Fluid Dynamics of Planetary Interiors

Basic fluid dynamics - Navier-Stokes equation, vorticity equation, Kelvin’s circulation theorem, energy and dissipation, helicity. Rotation - Coriolis force, linear inertial waves, formation of Taylor columns, geostrophy, quasi-geostrophic approximation. Stratification - Gravity waves, effect of rotation, Braginsky’s theory of stratified outer core of the Earth. Magnetic fields - Magnetohydrodynamic (MHD) equations, Lorentz force, low and high magnetic Reynolds number, Alfven waves, Magnetic-Coriolis (MC) waves, Rayleigh Benard convection with magnetic field and rotation, MHD of planetary cores. Turbulence - Richardson’s cascade, overview of classical theories, 2D turbulence, turbulence under moderate and rapid rotation, MHD turbulence, different length scales in planetary core turbulence.

References

• Davidson, P.A., Turbulence in rotating, stratified and electrically conducting fluids, Cambridge University Press, 2013.
• Acheson, D.J., Elementary fluid dynamics, by, Oxford University Press, 1990.
• Journal papers