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 telegraphic approximation (TA) is applied to the streamwise velocity component and air temperature time series acquired in the first metre above the salt flats of Utah, USA. The TA technique removes amplitude variations and retains only zero-crossing behaviour in a turbulent series, thereby allowing for an isolated examination of the role of clustering in intermittency. By applying the TA technique, clustering properties are analyzed to uncover dissimilarity in temperature and velocity across unstable, near-neutral, and stable atmospheric stratification. The spectral exponents of the original and of the TA series are examined, with the inertial-subrange behaviour conforming to prior empirical relations and the energy-containing range exhibiting deviations. These two distinct scale regimes are observed in the standard deviations of the running density fluctuations of the TA series, delineating scaling behaviour between fine and large scales. In the fine scales, clustering is not appreciably affected by the stability regime and is higher than in the large scales. In the large scales, the temperature series exhibits stronger clustering with increasing stability, and higher clustering compared with the streamwise velocity component series under stable conditions. Amplitude variations are shown to mitigate intermittency in the small scales of velocity, but play only a minor role in intermittency for temperature. Last, the inter-pulse period probability distributions are explored and implications to self-organized criticality as models for TA turbulence are discussed.