Energy Transfers in Magnetohydrodynamic Turbulence — Lesson 2

This lesson covers the concept of energy transfers in Magnetohydrodynamics (MHD). It explains the equations for energy, kinetic energy, and magnetic field. The lesson also discusses the energy transfer from mode to mode and the concept of triads in energy transfer. It further elaborates on the energy transfers for z plus z minus and the concept of fluxes in energy transfer. The lesson concludes with the discussion on shell to shell transfer in energy. For instance, it explains how energy can be transferred from one shell to another in the u b variables and z plus z minus variables.

Video Highlights

00:27 - Explanation of the equation for kinetic energy and the first non-linear term
01:54 - Discussion on the equation for the magnetic field
03:46 - Explanation of the mode to mode energy transfer
11:21 - Discussion on the energy transfer for z plus and z minus
15:05 - Explanation of the six fluxes
19:29 - Discussion on the two fluxes for z plus and z minus
22:27 - Explanation of the shell to shell transfer

Key Takeaways

- Energy transfers in MHD can be understood through equations for energy, kinetic energy, and magnetic field.
- The concept of triads is crucial in understanding energy transfers.
- Energy can be transferred from mode to mode, which was demonstrated in a study conducted in 2001.
- The energy transfers for z plus z minus are simpler than other forms.
- The concept of fluxes in energy transfer is important, with six fluxes for u b variables and two for z plus z minus variables.
- Shell to shell transfer in energy is another significant concept, with four transfers in u b variables and two in z plus z minus variables.