Characterizing atmospheric surface layer turbulence using chaotic return map analysis

Nonlinear time series analysis methods are used to investigate the dynamics of mechanical and convective turbulences in the atmospheric surface layer flow. Using dynamical invariant analysis (e.g. correlation dimension, Lyapunov exponent and mutual information) along with recurrence quantification analysis (e.g. recurrent rate, determinism, average diagonal length of recurrence plot, etc.) of the vertical wind component data, it is confirmed that a convective turbulence is a lower order manifold in its phase space exhibiting higher degree of organization than a mechanical turbulence. Applying a quasi-one-dimensional chaotic return map technique, the topological differences between the mechanical and convective turbulences are explored. These quasi-one-dimensional return maps are produced using the local maxima of the first principal component of the reconstructed turbulence data. A comparison of the probability distribution of the local maxima of a forced Lorenz model with the turbulence data indicates the possible existence of a stable fixed point for both type of turbulences. Furthermore, dynamically the mechanical turbulence is found to resemble an unforced Lorenz model whereas the convective turbulence resembles a forced Lorenz model.