Why the Wind Can’t Blow Where It May: Mathematical Rules for Vector Fields on the Surface of the Earth

As part of the Physics Spring 2015 Seminar Series, Professor Ockle Johnson will be discussing "Why the Wind Can’t Blow Where It May: Mathematical Rules for Vector Fields on the Surface of the Earth"

The wind on the surface of the earth is an example of a vector field. Wind has a magnitude (speed) and a direction, and so there is a wind vector at each point on the earth. At some points, the wind vector is zero, the eye of a hurricane being a well-known example. In this talk we will look at a way to categorize different types of zeroes of vector fields and discover that there is a mathematical relationship or constraint that the zeroes of any vector field on the surface of the earth must satisfy. The constraint involves the Euler Characteristic, which measures how the surface can be built up out of two-dimensional faces, one-dimensional edges, and zero-dimensional vertices. It is also relates to the critical points on the surface: the maxima, saddles, and minima.