Typhoon eye trajectory based on a mathematical model: comparing with observational data

摘要

We propose a model based on the primitive system of the Navier-Stokesequations in a bidimensional framework as the $l$ - plane approximation, whichallows us to explain the variety of tracks of tropical cyclones (typhoons). Ouridea is to construct special analytical solutions with a linear velocityprofile for the Navier-Stokes systems. The evidence of the structure of linearvelocity near the center of vortex can be proven by the observational data. Westudy solutions with the linear-velocity property for both barotropic andbaroclinic cases and show that they follow the same equations in describing thetrajectories of the typhoon eye at the equilibrium state (that relates to theconservative phase of the typhoon dynamics). Moreover, at the equilibriumstate, the trajectories can be viewed as a superposition of two circularmotions: one has period $2\pi/l,$ the other one has period $2\pi/b_0,$ where$l$ is the Coriolis parameter and $b_0$ is the height-averaged vorticity at thecenter of cyclone. Also, we compare our theoretical trajectories based on initial conditionsfrom the flow with tracks obtained from the observational database. It is worthto mention that under certain conditions our results are still compatible withobservational data although we did not truly consider the influence of steeringeffect. %Note that the %motion of the typhoon eye can not be totallydeterminated by initial %conditions due to the effect of ambient pressure field("steering" %effect). Finally, we propose the parameter-adopting method so thatone could correct the weather prediction in real time. Examples of our analysisand the use of parameter-adopting method for the historic trajectories areprovided.