Evolution of disturbance wavepackets in an oscillatory Stokes layer

Thomas, Christian; Davies, Christopher; Bassom, Andrew P.; Blennerhassett, P. J.

doi:10.1017/jfm.2014.291

Cited by 19 publications

(35 citation statements)

References 29 publications

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“…The experimental noise levels that are modelled here are comparable in size to the free stream turbulence levels seen in bypass experiments on turbulent spot generation in flat plate boundary layers (Brandt et al 2004). While a large amount of computational investigation needs to be conducted, at this stage, the calculations of Thomas et al (2014) on the fully nonlinear propagation of two-dimensional wavepackets in a Stokes layer have not shown any tendency towards a such a bypass scenario. However, there will need to be more analysis of the nonlinear stability properties of Stokes layers before a full understanding is reached, but having a linear mechanism bring theoretical predictions closer to experiment is an important result.…”

Section: Introductionmentioning

confidence: 73%

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

Thomas

Blennerhassett²,

Bassom³

et al. 2014

J. Fluid Mech.

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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.

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Section: Introductionmentioning

confidence: 73%

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

Thomas

Blennerhassett²,

Bassom³

et al. 2014

J. Fluid Mech.

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“…More recently, in a series of theoretical and numerical papers, Blennerhassett and Bassom, with Thomas and Davies, have used Floquet analysis and linear simulation to address the stability of a range of related time-periodic flows due to an oscillating plate (Blennerhassett & Bassom 2002;Thomas et al 2010Thomas et al , 2014Thomas et al , 2015, a streamwise oscillating channel (Blennerhassett & Bassom 2006;Thomas et al 2011) or pipe (Blennerhassett & Bassom 2006;Thomas et al 2011Thomas et al , 2012, as well as a torsionally oscillating pipe (Blennerhassett & Bassom 2007;Thomas et al 2012), thereby resolving some of the inconsistencies of previous linear stability analyses and establishing, among others, curves of marginal linear instability for this family of flows. The spatio-temporal impulse response of the Stokes layer is studied by Thomas et al (2014), and the fate of some disturbances when they become nonlinear is also considered.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The spatio-temporal impulse response of the Stokes layer is studied by Thomas et al (2014), and the fate of some disturbances when they become nonlinear is also considered. Luo & Wu (2010) revisit the linear instability of finite Stokes layers, comparing results obtained by instantaneous instability theory in a quasi-steady approach with those from Floquet analysis.…”

Section: Literature Reviewmentioning

confidence: 99%

“…For purely oscillating boundary layers, as investigated by Blennerhassett & Bassom (2002 and Thomas et al (2014), the onset of instability is expected to coincide with absolute instability, while steady plane Poiseuille flow is at most convectively unstable. Therefore, transition between convective and absolute instability is likely to occur when the pulsating base-flow component is increased or equivalently the steady component reduced; this could be investigated using the theory discussed by Brevdo & Bridges (1997).…”

Section: Summary and Future Workmentioning

confidence: 99%

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Linear and nonlinear dynamics of pulsatile channel flow

Pier

Schmid

2017

J. Fluid Mech.

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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.

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“…The simulation results that we were also able to obtain for the nonlinear evolution will only be mentioned in the concluding remarks. A much more thorough and detailed account has previously been given elsewhere 2 .…”

Section: Introductionmentioning

confidence: 99%

The linear impulse response for disturbances in an oscillatory stokes layer

Davies

Thomas

Bassom

et al. 2013

AIP Conference Proceedings

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A brief review is given of numerical simulation results for the evolution of disturbances in a flat oscillatory Stokes layer. A spatially localised form of impulsive forcing is applied to trigger the disturbances. For the linearized case, the disturbance development displays an intriguing family tree-like structure, which involves the birth of successive generations of wavepackets. Although some features of the wavepacket behaviour may be accounted for using a Floquet linear stability analysis, for Fourier modes with prescribed wavenumbers, the discovery of the tree-like structure was completely unexpected. Simulation results were also obtained for nonlinear disturbances, where highly localised spikes were found to develop.

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Evolution of disturbance wavepackets in an oscillatory Stokes layer

Cited by 19 publications

References 29 publications

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

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

Linear and nonlinear dynamics of pulsatile channel flow

The linear impulse response for disturbances in an oscillatory stokes layer

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