Application of nonlinear dynamical systems analysis to conditionally sampled concentration fluctuations of a passive scalar in the atmospheric boundary layer

Abstract

Time series and nonlinear dynamical systems analysis have been applied to the characterization of conditionally sampled concentration fluctuations (viz., zero concentration intervals censored) of a passive scalar from a unipolar ion plume experiment in an atmospheric boundary layer. The statistical characteristics of the scalar fluctuations are summarized in terms of basic descriptive statistics (e.g., mean concentration, fluctuation intensity, skewness, kurtosis, etc.), the concentration probability density function and the power spectral density function (or, equivalently, the autocorrelation function). In order to determine the origins for the variability and seemingly random behavior in concentration, new nonlinear dynamical systems-theoretical methods have been utilized for the analysis of concentration fluctuations. The concentration attractor, which is responsible for the temporal evolution of the observed concentration time series, has been reconstructed using phase-space techniques. The results provide compelling evidence for the existence of a strange attractor with an intriguingly low fractional correlation dimension of about 5.6. Furthermore, the spectra of generalized dimensions and of singularities have been determined for the concentration attractor and these results provide indications of the inhomogeneous, multifractal nature of the attractor. Finally, the most significant Lyapunov exponents have been extracted for the system and these exponents provide evidence that the nature of the dynamics is chaotic.