You can take the exam for this unit if you passed the following exam(s):
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The course is divided into two parts: the first deals with elementary fluid mechanics; the second deals with the subject of fully-developed turbulence both in the large-scale regime and in the ultraviolet (small-scale) regime.
The course aims to introduce the key concepts of fluid dynamics and turbulence. The study of turbulence will also be based on averaged equations and Reynolds Large-eddy simulation (LES).
At the end of of the course, it is expected from the students the ability to solve problems of fluids dynamics and turbulence that may be encountered in real life. Students are also expected to develop a strong critical opinion on concepts such as predictability and chaos of complex systems such as fluids.
The course is done in a traditional manner by means of lectures with ample space for exercises aimed at establishing the fundamental concepts. The exam will consist of a written test and an oral. Teachers can be contacted by students for questions or requests for further study during office hours or outside prior arrangement.
- Introduction to Fluid Mechanics
- Kinematics of incompressible fluids
- The Navier-Stokes and energy balances
- Irrotational flows and complex formalism
- Laminar Flows
- The boundary layer theory
- Phenomenological aspects of turbulence: Kolmogorov's 1941 theory and scale invariance in a global sense
- The problem of scale invariance violation and the appearance of intermittency: the fractal and multifractal approaches
- Introduction to exact models of passive scalar turbulence
P.K. Kundu, Fluid Mechanics, Fifth Edition, 2014.
U. Frisch, Turbulence, Cambridge Univ. Press. 1995;
E. Ott, Chaos in Dynamical Systems, Cambridge Univ. Press. 1993;
Office hours: To be arranged via email communication.
ANDREA MAZZINO (President)
PIERANTONIO ZANGHI' (President Substitute)
All class schedules are posted on the EasyAcademy portal.
Oral and written exam.
The oral exam is always conducted by the responsible professor and another expert in the subject (usually a tenured professor) and lasts about half an hour. Normally it consists of two questions, one that concerns the elementary fluid dynamic part and the other dealing with turbulence. In addition to the preparation, the Commission considers the degree of achievement of the communication objectives, the autonomy of the exposure and the technical level of the exposure.
The written test is usually organized on two or three problems related to the program of the course with graduated difficulties that allow the teacher to carry out an assessment of the degree of achievement of the training objectives. The members of the Examining Commission establish the criteria to assign partial scores to the various responses that also take into account the difficulty of the problems. Based on these criteria it is possible to accurately associate the total score acquired. The written test is considered passed (with subsequent access to the oral test) if the vote exceeds 18/30.
When the written test is not passed by the student, he / she is invited to deepen the study and to make use of further explanations by the professor.
The final grade is determined by the weighted average of the written and oral tests. The Commission decides in advance and uniformly for all the examination sessions, which relative weight should be given to the two tests.