Fluids and Plasmas in Astrophysics

Code:

AST3005

Acronym:

AST3005

Keywords
Classification	Keyword
OFICIAL	Astronomy

Instance: 2021/2022 - 1S

Active?	Yes
Responsible unit:	Department of Physics and Astronomy
Course/CS Responsible:	Bachelor in Chemistry

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:B	0	Official Study Plan	3	-	6	56	162
L:CC	13	study plan from 2021/22	2	-	6	56	162
			3
L:F	17	Official Study Plan	2	-	6	56	162
			3
L:G	0	study plan from 2017/18	3	-	6	56	162
L:M	0	Official Study Plan	3	-	6	56	162
L:Q	0	study plan from 2016/17	3	-	6	56	162

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 examples of applications of MHD.

Learning outcomes and competences

Being able to understand a number of phenomena associated with the behaviour of neutral fluids either in the ideal limit or considering the effects of viscosity. Being able to understand the behaviour of plasmas and some of the phenomena associated with them, either at the limit without collisions or in the limit dominated by collisions. Being able to apply magnetohydrodynamics (MHD) to simple cases.

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. 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.

PART 2: PLASMAS

5. Plasma physics: plasma orbital theory. Orbits of motion of particles in a plasma. Larmor radius and frequency. Effect of a perpendicular force. The gradient and curvature drifts. Magnetic mirrors. Van Allen Belt.

6. Dynamics of multiple charged particles and processes without collisions in plasmas. Approaches used in the theory of plasmas  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 cold and warm plasmas.

6. Magnetohydrodynamics (MHD): Fundamental equations. The plasma equations. The equation of induction and its consequences. Soluções of magnetohydrostatics. Force-free and potential fields.

Mandatory literature

Arnab Rai Choudhuri ;The physics of fluids and plasmas : an introduction for astrophysicists, Cambridge University Press, 1998. ISBN: 0-521-55543-4
Eric Priest; Magnetohydrodynamics of the Sun, Cambridge University Press. ISBN: 0521854717
J. Monteiro Moreira, J. Machado da Silva, J. Brochado Oliveira; Elasticidade e dinâmica dos fluidos, U.Porto, 2015. ISBN: 978-989-746-067-8

Complementary Bibliography

Landau & Lifshitz; Fluid Mechanics. 2nd edition, Butterworth-Heinemann, 1987. ISBN: 978-0750627672
F. Shu; The Physics of Astrophysics Volume II: Gas Dynamics, University Science books, 2009. ISBN: 978-1891389672
James Ward Brown, Ruel V. Churchill; "Complex variables and applications", McGraw-Hill, 1996. ISBN: 0071140654

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 > Astronomy > Astrophysics

Evaluation Type

Evaluation with final exam

Assessment Components

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

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

The student has frequency to the course if he/she misses no more than 1/4 of the planned theoretical-practical classes (TP's).

Calculation formula of final grade

Final Mark = Exam Mark

Classification improvement

Following the regulations of FCUP, the student that has passed this curricular unit, can improve grades one single time. Either in the appeal season of the academic year in which he passed or in the following academic year (not only in the appeal season).

Observations