About this course

It is advisable, but not mandatory to register for Aerospace: LINEAR STABILITY & LAMINAR-TURBULENT TRANSITION (Part I) - Theory at the same time as this course Part II - Numerical Transition.

The Linear Stability and Laminar-Turbulent Transition course, offered at Technion and shared within the EuroTeQ framework, introduces linear stability theory (LST) and laminar-turbulent transition of incompressible and compressible laminar flows. For reasons of effective delivery, the full scope of the taught material is divided in two parts, Theoretical Foundations and Numerical Implementation, both delivered during the winter semester. Concepts are introduced and equations are derived in LST Theoretical Foundations, while solved examples are discussed and practiced within LST Numerical Implementation. Both Theoretical Foundations and Numerical Implementation (this course) are stand-alone modules and can be taken independently of each other.

Semester Start Date: November 3, 2024

Day & Time: TBD

Contact Hours per week: 3

Recommended Literature: A single textbook describing the course content does not exist presently, but individual topics can be studied in:

Books on Flow Stability • Criminale WO, Jackson TL, Joslin RD (2019) Theory and Computation of Hydrodynamic Stability, Cambridge University Press, 2nd Ed. • Schmid PJ, Henningson DS (2001) Stability and Transition in Shear Flows, Springer

Mathematics Textbooks • Haberman R (2014) Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, Pearson, 5th Ed. • Kreyszig E (2006) Advanced Engineering Mathematics, John Wiley & Sons, 9th Ed.

Numerical Methods • Boyd JP (1989) Chebyshev and Fourier Spectral Methods, Springer. Also (2000) Dover 2nd Ed. • Trefethen LN (2000) Spectral Methods in Matlab, SIAM

Articles and Matlab Codes* • * Cossu C (2014) An Introduction to Optimal Control. Appl. Mech. Rev. 66(2):02480, • Fedorov A (2011) Transition and Stability of High-Speed Boundary Layers. Annu. Rev. Fluid Mech. Vol. 43, pp. 79–95, • * Juniper MP, Hanifi A, Theofilis V (2014) Modal Stability Theory. Appl. Mech. Rev. 66(2):024804, • Luchini P, Bottaro A (2014) Adjoint Equations in Stability Analysis. Annu. Rev. Fluid Mech.Vol. 46, pp. 493–517, • Mack LM (1984) Compressible boundary layer stability theory. AGARD Rep. R-709. • * Schmid PJ, Brandt L (2014) Analysis of Fluid Systems: Stability, Receptivity, Sensitivity. Appl. Mech. Rev. Mar 2014, 66(2):024803, • Taira K, Brunton SL, Dawson STM, Rowley CW, Colonius T, McKeon BJ, Schmidt OT, Gordeyev S, Theofilis V, Ukeiley LS (2017) Modal Analysis of Fluid Flows: An Overview. AIAA Journal 55(12):4013-4041, • Theofilis V (2011) Global Linear Instability. Annu. Rev. Fluid Mech. 43:319–352,

Learning outcomes

On successful completion, students will be able to formulate, discretize numerically and solve linear stability problems arising from incompressible to hypersonic flow using own-written algorithms and/or open-source linear algebra software. They will be exposed to the different facets of the linear stability eigenvalue and singular value problems, governing modal (exponential) or non-modal (algebraic, transient) growth of small-amplitude perturbations. They will have developed tools to predict whether a given laminar steady or time-periodic flow will break down to turbulence and estimate the transition location on canonical (flat plate and cone) surfaces using variants of the industry-standard e-to-the-N / amplitude method.


Lectures based on presentations will introduce the subject matter and selected topics will be demonstrated using Matlab-based computer codes, which will be provided to students. In the homework assignments the acquired knowledge will be consolidated and expanded into the compressible flow regime.

Student assessment will be based on preparing offline, and submitting within a week from the respective publication, three homework assignments, each counting 20% of the final grade. Each assignment will be graded out of 100 and 50 points will be required to pass. Submission of all three assignments is mandatory for completion of the course (i.e. an “incomplete” grade will be submitted if any of the assignments is not uploaded on time. The remaining 40% of the final grade will be obtained from one final exam, which will be published on Moodle at the end of the course, and for which a three-hour window will be given for answers to be submitted.

Course requirements

Incompressible and Compressible Fluid Mechanics, Advanced Engineering Mathematics, Numerical Analysis and Linear Algebra, Programming (compiled or interpreted computer languages).


Lectures and homework exercises

Additional information

  • Credits
    ECTS 4
  • Level
  • Contact hours per week
  • Instructors
    Prof. V. Theofilis
  • Mode of instruction
If anything remains unclear, please check the FAQ of Technion (Israel).


  • Start date

    3 November 2024

    • Ends
      2 March 2025
    • Term *
      Winter 2024/2025
    • Location
    • Instruction language
    • Register between
      14 May - 29 Jul 2024
    Only 8 days to enrol
    Apply now
These offerings are valid for students of TUM (Germany)