A typhoon-like vortex solution of incompressible 3D inviscid flow

This letter obtains a typhoon-like vortex solution by solving the Bragg-Hawthorne equation. The solution describes spiral paths of fluid material element on the Bernoulli surface, whereas some new exact solutions are obtained which are bounded in the whole region. The first one is a continued umbrella vortex solution, which is a typhoon-like vortex. The second one is a multi-planar solution, which is periodic in z-coordinate. Within each layer, there is an umbrella vortex solution similar to the first one. The above explicit solutions can be applied to the study of radial structure of typhoon. Both the solutions and the approaches used in the present work can also be applied to other complex flows.