A sub-Gaussian model of vortex wandering and its application to tornado-like surface pressures

Abstract

A sub-Gaussian probability distribution model for vortex wandering displacement is proposed in this study. The model can flexibly and accurately characterize the sub-Gaussian distribution characteristics of both primary and secondary vortex wandering displacements. Furthermore, it is capable of representing both unimodal and bimodal forms of the marginal/joint probability density function. Using this model, convolution and deconvolution formulas were established between the measured mean and variance of surface pressure and those of an idealized vortex. A comparison of vortex wandering correction methods shows that the deconvolution algorithm always yields the maximum variance for the ideal vortex pressure, implicitly assuming that the pressure is fully positively correlated. When the instantaneous pressure field deviates from the axisymmetric assumption, the recentering procedure may introduce some unknown errors in the corrected mean and variance profiles. This work provides a probabilistic framework for vortex-wandering description and offers insights into the selection and limitation of correction techniques for tornado-like vortices.