(1) Consider a westerly wind of the form u = λy, for λ contant and y northward distance. (a) Derive an expression for the circulation around a square with sides of length L by explicitly integrating the circulation equation around the square oriented so that the southernmost edge of the square is along y = 0. (b) Derive an expression for the circulation using only the mean value of the tangential wind around the square (i.e., the mean value of u · dl).

(2) Derive an expression for the wind flowing around a circular vortex having the same circulation and area as the shear flow and square in problem 1. Discuss cyclonic and anticylonic flow relative to the shear parameter, λ.