Boundary layer coherent structures
Abstract
The correlation dimension D is used commonly to quantify the chaotic structure of an attractor of a smooth dynamical system. The standard algorithm for estimating the value of D is based on finding the mean slope of the curve obtained by plotting ln C(r) versus ln r, where C(r) is the correlation integral and r is the distance between points on the attractor. The alternative, probabilistic method proposed by Takens is based on finding the sample means of the random variable ln(r/p), expressed as the conditional expected value E(ln(r/p):r<p). In this article, this first Takens estimator is extended and generalized.
 Publication:

Pennsylvania State Univ. Report
 Pub Date:
 August 1993
 Bibcode:
 1993psu..reptU....S
 Keywords:

 Atmospheric Circulation;
 Boundary Layers;
 Chaos;
 Dynamical Systems;
 Probability Theory;
 Strange Attractors;
 Algorithms;
 Remote Sensing;
 Time Series Analysis;
 Fluid Mechanics and Heat Transfer