Tollmien-Schlichting-wave resonant mechanism for subharmonic-type transition

Zel'man, M. B.; Maslennikova, I. I.

doi:10.1017/s0022112093003830

Cited by 59 publications

(16 citation statements)

References 35 publications

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“…The double-exponential resonant growth of three-dimensional subharmonics, found in previous, less strict weakly nonlinear theory by Volodin & Zelman (1978), has been corroborated. At a fully nonlinear stage of development the disturbances exhibited rapid explosive growth, which was, again, qualitatively similar to that found by other theoretical approaches (see Spalart & Yang 1987;Zelman & Maslennikova 1993). Approximately the same theoretical approach as that of Goldstein & Lee (1992) was applied by Mankbadi et al (1993) to the Blasius boundary layer.…”

supporting

confidence: 83%

“…This behaviour is explained by the phase locking phenomenon which, according to Wu et al (2007), can induce wavelength shortening and hence affect the phase speed at stages of the intensive resonant interaction. It is known from theoretical studies by Herbert (1988) and Zelman & Maslennikova (1993) that subharmonic resonance is also able to amplify spanwise-wavenumberdetuned three-dimensional subharmonics within a very broad band of spanwise wavenumbers. Experiments by Borodulin et al (2002d) observed the highest amplification of the detuned three-dimensional subharmonics at values close to the exact resonant spanwise wavenumbers for the frequency-tuned case.…”

Section: Mechanism For Rapid Amplification Of Low-frequency Modes At mentioning

confidence: 99%

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Weakly nonlinear stages of boundary-layer transition initiated by modulated Tollmien–Schlichting waves

et al. 2013

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Weakly nonlinear interactions involving amplitude-modulated Tollmien-Schlichting waves in an incompressible, two-dimensional aerofoil boundary layer are investigated experimentally. Selected resonant regimes are examined with emphasis on the regimes where more than one fundamental Tollmien-Schlichting (TS) wave is present in the flow. The experiments were performed on an NLF-type aerofoil section for glider applications. Disturbances with controlled frequency-spanwise-wavenumber spectra were excited in the boundary layer and studied by phase-locked hot-wire measurements. The results show that nonlinear mechanisms connected with the steepening of the primary TS wave modulation do not play any significant role in the transition scenarios studied. It is also shown that modulations of the twodimensional fundamental waves tend to generate additional modes at modulation frequency. These low-frequency disturbances are found to be produced by a nonresonant quadratic combination of spectral components of the primary, modulated TS wave. The investigations show that the efficiency of the process is higher for three-dimensional low-frequency modes in comparison with two-dimensional modes. Thus, the emergence of three-dimensionality for the low-frequency waves does not require any resonant interactions. In a subsequent nonlinear stage, the self-generated detuned subharmonics are found to be strongly amplified due to resonant interactions with the primary TS waves. The sequence of weakly nonlinear mechanisms found and investigated here seems to be the most likely route to the laminar-turbulent transition, at least for two-dimensional boundary layers of aerofoils with a long extent of laminar flow and in a 'natural' disturbance environment.

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supporting

confidence: 83%

Section: Mechanism For Rapid Amplification Of Low-frequency Modes At mentioning

confidence: 99%

Weakly nonlinear stages of boundary-layer transition initiated by modulated Tollmien–Schlichting waves

et al. 2013

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“…The reason for this behavior can be found from the explicit formulas for the coefficients S k presented in Ref. 24. A simplified analysis of the corresponding amplitude equations has shown that, similar to the experimental observations, the resonant interaction gives the same growth rates of the two modes at the parametric stage of disturbance development under discussion.…”

Section: Predominance Of Low-frequency Mode Amplitudes: Theoretical Esupporting

confidence: 52%

“…3 while it is presented in much more detail in Ref. 24. The application of the WNT techniques gives the system of equations for the amplitudes of the interacting waves.…”

Section: Weakly Nonlinear Stability Theorymentioning

confidence: 99%

Detuned resonances of Tollmien-Schlichting waves in an airfoil boundary layer: Experiment, theory, and direct numerical simulation

et al. 2012

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Previous studies of the interaction between boundary layer streaks and Tollmien-Schlichting (TS) waves have shown puzzling effects. Streaks were shown to reduce the growth rate of primary TS waves and, thereby, to delay transition; however, they can also promote transition by inducing a secondary instability. The outcome of the interaction depends on the spanwise wavelength and intensity of the streaks as well as on the amplitude of the TS waves. A Floquet analysis of secondary instability is able to explain many of these features. The base state is periodic in two directions: it is an Ansatz composed of a saturated TS wave (periodic in x) and steady streaks (periodic in z). Secondary instability analysis is extended to account for the doubly periodic base flow. Growth rate computations show that, indeed, the streak can either enhance or diminish the overall stability of the boundary layer. The stabilizing effect is a reduction in the growth rate of the primary two-dimensional TS wave; the destabilizing effect is a secondary instability. Secondary instability falls into two categories, depending on the spanwise spacing of the streaks. The response of one category to perturbations is dominated by fundamental and subharmonic instability; the response of the other is a detuned instability. Previous studies of the interaction between boundary layer streaks and Tollmien-Schlichting TS waves have shown puzzling effects. Streaks were shown to reduce the growth rate of primary TS waves and, thereby, to delay transition; however, they can also promote transition by inducing a secondary instability. The outcome of the interaction depends on the spanwise wavelength and intensity of the streaks as well as on the amplitude of the TS waves. A Floquet analysis of secondary instability is able to explain many of these features. The base state is periodic in two directions: it is an Ansatz composed of a saturated TS wave periodic in x and steady streaks periodic in z. Secondary instability analysis is extended to account for the doubly periodic base flow. Growth rate computations show that, indeed, the streak can either enhance or diminish the overall stability of the boundary layer. The stabilizing effect is a reduction in the growth rate of the primary two-dimensional TS wave; the destabilizing effect is a secondary instability. Secondary instability falls into two categories, depending on the spanwise spacing of the streaks. The response of one category to perturbations is dominated by fundamental and subharmonic instability; the response of the other is a detuned instability.

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“…In the simulations, however, the asymmetric subharmonic resonance can be strongly influenced by changing the phase relation between fundamental and subharmonic disturbances. The influence of the phase relation on the resonance mechanism of one particular triad was previously studied for incompressible boundary layers by Zelman & Maslennikova (1993) and for a Mach 3 boundary layer by Zengl (2005). In both investigations, it was possible to delay transition by changing the phase to a specific value.…”

Section: Simulation Of Asymmetric Subharmonic Resonancementioning

confidence: 99%

Numerical Investigation of Transition in Supersonic Boundary Layers Using DNS and LES

Fasel¹,

Husmeier²,

Mayer³

2008

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Tollmien-Schlichting-wave resonant mechanism for subharmonic-type transition

Cited by 59 publications

References 35 publications

Weakly nonlinear stages of boundary-layer transition initiated by modulated Tollmien–Schlichting waves

Weakly nonlinear stages of boundary-layer transition initiated by modulated Tollmien–Schlichting waves

Detuned resonances of Tollmien-Schlichting waves in an airfoil boundary layer: Experiment, theory, and direct numerical simulation

Numerical Investigation of Transition in Supersonic Boundary Layers Using DNS and LES

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