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Some observed statistical properties of small scale turbulence Wilson, John Ronald

Abstract

The purpose of this work was to investigate the characteristics of the small scales of the turbulent velocity and temperature fields in the atmospheric boundary layer. Of particular interest were the distributions of the spatial derivatives, the behaviour of the structure functions and the nature of the interactions leading to the inertial transfer of energy between the larger and smaller scales of the turbulent flow. The observed statistical distributions of the differentiated downstream and X-wire signals did not accurately conform to the theoretically predicted logarithmic normal model although there was good general agreement. The distribution of the sum of the squares of the differentiated X-wire signals was described extremely well by the log normal model. The temperature derivatives followed the log normal distribution somewhat better than did the velocity derivatives, but a poor signal to noise ratio prevented conclusive results. The observed structure functions conformed to present theory for the velocity and temperature data. The inertial transfer of energy in the downstream component was found to behave as would be intuitively expected. Specifically the net rate of arrival of energy was zero for wavenumbers where viscosity was unimportant and positive where viscosity was important. Interactions of scale sizes differing by more than a factor of ten in size did not contribute significantly to the energy transfers. The flow of downstream energy was observed to be from larger to smaller scale sizes for horizontal scales as large as twenty meters. The mean inertial transfer of energy associated with interactions between downstream components only, was found to be approximately equal to the mean rate of energy loss due to the corresponding dissipation term.

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