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