisation method. The results show strong amplifications during half a period. The energy transfer from the base flow involves an Orr mechanism with two-dimensional vorticity waves, and the maximum energy scales exponentially with the Reynolds number. Nonlinear simulations show that low-energy perturbations are sufficient to trigger turbulent flow.