Three-dimensional wave packets in a compressible boundary layer

Eric Forgoston, Anatoli Tumin

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

Abstract

A three-dimensional wave packet generated by a local disturbance in a two-dimensional hypersonic boundary layer flow is studied with the aid of the previously solved initial-value problem. The solution to this problem can be expanded in a biorthogonal eigenfunction system as a sum of modes consisting of continuous and discrete spectra of temporal stability theory. A specific disturbance consisting of an initial temperature spot is considered, and the receptivity to this initial temperature spot is computed for both the two-dimensional and three-dimensional cases. Using previous analysis of the discrete and continuous spectrum, the inverse Fourier transform is computed numerically. The two-dimensional inverse Fourier transform is calculated for two discrete modes: Mode F and Mode S. The Mode S result is compared with an asymptotic approximation of the Fourier integral, which is obtained using the Gaussian model as well as the method of steepest descent. It is shown that the method of steepest descent provides an excellent approximation to the more computationally intensive numerical evaluation of the inverse Fourier transform. Additionally, the three-dimensional inverse Fourier transform is found using an asymptotic approximation of the Fourier integral. A main feature of the resulting three-dimensional wave packet is its two-dimensional nature, which arises from an association of Mode S with Mack's second mode.

Original languageEnglish
Article number104103
JournalPhysics of Fluids
Volume18
Issue number10
DOIs
StatePublished - 1 Oct 2006

Fingerprint

compressible boundary layer
wave packets
continuous spectra
descent
disturbances
approximation
two dimensional boundary layer
hypersonic boundary layer
boundary layer flow
boundary value problems
eigenvectors
temperature
evaluation

Keywords

  • Boundary layer turbulence
  • Compressible flow
  • Eigenvalues and eigenfunctions
  • Flow instability
  • Fourier transforms
  • Hypersonic flow
  • Initial value problems
  • Laminar flow
  • Laminar to turbulent transitions
  • Waves

Cite this

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abstract = "A three-dimensional wave packet generated by a local disturbance in a two-dimensional hypersonic boundary layer flow is studied with the aid of the previously solved initial-value problem. The solution to this problem can be expanded in a biorthogonal eigenfunction system as a sum of modes consisting of continuous and discrete spectra of temporal stability theory. A specific disturbance consisting of an initial temperature spot is considered, and the receptivity to this initial temperature spot is computed for both the two-dimensional and three-dimensional cases. Using previous analysis of the discrete and continuous spectrum, the inverse Fourier transform is computed numerically. The two-dimensional inverse Fourier transform is calculated for two discrete modes: Mode F and Mode S. The Mode S result is compared with an asymptotic approximation of the Fourier integral, which is obtained using the Gaussian model as well as the method of steepest descent. It is shown that the method of steepest descent provides an excellent approximation to the more computationally intensive numerical evaluation of the inverse Fourier transform. Additionally, the three-dimensional inverse Fourier transform is found using an asymptotic approximation of the Fourier integral. A main feature of the resulting three-dimensional wave packet is its two-dimensional nature, which arises from an association of Mode S with Mack's second mode.",
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Three-dimensional wave packets in a compressible boundary layer. / Forgoston, Eric; Tumin, Anatoli.

In: Physics of Fluids, Vol. 18, No. 10, 104103, 01.10.2006.

Research output: Contribution to journalArticleResearchpeer-review

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