In this series, I demonstrate how to apply simple numerical solution methods to meteorology and, in particular, atmospheric dynamics. These methods, which require only a hand-held calculator to perform, are used to solve problems in meteorology that are otherwise often glossed or skipped by instructors and textbooks. The advantage to this approach is that students learn more about meteorology and advanced techniques of problem-solving, and do so in a context that is intriguing, accessible, and user-friendly.
In this fourth installment, we examine the equation for the minimum wavelength Lcrit of a growing wave in the Eady (1949) model of the extratropical cyclone. The governing equation is pi*R/Lcrit = coth(pi*R/Lcrit), where R is the Rossby radius of deformation. The solution is Lcrit = 2620 km. However, most undergraduate- and graduate-level textbooks (e.g., Dutton 1976; Gill 1982; Holton 1992; Kundu 1990; Pedlosky 1979) do not attempt to explain how the fundamental length scale Lcrit is obtained from a nonlinear hyperbolic-trigonometric equation.
In this poster I show how to arrive at this critical wavelength easily via both analytic (Taylor series) and numerical (iterative) methods. I also illustrate how the numerical result can be approximated through graphical iteration, an approach that is even more student-friendly.
These results fill in a gap in today's dynamics textbooks and provide a simple way to explain to non-scientists why an extratropical cyclone is so much larger than a tornado or a hurricane