Curl in fluid flow - Burch & Choi, 2006

[torquetum]

 Burch, K.J. & Choi, Y. (2006). The curl of a vector field: beyond the formula. PRIMUS: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 16(3), 275-287.

 

The authors contextualise curl and Stoke’s Theorem in fluid flow. They begin by considering an infinitesimal rectangle deformed by a vector field. They calculate the angular velocities of two adjacent edges and show how that relates to the concept of viscosity in fluid dynamics and to the familiar curl formula. They show how that means that curl relates to spin about an object's own axis (independent of translation through a fluid) and give some examples. For several given vector fields, they draw the direction field and intuitively predict spin, then they back that up with curl calculations. The authors close with a discussion of the meaning of the Stokes’ Theorem formula and how the curl side of the formula is measuring the viscosity flux of V across S. I found this paper really interesting.

 

Do not treat this blog entry as a replacement for reading the paper. This blog post represents the understanding and opinions of Torquetum only and could contain errors, misunderstandings or subjective views.