Course program
Knowledge of the physics of ideal and real fluids, including the ability to write key equations and solve some cases of physical and astrophysical interest. It also explores concepts of stability/instability and perturbation propagation. The theory of gravitational collapse and explosions will also be a focus of the course.
Program (preliminary)
Basic Concepts of Fluid Theory
Real, Ideal, and Plasma Fluids
Viscosity
Compressive/Expansive Stresses and Shear Stresses
Rigid Transformations and Deformability - Strain Rates
Continuity of the Field
Newtonian and Non-Newtonian Fluids
Introduction to the Classical Continuous Field
Field Lines and the Meaning of Divergence and Curl
Key Equations of Ideal Fluids
Lagrangian and Eulerian Description
Continuity Equation
Equation of Motion
Energy Equation
Thermodynamic Equation of State of the Fluid
Modified Equations for Ideal Fluids
Model of Forces in a Continuous Field
Navier-Stokes Equations
Thermodynamics of Real Fluids
Stability and Instability
Self-Gravitating Fluids
Terrestrial and Astrophysical Fluids
Jeans Collapse
Fluid-Dynamic Instabilities
The Role of Viscosity
Shock Theory
Structure and Behavior of Variables: Boundary Conditions
Longitudinal and Tangential Discontinuities
Shock Propagation: Mach Numbers
Strong/Weak Shocks
Astrophysical Examples of Shock Fronts
Explosions and Perturbation Propagation
Blast Waves
Supernova Explosions
Self-similar Solutions
Turbulence
The Laboratory and in Plasmas
In Astrophysics
Stellar Convection (Optional / Overview)
Supersonic and Subsonic Flows (Optional / Overview)
Winds
Accretion
Radiative Transport Problem
Transport Equation
Physical Processes: Absorption, Emission, Scattering
Generalization to the Classical Continuous Field and PDE Theory
The Density Function
Key Theorems
Elliptic/Parabolic/Hyperbolic Problems
Method of Characteristics
Prerequisites
Prerequisites:
1. Vector Calculus and Mathematical Analysis.
2. Linear Geometry and Mathematical Methods of Physics.
3. Classical and Analytical Mechanics
4. Classical Electrodynamics
To fill any gaps in the knowledge, the instructor will provide additional resources upon request.
Books
Physics of Fluids, R. Capuzzo Dolcetta, Springer (course reference text)
Frequency
Attendance is not mandatory but is strongly recommended to encourage interaction with the teacher.
Exam mode
The final exam consists of an oral exam with the instructor on the syllabus covered and requires the ability to solve some cases covered in class or their variations. The derivation of key equations and the proof of theorems covered in class are also required.
The exam may be supplemented with an individual in-depth study on a topic agreed upon with the instructor, presented to the class before the final exam on Wednesdays from 8:00 to 9:00. Attendance is not mandatory, and the specific topic of the in-depth study is not part of the course syllabus.
Please note that the various homework assignments are not mandatory and are not subject to ongoing assessment.
Bibliography
An Introduction to Astrophysical Hydrodynamics (S. N. Shore), Academic Press (only some sections indicated in class)
Fluid Mechanics - Vol. 6 Course of Theoretical Physics, L. D. Landau, E. M. Lifschitz, Pergamon Press (only some sections indicated in class)
Principles of Astrophysical Fluid Dynamics, C. Clarke and B. Carswell, Cambridge University Press (only some sections indicated in class)
Physics of the Interstellar and Intergalactic Medium, B. Draine, Princeton University Press (only some sections indicated in class)
Turbulence, an Introduction for Scientists and Engineers, P.A. Davidson, Cambridge University Press (only some sections indicated in class)
The Equations of Radiation Hydrodynamics, Pomraning, Dover Publications (only some sections indicated in class)
Accretion Power in Astrophysics, Frank, King, Raine, Cambridge University Press (only some sections indicated in class)
Lesson mode
Students who successfully complete the course, delivered in traditional, in-person format, will develop a knowledge of the physics of ideal and real fluids, being able to write key equations and solve some cases of physical and astrophysical interest. They will also delve into concepts of stability/instability and the propagation of perturbations. The theory of gravitational collapse and explosions will also be a focus of the course. Students are also encouraged to engage actively with the instructor to develop their own preferences for specific topics and seek individual in-depth study for the final exam.