Understanding the Vorticity Equation (or One Term) with a Pool Noodle

Deriving the vorticity equation from the momentum equations can be like jumping into the deep end of a pool. However, taking the cross product, gathering like terms, and finding the vector terms can be a successful medley relay race to the final equation. Understanding each term physically creates a new challenge. The twisting-tilting term, with two sets of derivatives multiplied together, is especially complex looking. Explaining the terms in each product (i.e., vertical shear and a horizontal gradient of vertical motion) helps a little, but it is still difficult for students to understand physically how the products generate vorticity. A simple pool noodle provides the perfect flotation device to understanding the twisting-tilting term.

In a 5-minute, hands-on demonstration, students quickly achieve a physical understanding of the twisting-tilting term. Students grasp how forces on the pool noodle creates shear. Tilting their demonstration into the vertical provides the final life preserver. Slight changes to the demonstration show the complexity of the term and students realize how each derivative in the product changes the outcome. Students immediately jump in to picture complex applications to vortex structures.