Elasticity and Fluid Dynamics

Code:

F308

Acronym:

F308

Keywords
Classification	Keyword
OFICIAL	Physics

Instance: 2014/2015 - 2S

Active?	Yes
Web Page:	https://moodle.up.pt/course/view.php?id=2465
Responsible unit:	Department of Physics and Astronomy
Course/CS Responsible:	Bachelor in Physics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:AST	4	Plano de Estudos a partir de 2008	3	-	7,5	-
L:B	0	Plano de estudos a partir de 2008	3	-	7,5	-
L:F	7	Plano de estudos a partir de 2008	3	-	7,5	-
L:G	0	P.E - estudantes com 1ª matricula anterior a 09/10	3	-	7,5	-
		P.E - estudantes com 1ª matricula em 09/10	3	-	7,5	-
L:M	0	Plano de estudos a partir de 2009	3	-	7,5	-
L:Q	0	Plano de estudos Oficial	3	-	7,5	-

Teaching language

Portuguese

Objectives

In the first part of the course, we will introduce the fundamental tools and concepts in fluid mechanics and some applications of this theory to physics and astrophysics. In the second part, this approach will be extended to the study of plasmas and particular emphasis on the orbital theory of plasmas and on magnetohydrodynamics (MHD) will be devoted. At the end of the course, some basic concepts on Elasticity will be addressed together with some applications to Physics.

Learning outcomes and competences

Being able to understand a number of phenomena associated with the behaviour of neutral fluids either in the ideal limit orconsidering the effects of viscosity. Being able to understand the behaviour of plasmas and some of the phenomena associated with them either at the limit or the limit without collisions or in the limit dominated by collisions. Being able to describe tensions and deformations in a solid and to relate them.

Working method

Presencial

Program

PART 1: FLUIDS

1. Introduction Fluids and plasmas in Physics and Astrophysics

2. Ideal fluid Properties Derivation of macroscopic equations of hydrodynamics. The equation of continuity. The equation of motion - Euler's equation. The energy equation. The condition for absence of convection. The flow of energy and the flow of momentum. Barotropic and incompressible fluids. The conservation of motion. The Kelvin's vorticity theorem. The Bernoulli principle for stationary flows. Hydrostatics. Forces on submerged solid surfaces. Modelling the solar corona. Potential flow. Flow around a cylinder Stream function.

3. Viscous fluids Properties. Tangential stresses in a Newtonian fluid. The Navier-Stokes equations. Energy dissipation in incompressible fluids. Flow between two parallel planes subjects, in a circular tube and between two rotating cylinders. Factors of scale and the Reynolds number. Viscous flows around solid bodies. Boundary layers. Accretion disks in astrophysics: dynamics of accretion disks; stationary solutions.

4. Linear theory of waves and instabilities The philosophy of the analysis of disturbances. Convective instability and internal gravity waves: the Schwarzschild criterion. Rayleigh-Benard convection cells and Benard convection (for information). Surface gravity waves. Disturbances in the separation between two fluids: the Rayleigh-Taylor instability; Kelvin-Helmholtz instability. Jeans instability and the process of star formation. Oscillations in stars. Helioseismology.

PART 2: PLASMAS

5. Plasma physics: plasma orbital theory, dynamics of multiple charged particles and processes without collisions in plasmas. Approaches used in the theory of plasmas Orbits of motion of particles in a plasma. Effect of a perpendicular force, gradient and curvature. Larmor radius and frequency. Magnetic mirrors. Particle acceleration in astrophysics. Van Allen Belt. Cosmic rays. Basic properties of plasmas. Different types of plasma. Electrical neutrality in a plasma. Shielding and the Debye length. The plasma parameter. Oscillations in plasmas. The plasma frequency. Electromagnetic waves in hot and cold plasmas.

6. Magnetohydrodynamics (MHD) Fundamental equations. The plasma equations. The equation of induction and its consequences. Magnetohydrostatics. Applications to Fusion and Tokamaks. Applications to the solar atmosphere. Magnetohydrodynamic waves. Alfvén waves and magnetoacoustic waves. Magnetoconvection and sunspots. The buoyancy of magnetic flux tubes. The Parker instabilityof the magnetic field. The magnetic field as a carrier of angular momentum, magnetic braking and magnetized winds.

PART 3-ELASTICITY

7. Analysis of deformations. Displacement vector. Infinitesimal transformations (commutativity). Rotation (antissimetric part of the strain tensor). Values and eigenvectors of the deformation tensor. Relative variation on length, area and volume. Trace and invariants. Saint-Venant pronciple and the strain ellipsoid.

8. Analysis of tensions. Equations of balance and motion. The stress tensor. Values and principal directions of tension. The Mohr diagram and its application. The quadric of tensions. Utility; calculation of stress and its componentes. Extremes.

9. Hooke's generalized law. The elastic tensor coefficientsas a 4th order tensor. Isotropic media. Lamé parameters. Generalizeed Hooke's law for an isotropic media. Calculation of deformations given the tensions and vice-versa. Relations between Young modules, Poisson's ratio and compressibility and Lamé parameters. Energy density of elastic deformation. elástica. Clapeyron Tehorem.

Mandatory literature

Arnab Rai Choudhuri; The physics of fluids and plasmas: an introduction for astrophysicists, Cambridge University Press, 1998. ISBN: 0-521-55543-4

Complementary Bibliography

Landau & Lifshitz; Fluid Mechanics, 2nd edition, Butterworth-Heinemann, 1987. ISBN: 978-0750627672
F. Shu; The physics of astrophysics, Vol II: Gas Dynamics, University Science books, 2009. ISBN: 978-1891389672

Teaching methods and learning activities

Expository methods in theoretical lectures (T). In theoretical-practical classes (TP) resolution of exercises by the students.

keywords

Physical sciences > Physics > Classical mechanics > Fluid dynamics
Physical sciences > Physics > Solid state physics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Teste	100,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	139,50
Frequência das aulas	63,00
Total:	202,50

Eligibility for exams

The student has frequency to the course if he/she misses no more than 1/3 of the planned theoretical-practical classes (TP's).

Calculation formula of final grade

Continuous evaluation with 2 assessment tests
T1 <= 10, T2 <= 10, minimum note in each test 7/20.
Final Mark = T1+T2, which is the note of the normal exam epoch (1st sit).

Evaluation by final exam
If the student chooses not to undergo continuous evaluation he/she must inform the lecturer (by email) until the normal exam date and, in this case,
Final Mark = Exam Mark (without consultation, marked up to 20).

Classification improvement

It is possible to improve grades only through the resit exam (without consultation, marked up to 20).

Observations

This course runs simultaneously with Fluids and Plasmas in Astrophysics (AST379). For this reason, a student cannot register simultaneously on these two courses.