Header menu link for other important links
X
On Chus disturbance energy
Published in
2011
Volume: 330
   
Issue: 22
Pages: 5280 - 5291
Abstract
Chu [On the energy transfer to small disturbances in fluid flow (part I), Acta Mechanica 1 (1965) 215234] proposed a positive definite energy norm for characterizing the level of fluctuation in a disturbance. In the absence of heat transfer at the boundaries, work done by boundary or body forces, heat and material sources of energy, this norm is a monotone, non-increasing function of time. In this paper, we show that Chus disturbance energy defines an inner product, with respect to which the conservation equations of fluid motion linearized about a uniform base flow are self-adjoint. This ensures that the eigenvectors of the linearized operator are orthogonal to each other, and the property that the energy norm is a non-increasing function of time in the absence of physical sources of energy follows as an immediate consequence. Examples from numerical simulations of Euler equations are presented to highlight the importance of choosing an energy norm that is consistent with the underlying physics. We demonstrate that the disturbance energy as measured by Chus norm does not exhibit spurious transient growth in the absence of physical sources of energy and hence is suitable for analyzing thermoacoustic instability. © 2011 Elsevier Ltd.
About the journal
JournalJournal of Sound and Vibration
ISSN0022460X
Open AccessNo
Concepts (21)
  •  related image
    A-monotone
  •  related image
    BASEFLOWS
  •  related image
    BODY FORCES
  •  related image
    Conservation equations
  •  related image
    ENERGY NORM
  •  related image
    Fluid motions
  •  related image
    Function of time
  •  related image
    Inner product
  •  related image
    LINEARIZED OPERATORS
  •  related image
    Positive definite
  •  related image
    SMALL DISTURBANCES
  •  related image
    SOURCES OF ENERGY
  •  related image
    Thermoacoustic instability
  •  related image
    TRANSIENT GROWTH
  •  related image
    Energy transfer
  •  related image
    Euler equations
  •  related image
    Linearization
  •  related image
    Mathematical operators
  •  related image
    Orthogonal functions
  •  related image
    Thermoacoustics
  •  related image
    Flow of fluids