Checking date: 13/03/2024

Course: 2024/2025

Máster Universitario en Matemática Industrial (RD 1393/2007) (Plan: 330 - Estudio: 258)

Coordinating teacher: VELA MARTIN, ALBERTO

Department assigned to the subject: Aerospace Engineering Department, Thermal and Fluids Engineering Department

Type: Electives
ECTS Credits: 6.0 ECTS


Requirements (Subjects that are assumed to be known)
Ordinary Differential Equations / Dynamical Systems Partial Differential Equations
Description of contents: programme
1. Introduction 1.1 Laminar flow, turbulence and transition 1.2 Bifurcations 2 Stability of confined flows 2.1 Rayleigh¿Benard 2.2 Taylor¿Couette 3 Stability of parallel and quasi-parallel flows 3.1 Spatial, temporal, and spatiotemporal instability 3.2 Viscous and non-viscous instabilities 3.4 Stability of quasi-parallel flows 4 Global and non-modal stability (transient growth) 5 Transition 5.1 Pipes, boundary layers, jets, and mixing layers 5.2 Secondary instabilities, by-pass transition 6 Turbulence 6.1 Statistical description: Reynolds-averaged Navier Stokes and the closure problem. 6.2 Free shear flows: mixing layers, jets, wakes. 6.3 The scales of turbulent flows: the energy cascade 6.4 Wall-bounded flows: channels, pipes and boundary layers. 7 Introduction to turbulence modeling 7.1 DNS 7.2 LES 7.3 RANS
Learning activities and methodology
There will be theory lectures to introduce the theory of stability and the physics of transition and turbulence. The students will need to solve simple problems with analytical solution. In addition they will need to solve numerical problems using Matlab or any other programming environment of their choice.
Assessment System
  • % end-of-term-examination 60
  • % of continuous assessment (assigments, laboratory, practicals...) 40

Basic Bibliography
  • C. Godreche, P. Manneville. Hydrodynamics and nonlinear instabilities. Cambridge University Press. 2005
  • P.J. Schmid, D.S. Henningson. Stability and transition in shear flows. Springer. 2001
  • S.B. Pope. Turbulent Flows. Cambridge Univ. Press. 2000
Additional Bibliography
  • H. Tennekes, J.L. Lumley. A first course in turbulence. MIT Press. 1972
  • P. A. Davidson. Turbulence: An Introduction for Scientists and Engineers: An Introduction for Scientists and Engineers. . Oxford Univ. Press. 2004
  • P. A. Durbin, B.P. Reif. Statistical theory and modeling for turbulent flows.. John Wiley & Sons.. 2011
  • Wilcox, D. C. . Turbulence modeling for CFD . DCW industries. 1998

The course syllabus may change due academic events or other reasons.