This video is part of the Differential Equations video series.

Video Summary

This video leads students through the physical definition of the curl, and its connection to the mathematical description. A variety of classical fluid flow environments are analyzed for the existence of curl. Finally, the connection between curl and momentum transfer in fluid flow are explored in the context of biological locomotion.

Learning Objectives

After watching this video students will be able to:

  • Understand curl as a measurement of the magnitude and direction of maximum circulation per unit area.
  • Recognize curl in 2-dimensional fluid flows.
  • Describe the relationship between curl and vorticity.
  • Connect vorticity to momentum transfer for a collection of familiar physical phenomena.

Student Experience

It is highly recommended that the video is paused when prompted so that students are able to attempt the activities on their own and then check their solutions against the video.

During the video, students will:

  • Recall the physical and mathematical descriptions of divergence, gradient, and curl.
  • Derive the formula for a 2-dimensional curl in the xy-plane.
  • Predict whether different fluid flow regimes have vorticity.
  • Explain why a channel flow has vorticity, given the velocity field.