Flow with Vectors — Lesson 3

This lesson covers the concept of flows with vectors, focusing on how velocity, a vector, advects another vector. The lesson uses examples such as magnetic fields and electric dipoles to illustrate the concept. It also introduces the equations used to solve these flows, including the general equation and the equation for vector fields. The lesson further explains the concept of advection and the role of pressure gradient. It also introduces the Reynolds number and Prandtl number, which are used to define the flow. The lesson concludes with a discussion on passive vectors and magneto hydrodynamics.

Video Highlights

00:22 - Explanation of how velocity is a vector and how it advects another vector
01:03 - Explanation of the equations related to the flow with a vector
05:26 - Explanation of the equations in Fourier space
07:22 - Discussion on the concept of mode to mode transfer
09:42 - Explanation of the concept of energy flux
13:50 - Discussion on the concept of passive vector
14:48 - Explanation of the spectrum for kinetic energy

Key Takeaways

- Velocity, a vector, can advect another vector, such as a magnetic field or electric dipole.
- The general equation for flows with vectors includes a viscous term.
- Advection is a key concept in understanding flows with vectors.
- The Reynolds number and Prandtl number are used to define the flow.
- Passive vectors and magneto hydrodynamics are two types of flows that can be considered.