Christophe Brun, Stéphane Barre, Pierre Hily-Blant

Image courtesy C.B. TCFD publication

Abstract :

Training in the basics of compressible turbulence including astrophysics medium.

Distribution CM/TD:

approximately 4 CM (6h), 4 TD (6h), 6 CM/TD (9h) and 1 TP (3h).

Content :

Part 1: Compressible turbulence in astrophysics (Lecture slides and notes are in english, but oral presentation is in french)

  1. Compressible turbulence in the interstellar medium (ISM):    * Role of turbulence in star formation    * Feedback of star formation on galaxy evolution    * Toward the gravo-turbulence framework

  2. The ISM: a very brief introduction    * Composition    * ISM phases: thermodynamics of the ISM and the bistable equation of state    * Pieces of evidence of interstellar turbulence      - Pressure: thermal, magnetic, cosmic-rays, non-thermal      - Scaling laws (in ionized and neutral medium)      - Reynolds number      - What is ISM turbulence?

  3. Observation of ISM turbulence    * Power spectrum    * Structure function analysis and intermittency

  4. Theory and numerical simulations    * Modifications to K41 for compressible turbulence    * Comparison between compressible and incompressible      - Power spectrum      - Structure functions and (multi-)fractal models    * Magnetized turbulence: challenges    * Predictions from numerical simulations

  5. Open questions in ISM turbulence

Part 2: Compressible turbulence in aerodynamics

  1. transonic compressible fluid mechanics

    • Kovasznay entropic, acoustic, vortical waves. Morkovin hypothesis Non-hypersonic turbulence
    • compressible Navier-Stokes equations - adimmension of Reynolds and Mach numbers
    • compressible numerical methods: conservative schemes (Mac Cormak, shock capture...), non-reflective boundary conditions,
    • oblique shocks - Rankine Hugoniot relations
    • compressible turbulence - dynamic and thermal boundary layer: SRA Reynolds analogy, Crocco Busemann relations
    • Numerical experiments: shock tube, turbulent compressible plane channel, turbulent compressible plane jet
  2. compressible turbulence and instrumentation

    • nozzle, oblique shock type air intake, shock tube,...
    • Experimental demonstration of linearized modes of compressible turbulence (Kovasznay) by using the hot wire and fluctuation diagrams.