Hugoniot-Maslov chains for solitary vortices of the shallow water equations, II. The analysis of the solutions of the truncated chain and an approximate description of possible trajectories of mesoscale vortices (typhoons)

This is the second part of tie paper (Part I was published in RJMP, vol. 6 (1999), no. 2). Here we analytically and numerically study some special fam ilies of solutions to truncated chains of Hugoniot-Maslov equations for sol itary vortices of the shallow wave equations. The solutions belonging to th ese families are in a sense critical and describe sufficiently smooth appro ximate trajectories of solitary vortices. The existence of such solutions i s closely related to the so-called beta-effect (the slow dependence of the Coriolis frequency on latitude). The asymptotic analysis of such equations, which is essentially based on the (partial) averaging method, quite unexpe ctedly results in a simple system of second-order equations that is integra ble in quadratures and coincides in some approximation with the physical pe ndulum equations. We compare the approximate trajectories of solitary vorti ces thus obtained with the trajectories of several actual typhoons.