Velocity and Temperature Dissimilarity in the Surface Layer Uncovered by the Telegraph Approximation

Abstract:

The physicist and mathematician Shang-Keng Ma once commented that "the simplest possible variable is one that can have two values. If there is only one value, no variation is possible". Guided by this dictum, the telegraph approximation (TA) is applied to streamwise velocity and temperature time series acquired in the first meter above the ground at the Surface Layer Turbulence and Environmental Science Test (SLTEST) facility. By applying the TA, clustering properties and their dependence on atmospheric stability are analyzed to uncover dissimilarity in temperature and velocity. The TA technique removes amplitude variations and retains only the zero-crossing behavior in a turbulent series thereby allowing for an isolated examination of the role of clustering in intermittency. The spectral exponents of the original and the TA series for both velocity and temperature are examined for all atmospheric stability regimes and appear to conform to prior empirical relations, especially in the inertial subrange. A distinct double regime is observed in the standard deviations of the running density fluctuations of the TA series. In the smaller scales, clustering does not seem to be appreciably affected by distance from the surface, and clustering in temperature appears to increase with increasing stability. In the larger scales, both velocity and temperature exhibit stronger clustering with increasing stability. When examining the intermittency between the original series and its TA, amplitude variations are shown to mitigate intermittency for velocity, but play only a minor role in intermittency for temperature. Last, the interpulse period duration probability distributions are well-approximated by log-normal models across both variables and all stability conditions. Implications to self-organized critically as models for TA turbulence are discussed.