A Clustering Method to Characterize Intermittent Bursts of Turbulence and Submeso Motions Interaction in the Stable Boundary Layer.

Abstract:

Atmospheric boundary layers with stable stratification include a variety of small-scale non-turbulent motions such as waves, microfronts and other complex structures. When the thermal stratification becomes strong, the presence of such submeso motions could affect the turbulent mixing to a large extent and common similarity theory that is used to describe weakly stable conditions may become unreliable. The scientific community clearly lacks understanding of what these motions are and of the extent to which they affect turbulent mixing in the stable boundary layer.

We use a data-based approach to isolate regimes in which small-scale, non-turbulent motions are a main influencing parameter of turbulent mixing. We apply a clustering methodology derived for multidimensional nonstationary timeseries. The technique is based on a bounded variation, finite element method (FEM-BV) and we use it to characterize the interaction between small-scale non-turbulent motions and turbulence. Turbulence data are approximated by an optimal sequence of locally stationary multivariate autoregressive factor models (VARX) processes and some slow hidden process switching between them (FEM-BV-VARX (Horenko 2010, JAS)). The VARX processes that approximate the data include influence from external forcing. We perform prefiltering of the turbulence data to isolate submeso motions and use them as external forcing in the clustering strategy. Thus the strategy separates periods for which the influence of the external factors, i.e. non-turbulent motions on the turbulence differs.

We use this strategy to derive a stochastic representation of the interactions between non-turbulent motions and turbulence under stable stratification. Our results show that submeso motions are a main forcing of turbulence in the most stable cases and not for the weakly stable cases. As these different influence regimes are isolated by the FEM-BV-VARX technique, a Markov transition matrix describes the probability of switching between the different clusters. This transition matrix represents a slow, hidden process governing the response of turbulence data to the chosen influencing factors. Derivation of a stochastic process that represents the reaction of turbulence to forcing by submeso motions and its evolution in time is based on this matrix.