Eigenvalue enclosures and exclosures for non-self-adjoint problems in hydrodynamics

B. Malcolm Brown, M. Langer, M. Marletta, C. Tretter, M. Wagenhofer

Research output: Contribution to journalArticle

7 Citations (Scopus)
69 Downloads (Pure)

Abstract

In this paper we present computer-assisted proofs of a number of results in theoretical fluid dynamics and in quantum mechanics. An algorithm based on interval arithmetic yields provably correct eigenvalue enclosures and exclosures for non-self-adjoint boundary eigenvalue problems, the eigenvalues of which are highly sensitive to perturbations. We apply the algorithm to: the Orr-Sommerfeld equation with Poiseuille profile to prove the existence of an eigenvalue in the classically unstable region for Reynolds number R=5772.221818; the Orr-Sommerfeld equation with Couette profile to prove upper bounds for the imaginary parts of all eigenvalues for fixed R and wave number α; the problem of natural oscillations of an incompressible inviscid fluid in the neighbourhood of an elliptical flow to obtain information about the unstable part of the spectrum off the imaginary axis; Squire's problem from hydrodynamics; and resonances of one-dimensional Schrödinger operators.
Original languageEnglish
Pages (from-to)65-81
Number of pages17
JournalLMS Journal of Computation and Mathematics
Volume13
DOIs
Publication statusPublished - 2010

Keywords

  • eigenvalue
  • enclosures
  • exclosures
  • hydrodynamics

Fingerprint Dive into the research topics of 'Eigenvalue enclosures and exclosures for non-self-adjoint problems in hydrodynamics'. Together they form a unique fingerprint.

  • Projects

    Cite this