Assessing Turbulence Strength via Lyaponuv Exponents

In this paper we study the link between `turbulence strength’ in a flow and the leading Lyaponuv exponent that characterize it. To this end we use two approaches. The first, analytical, considers the truncated convection equations in 2-dimensions with three (Lorenz model) and six components and study their leading Lyaponuv exponent as a function of the Rayleigh number. For the second approach we analyze fifteen time series of measurements taken by a plane flying at constant height in the upper troposphere. For each of these time series we estimate the leading Lyaponuv exponent which we then correlate with the structure constant for the temperature.