About this course:

  • Course Name: Hydrodynamic Stability and Transition to Turbulance
  • Course Code: ME 690
  • L-T-P-C : 3-0-0-6
  • Syllabus: Download
  • Course Type: Department Elective


    • Hydrodynamic Stability and Transition to Turbulanc

    Description:

    Syllabus

    Introduction: overview of methods of stability analysis (linear and nonlinear theories), normal mode analysis; Common examples of gravitational, thermal and centrifugal instabilities: Rayleigh-Taylor instability, Rayleigh-Bénard instability, instabilities in Taylor–Couette flow; Instabilities in parallel flows: temporal instability, Rayleigh equation, Orr-Sommerfeld equation and Squire’s transformation, numerical technique for solving the Orr-Sommerfeld equation, spatial instability and Gaster’s transformation; Spatio-temporal instability: evolution of perturbations in space-time, absolute and convective instabilities, Brigg's method and the pinch point criteria; Stability of non-parallel flows: instabilities in weakly nonparallel flows, parabolised stability equations, bi-global and tri-global stability analysis; Nonlinear stability theory: weak nonlinearity, Landau equation, interaction of linear modes, energy methods; Transition to turbulence: transient growth, pseudo spectra and nonmodal instabilities, receptivity, secondary instability, Morkovin map of roads to wall turbulence, regimes of laminar-turbulent transition in boundary layer flows, routes to chaos and turbulence.

    Textbooks:

    1. P. G. Drazin, Introduction to Hydrodynamic Stability, Cambridge University Press, 2002.
    2. P. J. Schmid, D. S. Henningson, Stability and Transition in Shear Flows, Springer-Verlag, 2001.
    3. P. G. Drazin and W. H. Reid, Hydrodynamic Stability, Second Edition, Cambridge University Press, 2004.

    References:

    1. Francois Charru, Hydrodynamic Instabilities, Cambridge University Press, 2011.
    2. S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Oxford University Press, 1961.
    3. C. Godrèche, P. Manneville, Hydrodynamics and Nonlinear Instabilities, Cambridge University Press, 1998.
    4. A. Georgescu, Hydrodynamic stability theory, Springer, 1985.
    5. S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Westview Press, 2014.
    6. Akiva M. Yaglom, Hydrodynamic Instability and Transition to Turbulence, Springer, 2012.