Algebraic instability caused by acoustic modes in supersonic shear flows

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Abstract

Perturbations in a shear flow exhibit rather complex behavior - waves may grow algebraically even when the spectrum of disturbances is entirely neutral (no exponential instability). A shear flow brings about non-selfadjoint property, invalidating the standard notion of dispersion relations, and it also produces a continuous spectrum that is a characteristic entity in an infinite-dimension phase space. This paper solves an initial value problem using the Laplace transform and presents a new-type of algebraic instability that is caused by resonant interaction between acoustic modes (point spectrum) and vortical continuum mode (continuous spectrum). Such a resonance is possible when variation of velocity shear is comparable to sound speed.

Journal

  • JMI

    JMI 1, 123-130, 2009

    Faculty of Mathematics, Kyushu University

Codes

  • NII Article ID (NAID)
    120001633481
  • NII NACSIS-CAT ID (NCID)
    AA12444018
  • Text Lang
    ENG
  • Article Type
    journal article
  • Journal Type
    大学紀要
  • ISSN
    18844774
  • NDL Article ID
    10948678
  • NDL Source Classification
    ZM31(科学技術--数学)
  • NDL Call No.
    Z63-D421
  • Data Source
    NDL  IR 
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