Analytical Research On Linear And Nonlinear Vorticity Equations With Initial Value

In this paper, we have investigated the vortex axisymmetrezation in the atmosphere and also discovered some useful mechanisms about the vortex energy effected by basic flow and a new vorticity-value in a nonlinear equation. For many years, academicians bend themselves to the study which lead to the change of theperturbation energy and have found that the vortex advection, baroclinic, f -effect,β -effect and so on were effective on the vortex energy. Now we discuss the energymechanism under the basic flow. It is not only academic but also practical. First, we changed the simple shear flow into the weakly second-time shear flow to show some useful conclusions. It is shown that the vortex energy has relationships with the weakly second-time shear intensity parameter s and the meridional margin of the hurricane vortex which neglected in the first-time shear basic flow. Second, we add an nonlinear perturbation into the linear vorticity equation and get a new perturbation-value and perturbation-vorticity in a nonlinear equation.