Iterative solutions of the gradient wind equation

The gradient wind equation from meteorology plays a fundamental role in the understanding of atmospheric dynamics: it describes the circulation associated with high- and low-pressure systems as well as the flow of the jet stream. While it is easily solved analytically, iterative solutions of the gradient wind equation illustrate many of the characteristics of numerical solutions to the full dynamical equations, including convergence, dependence on initial conditions, and the impact of different solution approaches on the character of the solution. We explore these properties of the gradient wind equation, and in so doing rectify an error in the research literature. Our analysis should be of particular interest to teachers of computational methods in the geosciences as well as their students.