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Vortices play an unique role in heat and momentum transports in astro- andgeo-physics, and it is also the origin of the Earth's dynamo. A questionexisting for a long time is whether the movement of vortices can be predictedor understood based on their historical data. Here we use both the experimentsand numerical simulations to demonstrate some generic features of vortex motionand distribution. It can be found that the vortex movement can be described onthe framework of Brownian particles where they move ballistically for the timeshorter than some critical timescales, and then move diffusively.Traditionally, the inertia of vortex has often been neglected when one accountsfor their motion, our results imply that vortices actually haveinertial-induced memory such that their short term movement can be predicted.Extending to astro- and geo-physics, the critical timescales of transition arein the order of minutes for vortices in atmosphere and ocean, in which thisinertial effect may often be neglected compared to other steering sources.However, the timescales for vortices are considerably larger which range fromdays to a year. It infers the new concept that not only the external sourcesalone, for example the solar wind, but also the internal source, which is thevortex inertia, can contribute to the short term Earth's magnetic fieldvariation.

Crossover from ballistic to diffusive vortex motion in convection