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Resonant interaction of wave packets in a boundary layer

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Abstract

The space-time evolution of resonance-coupled triads of wave packets in a Blasius boundary layer is studied within the framework of weakly nonlinear stability theory. The amplitude behavior of the packet envelopes is determined in relation to their initial shape, the carrier frequency and the region of propagation. As in the case of triads with a discrete spectrum, interaction leads to parametric pumping of the low-frequency fluctuations and explosive nonlinear growth of the packet maxima. The space-time evolution characteristics are expressed in the deformation of the shape and the spectra of the disturbance. Parts of the envelopes are amplified, depending on the local values of the parameters. This leads to sharp discrimination of the peaks and the equalization of their propagation velocities. These effects make it possible to explain the broadening of the spectrum, the stable distribution of the visualization pattern, and the appearance of irregularities in the oscillograms observed in the S transition. In order to analyze the nonlinear evolution of a disturbance initiated by an instantaneous point source, the interaction of a two-dimensional wave train with variable carrier frequency and pairs of three-dimensional low-frequency packets is examined. (The train frequency corresponds to the local maximum of the linear growth rate with respect to R.) The possibility of the progressive parametric excitation of fluctuations over the entire band of frequency parameters is established. This may explain the acceleration of the transition process in the presence of an impulsive disturbance of the boundary layer.

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Authors and Affiliations

  1. Novosibirsk

    M. B. Zel'man & B. V. Smorodskii

Authors
  1. M. B. Zel'man
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  2. B. V. Smorodskii
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 67–71, November–December, 1988.

The authors are grateful to I. I. Maslennikov for useful discussions.

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Zel'man, M.B., Smorodskii, B.V. Resonant interaction of wave packets in a boundary layer. Fluid Dyn 23, 857–861 (1988). https://doi.org/10.1007/BF01051819

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  • DOI: https://doi.org/10.1007/BF01051819

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