Hydromagnetic dynamo theory in geo- and astrophysics 1 1100-TDH1

1. History of theories describing the generation of the geomagnetic field.
2. The Earth's dynamo compared to the dynamo on other objects of the solar system (the Sun, Mercury, Venus, Jupiter's moon Io, Jupiter and Mars, the Moon in the past). Why is the Earth Dynamo still so effective?
3. Magnetohydrodynamics equations
a. Navier-Stokes equation with Lorentz force
b. Maxwell's equations
c. Derivation of the equation of the magnetic field induction
d. Helmholtz theorem of the frozen magnetic field.
e. Taylor-Proudman theorem
f. Basics of the theoretical description of turbulence, renormalization of the Navier-Stokes equations.
4. Mechanisms of magnetic field generation
a. Omega effect and alpha effect - mean field theory.
b. Dynamo type alpha-Omega and alpha^2
c. Magnetic instabilities - magnetorotational instability and instability of magnetic buoyancy in the context of the Solar Tachocline.
d. Tidal instability (source of the magnetic field on Io).

During the exercise classes, some introductory and supplementary problems will be solved on the above-mentioned aspects of the hydromagnetic dynamo, including the use of MATLAB and MATHEMATICA packages. The exercises will take place partly at the blackboard (solving simple examples), but mostly at the computer (programming with the use of the above-mentioned packages).