Three-wave resonance interaction of disturbances in a boundary layer

Volodin, A. G.; Zel'man, M. B.

doi:10.1007/bf01050233

Cited by 21 publications

(7 citation statements)

References 6 publications

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“…Such behavior of the fundamental wave and the subharmonic agrees with the results of calculations of the nonlinear resonant interaction of waves in a three-dimensional triplet [14].…”

Section: Development Of Finite-amplitude Perturbations In the Case Ofsupporting

confidence: 85%

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Formation of three-dimensional structures on the transition to turbulence in boundary layers

1984

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“…Such behavior of the fundamental wave and the subharmonic agrees with the results of calculations of the nonlinear resonant interaction of waves in a three-dimensional triplet [14].…”

Section: Development Of Finite-amplitude Perturbations In the Case Ofsupporting

confidence: 85%

“…In [12], it is asserted that there is complete agreement between the experimental results and the theoretical model of Craik [13,14]. In [12], it is asserted that there is complete agreement between the experimental results and the theoretical model of Craik [13,14].…”

mentioning

confidence: 91%

Formation of three-dimensional structures on the transition to turbulence in boundary layers

1984

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“…A systematic theory of the resonant interaction of inviscid Rayleigh waves developing in a boundary layer with a weak adverse pressure gradient was developed by Goldstein & Lee (1992). 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).…”

mentioning

confidence: 86%

“…For nonlinear stages of boundary-layer transition, the first theories of resonant interactions of TS waves were developed by Maseev (1968) and Craik (1971) and later by Herbert (1975), Volodin & Zelman (1978), Smith & Stewart (1987), Goldstein & Lee (1992), Mankbadi, Wu & Lee (1993) and Wu (1995) and in a great number of other subsequent studies; for a review see Borodulin, Kachanov & Koptsev (2002b), for example. The classical Craik's triad consists of a two-dimensional (2D) primary (fundamental) instability wave, with frequency f 1 , having relatively large amplitude and two weak oblique subharmonic waves, with frequency f s = f 1 /2, propagating at angles to the mean flow direction with the same values but opposite signs.…”

Section: Introductionmentioning

confidence: 98%

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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“…A similar anomalous behavior is also characteristic of the boundary layer transition to turbulent state in the sub-harmonic regime [3].…”

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confidence: 60%

Harmonics of Tollmien — Schlichting waves in a compressible boundary layer

Петров

2008

Thermophys. Aeromech.

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The harmonics of Tollmien-Schlichting waves in a compressible boundary layer of a plate are computed with the aid of nonlinear parabolized stability equations. At the (downstream) growth of the second harmonic amplitude up to the values of the order of the basic harmonic amplitude, the amplification rate of the latter is shown to increase abruptly. A similar rapid deviation from the results of the linear theory characterizes the onset of the boundary-layer transition to turbulent state. Computations are carried out for the Mach numbers М = 0.01 and 2.

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Three-wave resonance interaction of disturbances in a boundary layer

Cited by 21 publications

References 6 publications

Formation of three-dimensional structures on the transition to turbulence in boundary layers

Formation of three-dimensional structures on the transition to turbulence in boundary layers

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

Harmonics of Tollmien — Schlichting waves in a compressible boundary layer

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