Karhunen-Loéve expansion of the derivative of an inhomogeneous process

H. J. Sung, R. J. Adrian

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


The properties of the Karhunen-Loéve (KL) expansion of the derivative ux(x) of an inhomogeneous random process possessing viscous boundary-layer behavior are studied in relation to questions of efficient representation for numerical Galerkan schemes for computational simulation of turbulence. Eigenfunctions and eigenvalue spectra are calculated for the randomly forced one-dimensional Burgers' model of turbulence. Convergence of the expansion of ux is much slower than convergence of the expansion of u(x), and direct expansion of ux is not significantly more efficient than differentiating the expansion of u. The ordered eigenvalue spectrum of ux is proportional to the square of the order parameter times the eigenvalue spectrum of u. The underlying cause of slow convergence is the earlier onset of locally sinusoidal behavior of the KL eigenfunctions when the expansion is performed over the entire domain of the solution.

Original languageEnglish (US)
Pages (from-to)2233-2235
Number of pages3
JournalPhysics of Fluids
Issue number6
StatePublished - 1994
Externally publishedYes

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


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