The resonant interaction of disturbances at laminar-turbulent transition in a boundary layer

Kachanov, Y. S.; Levchenko, V. Ya.

doi:10.1017/s0022112084000100

Cited by 374 publications

(172 citation statements)

References 15 publications

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“…Indeed, we have confirmed that compressibility effects are negligible by examining the growth rate of the low-amplitude perturbations in the linear and weakly nonlinear regimes. In a recently published work involving the same dataset (Sayadi et al 2013 we found that the evolution of the perturbations in the early transitional regime agrees with the evolution of the perturbations in H-and K-type experiments (Kachanov & Levchenko 1984). In addition, the turbulence statistics in the fully turbulent section of the present simulation compare well with equivalent statistics taken from the incompressible DNS of Wu & Moin (2009).…”

Section: Computational Set-upsupporting

confidence: 82%

“…Both H-and K-type transitions are 280 T. Sayadi, P. J. Schmid, J. W. Nichols and P. Moin examples of transitions in which prescribed low-amplitude waves, confined near the wall, develop without external perturbations. Experiments by Schubauer & Skramstad (1947), Klebanoff, Tidstrom & Sargent (1962) and Kachanov & Levchenko (1984) demonstrated that the interaction of two-dimensional Tollmien-Schlichting (TS) waves with lower-amplitude oblique waves results in three-dimensionality in the flow. This interaction is well described by the linear Orr-Sommerfeld equation and precedes the development of Λ-vortices (Berlin, Wiegel & Henningson 1999;Bake, Fernholz & Kachanov 2000).…”

Section: Introductionmentioning

confidence: 99%

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Reduced-order representation of near-wall structures in the late transitional boundary layer

et al. 2014

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Direct numerical simulations (DNS) of controlled H-and K-type transitions to turbulence in an M = 0.2 (where M is the Mach number) nominally zero-pressuregradient and spatially developing flat-plate boundary layer are considered. Sayadi, Hamman & Moin (J. Fluid Mech., vol. 724, 2013, pp. 480-509) showed that with the start of the transition process, the skin-friction profiles of these controlled transitions diverge abruptly from the laminar value and overshoot the turbulent estimation. The objective of this work is to identify the structures of dynamical importance throughout the transitional region. Dynamic mode decomposition (DMD) (Schmid, J. Fluid Mech., vol. 656, 2010, pp. 5-28) as an optimal phase-averaging process, together with triple decomposition (Reynolds & Hussain, J. Fluid Mech., vol. 54 (02), 1972, pp. 263-288), is employed to assess the contribution of each coherent structure to the total Reynolds shear stress. This analysis shows that low-frequency modes, corresponding to the legs of hairpin vortices, contribute most to the total Reynolds shear stress. The use of composite DMD of the vortical structures together with the skin-friction coefficient allows the assessment of the coupling between near-wall structures captured by the low-frequency modes and their contribution to the total skin-friction coefficient. We are able to show that the low-frequency modes provide an accurate estimate of the skin-friction coefficient through the transition process. This is of interest since large-eddy simulation (LES) of the same configuration fails to provide a good prediction of the rise to this overshoot. The reduced-order representation of the flow is used to compare the LES and the DNS results within this region. Application of this methodology to the LES of the H-type transition illustrates the effect of the grid resolution and the subgrid-scale model on the estimated shear stress of these low-frequency modes. The analysis shows that although the shapes and frequencies of the low-frequency modes are independent of the resolution, the amplitudes are underpredicted in the LES, resulting in underprediction of the Reynolds shear stress.

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Section: Computational Set-upsupporting

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Reduced-order representation of near-wall structures in the late transitional boundary layer

et al. 2014

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“…All the modes have the same constant downstream propagation velocity throughout the whole box. This wave synchronism condition, which should be satis ed in order to have resonant w a v e i n teractions between all these modes, was observed in the experiments of Corke andMangano 1989 andKachanov andLevchenko 1984 . Wall-normal distributions of amplitude and phase of the fundamental and subharmonic modes for the velocity u are shown in Fig. 4.…”

Section: Linear and Weakly Nonlinear Stagesmentioning

confidence: 71%

“…Figure 3 shows the streamwise evolution of amplitude and phase of several harmonics for the streamwise velocity u, compared with the experiment b y Kachanov and Levchenko 1984 , where the Reynolds number is de ned as Re x = xU 1 = and x is the distance from the leading edge of the plate. Goodoverall agreement is obtained between the numerical simulation and the experiment.…”

Section: Linear and Weakly Nonlinear Stagesmentioning

confidence: 99%

Large-Eddy Simulation of Transition to Turbulence in Boundary Layers

Xiaoli

Ronald

Piomelli

1997

Theoretical and Computational Fluid Dynamics

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Large-eddy simulation results for laminar-to-turbulent transition in a spatially developing boundary layer are presented. The disturbances are ingested into a laminar ow through an unsteady suction-and-blowing strip. The ltered, three-dimensional timedependent N a vier-Stokes equations are integrated numerically using spectral, high-order nite-di erence, and three-stage low-storage Runge-Kutta methods. The bu er-domain technique is used for the out ow boundary condition. The localized dynamic model used to parameterize the subgrid-scale stresses begins to have a signi cant impact at the beginning of the nonlinear transition or intermittency region. The ow structures commonly found in experiments are also observed in the present simulation; the computed linear instability modes and secondary instability lambda-vortex structures are in agreement with the experiments, and the streak-like-structures and turbulent statistics compare with both the experiments and the theory. The physics captured in the present LES are consistent with the experiments and the full Navier-Stokes simulation DNS , at a signi cant fraction of the DNS cost. A comparison of the results obtained with several SGS models shows that the localized model gives accurate results both in a statistical sense and in terms of predicting the dynamics of the energy-carrying eddies, without ad hoc adjustments.

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“…Experimentally, Kachanov & Levchenko (1984) and Borodulin, Kachanov & Koptsev (2002) discussed the influence of the initial phase shift between the fundamental wave and the sub-harmonic pair on the resonant amplification. The phase shift has particular importance for the H-type interaction.…”

mentioning

confidence: 99%

Influence of localised smooth steps on the instability of a boundary layer

Lombard

Sherwin

2017

J. Fluid Mech.

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We consider a smooth, spanwise-uniform forward-facing step defined by a Gauss error function of height 4 %-30 % and four times the width of the local boundary layer thickness δ 99 . The boundary layer flow over a smooth forward-facing stepped plate is studied with particular emphasis on stabilisation and destabilisation of the twodimensional Tollmien-Schlichting (TS) waves and subsequently on three-dimensional disturbances at transition. The interaction between TS waves at a range of frequencies and a base flow over a single or two forward-facing smooth steps is conducted by linear analysis. The results indicate that for a TS wave with a frequency F ∈ [140, 160] (F = ων/U 2 ∞ × 10 6 , where ω and U ∞ denote the perturbation angle frequency and free-stream velocity magnitude, respectively, and ν denotes kinematic viscosity), the amplitude of the TS wave is attenuated in the unstable regime of the neutral stability curve corresponding to a flat plate boundary layer. Furthermore, it is observed that two smooth forward-facing steps lead to a more acute reduction of the amplitude of the TS wave. When the height of a step is increased to more than 20 % of the local boundary layer thickness for a fixed width parameter, the TS wave is amplified, and thereby a destabilisation effect is introduced. Therefore, the stabilisation or destabilisation effect of a smooth step is typically dependent on its shape parameters. To validate the results of the linear stability analysis, where a TS wave is damped by the forward-facing smooth steps direct numerical simulation (DNS) is performed. The results of the DNS correlate favourably with the linear analysis and show that for the investigated frequency of the TS wave, the K-type transition process is altered whereas the onset of the H-type transition is delayed. The results of the DNS suggest that for the perturbation with the non-dimensional frequency parameter F = 150 and in the absence of other external perturbations, two forward-facing smooth steps of height 5 % and 12 % of the boundary layer thickness delayed the H-type transition scenario and completely suppressed for the K-type transition. By considering Gaussian white noise with both fixed and random phase shifts, it is demonstrated by DNS that transition is postponed in time and space by two forward-facing smooth steps.

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The resonant interaction of disturbances at laminar-turbulent transition in a boundary layer

Cited by 374 publications

References 15 publications

Reduced-order representation of near-wall structures in the late transitional boundary layer

Reduced-order representation of near-wall structures in the late transitional boundary layer

Large-Eddy Simulation of Transition to Turbulence in Boundary Layers

Influence of localised smooth steps on the instability of a boundary layer

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