5.00 credits

37.5 h + 30.0 h

Q2

Teacher(s)

Language

French

Prerequisites

LPHYS1112 or equivalent teaching unit from another programme. Having followed LPHYS1202 and having followed and passed LMAT1121 are assets.

*The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.*
Main themes

This teaching unit aims to enable one to understand the basic principles of fluid dynamics and the associated reactive transport processes (kinematics, budget of mass, momentum and energy) and comprehend important flow regimes (incompressible viscous, geophysical and free-surface flows).

Learning outcomes

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a. Contribution of the teaching unit to the learning outcomes of the programmeAA1: 1.1, 1.4, 1.5 AA2: 2.3, 2.4 AA3: 3.4, 3.5 AA6: 6.3 b. Specific learning outcomes of the teaching unitAt the end of this teaching unit, the student will be able to: 1. understand the difference between physical principles and phenomenological laws; 2. assess the reliability and coherence of mathematical models; 3. estimate relevant orders of magnitude in a mathematical model based on partial differential equations; 4. study the budget of physical quantities on fixed or moving control volumes; 5. select the mathematical models relevant to specific flows; 6. solve simple fluid dynamics and reactive transport problems; 7. grasp the specific aspects of geophysical and free-surface flows. |

Content

Basic assumptions of continuum mechanics.

Lagrangian and Eulerian descriptions.

Mass balance, momentum balance, energy and entropy balance.

Non-inertial reference frame.

Dynamic similitude: dimensionless parameters.

Incompressible irrotationnal flows.

Incompressible viscous flows.

Flows with two space scales: lubrication and boundary layers theory.

Natural and forced convection: Boussinesq approximation.

Reactive flows.

Geophysical flows: geohydrodynamics equations, dimensionless parameters, idealised models.

Free surface flows: 1D and 2D models, linear and non-linear waves, tides, tsunamis.

Lagrangian and Eulerian descriptions.

Mass balance, momentum balance, energy and entropy balance.

Non-inertial reference frame.

Dynamic similitude: dimensionless parameters.

Incompressible irrotationnal flows.

Incompressible viscous flows.

Flows with two space scales: lubrication and boundary layers theory.

Natural and forced convection: Boussinesq approximation.

Reactive flows.

Geophysical flows: geohydrodynamics equations, dimensionless parameters, idealised models.

Free surface flows: 1D and 2D models, linear and non-linear waves, tides, tsunamis.

Teaching methods

Lecture courses.

Exercise sessions aimed at solving problems as realistic as possible.

Invitation to self learning.

Exercise sessions aimed at solving problems as realistic as possible.

Invitation to self learning.

Evaluation methods

Continuous assessment of knowledge based on homeworks, the development of codes in MATLAB (or any other relevant programming language) and/or oral presentations.

Written exam consisting of problems.

Written exam consisting of problems.

Bibliography

Cushman-Roisin B. and J.-M. Beckers, 2011 (2nd ed.), Introduction to Geophysical Fluid Dynamics - Physical and Numerical Aspects, International Geophysics Series (Vol. 101), Elsevier, Amsterdam, 828 pages.

Kundu P., I. Cohen and D. Dowling, 2015 (6th ed.) (ou éditions précédentes), Fluid Mechanics, Elsevier, Amsterdam, 928 pages.

Kundu P., I. Cohen and D. Dowling, 2015 (6th ed.) (ou éditions précédentes), Fluid Mechanics, Elsevier, Amsterdam, 928 pages.

Faculty or entity