Eric Mittelstaedt, University of IdahoE
xperienced modelers are familiar with how non-dimensionalizing mathematical systems can help improve numerical stability, reduce the number of free variables needed to explain a physical system, capture the essential driving processes of a problem of interest, and scale laboratory experiments to the Earth. However, when first introduced to non-dimensional numbers, students often have difficulty understanding how the mantle can have a depth of 1, or how numbers such as the Nusselt number or the Rayleigh number are derived. In this webinar, I will discuss a hands-on, in-class experiment involving a simple oscillator (mass on a spring) that I have used to introduce students to non-dimensionalizing equations, deriving non-dimensional numbers, and scaling experimental results. The mass-spring system is familiar to many students from their introductory physics classes and the mathematical system is simpler than many problems of interest in geodynamics. The combination of familiarity, basic mathematics, and a hands-on experiment facilitate student comprehension and future application of non-dimensional numbers. These methods are aimed at an introductory graduate course or senior level undergraduate course on modeling.