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Subject: TURBULENCE (A.A. 2023/2024)

master degree course in AUTOMOTIVE ENGINEERING

Course year 1
Teaching units Unit turbulence
To be chosen by the student (lesson)
  • TAF: Optional subjects SSD: ING-IND/06 CFU: 6
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Aula virtuale su Microsoft Teams

Exam type written
Evaluation final vote
Teaching language inglese
Contents download pdf download




The course aims to provide the necessary tools for the understanding of turbulent flows and for their control in industrial design. These tools include the knowledge of the statistical and theoretical formalisms underlying the dynamics of turbulence. The student will therefore be able to understand the evolution of turbulent flows through the knowledge provided by the theoretical tools, to quantitatively predict their main characteristics through the results of the theories themselves and finally to identify the most suitable statistical tools for their characterization.

Admission requirements

Vector analysis, differential equations, classical mechanics, statistics and fluid dynamics.

Course contents

1) Universal properties of turbulence (1 cfu)
2) Homogenous and isotropic turbulence theory (1.5 cfu)
3) Reynolds decomposition (0.5 cfu)
4) Wall turbulence (0.5 cfu)
5) Free turbulence (wakes, jets, mixing layers) (1 cfu)
6) Active and passive scalar turbulence mixing (0.5 cfu)
7) Entrainment: mixing, drag and reattachment (0.5 cfu)
8) Turbulence control techniques (0.5 cfu)

Teaching methods

During lessons, the subjects are presented by the lecturer, including the explicit proofs of mathematical formulas introduced and the presentation of the methods to solve the problems.

Assessment methods

The exam will be performed at the end of the lesson period. The students will sustain a written exam (3 hours) composed by open questions and followed by an oral discussion of the result of the written exam itself. The final score is given by the result of the written exam possibly refined by the oral discussion and will be communicated at the end of the oral discussion. It is not allowed to consult texts or lecture notes during the exam.

Learning outcomes

1- Knowledge of the statistical tools for the characterization of turbulent flows;
2- Knowledge of the fundamental results of turbulence theories;
3- Knowledge of the theoretical estimates on the properties of turbulent flows;
4- Knowledge of the fundamental techniques for the control of turbulence;


1- "Turbulent flows", Stephen B. Pope.
2- "Turbulence", Uriel Frish.
3- "A first course in turbulence", H. Tennekes and J.L. Lumley