Statistical analysis of a numerical simulation of two-dimensional turbulence

An important feature of the time evolution of the vorticity fields in two-dimensional turbulence is the emergence of isolated and coherent structures or vortices. A vortex is a region enclosed by a closed contour, or equivalently a disjoint component, of a sufficiently high value of the vorticity field.This thesis proposes two estimators of the population of vortices in a vorticity field. They are constructed by discretizing the analytical expression for the number of disjoint components in a contour of a random field derived by Swerling, [13]. One is based on a Riemann sum approximation, while the other employs Monte Carlo integration. The performance of the two estimators is evaluated and it is found that the Monte Carlo based estimator is superior. It is used to estimate the population of vortices from a single simulation of the vorticity equation governing two-dimensional turbulence. Finally, the method is applied to analyze the time evolution of the population of vortices