“…In the present paper we consider idealized vortex structures and idealized vertical structures of Q that allow the transverse circulation equation to be solved analytically via three different methods. These simple theoretical arguments illustrate the usefulness of the complementary concepts of Rossby length (also sometimes referred to as the “Rossby radius of deformation”) and Rossby depth, and thereby elaborate on ideas discussed in the extensive literature on applications of the balanced vortex model to tropical cyclones (e.g., Ooyama , 1969, Sundqvist , 1970a, b, Smith , 1981, Shapiro and Willoughby , 1982, Schubert and Hack , 1982, Hack and Schubert , 1986, Nolan et al , 2007, Vigh and Schubert , 2009, Pendergrass and Willoughby , 2009, and Willoughby , 2009).…”