This article contains a review of modal stability theory. It covers local stability analysis of parallel flows including temporal stability, spatial stability, phase velocity, group velocity, spatio-temporal stability, the linearized Navier–Stokes equations, the Orr–Sommerfeld equation, the Rayleigh equation, the Briggs–Bers criterion, Poiseuille flow, free shear flows, and secondary modal instability. It also covers the parabolized stability equation (PSE), temporal and spatial biglobal theory, 2D eigenvalue problems, 3D eigenvalue problems, spectral collocation methods, and other numerical solution methods. Computer codes are provided for tutorials described in the article. These tutorials cover the main topics of the article and can be adapted to form the basis of research codes.
Modal Stability Theory
: Lecture notes from the FLOW-NORDITA Summer School on Advanced Instability Methods for Complex Flows, Stockholm, Sweden, 2013
Not to be confused with the term mean flow/state, which is reserved for time and/or space-averaged turbulent flow.
Manuscript received August 11, 2013; final manuscript received January 20, 2014; published online March 25, 2014. Assoc. Editor: Gianluca Iaccarino.
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Juniper, M. P., Hanifi, A., and Theofilis, V. (March 25, 2014). "Modal Stability Theory
: Lecture notes from the FLOW-NORDITA Summer School on Advanced Instability Methods for Complex Flows, Stockholm, Sweden, 2013." ASME. Appl. Mech. Rev. March 2014; 66(2): 024804. https://doi.org/10.1115/1.4026604
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