Non-Gaussian Statistics of Atmospheric Turbulence and Related Effects on Aircraft Loads

Abstract

Non-Gaussian statistical properties of turbulence in the inertial range can be characterized in terms of an exponent (k) that defines the scaling of velocity increments together with a fractal dimension (D) that quantifies “intermittency.” A new method of data analysis, for measuring k and D ,i sp resented based on the collapsing of appropriately normalized probability distributions measured at different scales. The method is illustrated by its application to records of turbulence measured at low altitudes by a specially instrumented Gnat trainer aircraft. The resulting “multifractal” statistical description of velocity increments is consistent with results obtained by previous authors using a different method of analysis, based on the scaling of velocity structure functions, and with the predictions of recent theoretical models of physical processes in the inertial range. It is demonstrated how the results can be applied directly to the estimation of aircraft loads, using a new multifractal formulation of statisticaldiscrete-gust theory. Qualitative differences between the resulting estimated loads and the loads predicted by the statistical method prescribed in the current airworthiness regulations, the power-spectral-density method, are identified.