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.
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Modal Stability Theory
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March 2014
Tutorial
Modal Stability Theory
: Lecture notes from the FLOW-NORDITA Summer School on Advanced Instability Methods for Complex Flows, Stockholm, Sweden, 2013
Matthew P. Juniper,
Matthew P. Juniper
Engineering Department,
e-mail: mpj1001@cam.ac.uk
Cambridge University
,Trumpington Street
,Cambridge CB2 1PZ
, UK
e-mail: mpj1001@cam.ac.uk
Search for other works by this author on:
Ardeshir Hanifi,
Ardeshir Hanifi
Swedish Defence Research Agency
,FOI, SE-164 90 Stockholm
, Sweden
Linné FLOW Centre,
e-mail: ardeshir.hanifi@foi.se
KTH Royal Institute of Technology
,Stockholm SE-100 44
, Sweden
e-mail: ardeshir.hanifi@foi.se
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Vassilios Theofilis
Vassilios Theofilis
School of Aeronautics,
e-mail: vassilis@aero.upm.es
Universidad Politécnica de Madrid
,Plaza Cardenal Cisneros 3
,Madrid E-28040
, Spain
e-mail: vassilis@aero.upm.es
Search for other works by this author on:
Matthew P. Juniper
Engineering Department,
e-mail: mpj1001@cam.ac.uk
Cambridge University
,Trumpington Street
,Cambridge CB2 1PZ
, UK
e-mail: mpj1001@cam.ac.uk
Ardeshir Hanifi
Swedish Defence Research Agency
,FOI, SE-164 90 Stockholm
, Sweden
Linné FLOW Centre,
e-mail: ardeshir.hanifi@foi.se
KTH Royal Institute of Technology
,Stockholm SE-100 44
, Sweden
e-mail: ardeshir.hanifi@foi.se
Vassilios Theofilis
School of Aeronautics,
e-mail: vassilis@aero.upm.es
Universidad Politécnica de Madrid
,Plaza Cardenal Cisneros 3
,Madrid E-28040
, Spain
e-mail: vassilis@aero.upm.es
1
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.
Appl. Mech. Rev. Mar 2014, 66(2): 024804 (22 pages)
Published Online: March 25, 2014
Article history
Received:
August 11, 2013
Revision Received:
January 20, 2014
Citation
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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