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Semester (Sem)
1First Semester
2Second Semester
AAnnual course
Educational activities
BIdentifying activities
Course completely offered in italian
Course completely offered in english
--Not available
Innovative teaching
The credits shown next to this symbol indicate the part of the course CFUs provided with Innovative teaching.
These CFUs include:
  • Subject taught jointly with companies or organizations
  • Blended Learning & Flipped Classroom
  • Massive Open Online Courses (MOOC)
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Course Details
Academic Year 2019/2020
School School of Industrial and Information Engineering
Name (Master of Science degree)(ord. 270) - BV (469) Aeronautical Engineering
Track AAD - Aerodinamica
Programme Year 2

Course Details
ID Code 091254
Course Type Mono-Disciplinary Course
Credits (CFU / ECTS) 8.0
Semester First Semester
Course Description General concepts of fluid dynamics stability: disturbance equations, definitions of stability, critical values of the Reynolds number. Reynolds-Orr equation. Spatial and temporal stability. Temporal stability of parallel flows, inviscid analysis. The linear case: Rayleigh equation, modal stability. Interpreting the results: criteria by Rayileygh and Fjortoft. Applications. Discussion of the lift-up effect, algebraic instability. Temporal stability of parallel flows, viscous analysis. The linear case: Orr-Sommerfeld-Squire equations, modal stability. Squire transformation, Squire theorem. Pipe flow, plane channel flow, plane Couette flow. Spectra and eigenfunctions, neutral curves. Response to initial conditions: non-modal stability for the Orr-Sommerfeld-Squire equations. Transient growth, energy norm, maximum amplification. Results for the plane channel flow. Optimal initial conditions, max transient growth, numerical range. Survey of non-linear stability, stability of oscillating flows, Floquet and pseudo-Floquet techniques; spatial stability, absolute and convective instability, receptivity. Transition. Transition scenarios, modal amplification, bypass transition. Transition thresholds. Nature of turbulent flows, matemathical chaos. Strong sensitivity to initial conditions. Lack of scale separation. 1-D examples of estimates of turbulent scales. Techniques for studying turbulent flows. Statistical description of turbulence. Space- and time-scales in a turbulent flow. Equations for isotropic turbulence in Fourier space. The Kolmogorov hypotheses. Energy spectra and correlations. The various spectral ranges, effect of Re. Grid turbulence, free turbulent boundary layers (planar jet, planar mixing layer, planar wake, axisymmetric wake). Homogeneous shear flow. Wall flows. Turbulent flow in a plane channel. Logarithmic law and Prandtl formula for skin friction. Pipe flow. Roughness effects. Turbulent boundary layer. Wall turbulence cycle. Conceptual models for the self-sustaining cycle in wall flows: how turbulence works. Coherent structures. Controlling turbulence. Review of current techniques, passive and active, closed-loop and open-loop, for the control of turbulent flow. RANS equations. Averaging, limits of validity need for a closure hypothesis. Closure with eddy-viscosity-based models: pros and cons. Algebraic models, one- and two-equations models, (k-). Closure via RSM models: pros and cons. General structure of a RSM model: the Launder-Rice-Rodi-Isotropization of Production (LRR-IP) model. LES equations: analogies and differences with RANS equations. Filtering in phisical space and in Fourier space. Sub-Gris-Scale models. Backscatter and dynamic (Germano) models.
Scientific-Disciplinary Sector (SSD)
Educational activities SSD Code SSD Description CFU

Schedule, add and removeAlphabetical groupLecturer(s)LanguageTeaching Assignment Details
From (included)To (excluded)
---AZZZZQuadrio Maurizio
manifesti v. 3.7.0 / 3.7.0
Area Servizi ICT