Nonequilibrium scaling vs. the temporal evolution of turbulence

Despite many airborne measurements and research campaigns our understanding of turbulence in free atmosphere is still far from sufficient. Part of the problem is the limited amount of measurement data, another part is measurement errors and last, but not least element is inadequate or not satisfactory data analysis. This presentation addresses some aspects of this last issue. The simplest way to characterize turbulence is to define/measure characteristic velocity U and length L (or time T) scales of turbulent  eddies. Two quantities necessary to estimate them are the turbulence kinetic energy K and the turbulence kinetic energy dissipation rate. A universal scaling relation between dissipation rate, turbulence kinetic energy and the turbulence length scale follows from the classical picture of the equilibrium Richardson-Kolmogorov cascade. There, the energy is transported between scales in a downward cascade until it is dissipated into heat by the smallest eddies. This universal scaling is a basis of many turbulence models, also in the context of atmospheric applications. However, a number of recent papers suggest that a universal, although different from the classical, scaling could also be observed in unsteady turbulent flows, which ate typical in the free atmosphere. In this study we investigate the nonequilibrium scaling relation between the integral length scale of turbulence and dissipation rate using velocity signals from various airborne measurements of atmospheric cloud turbulence, including that in and around convective clouds. A research aircraft measures 1D intersection of turbulent velocity field as a time series collected along the flight tajectory. Hence,  information on  temporal behavior (decay or development) of turbulence is not directly available. In this study we show how this important information can be recovered based on the observed scaling relations.