A theoretical model of lateral coherence in isotropic turbulence based on stochastic Fourier wave-number spectrum

Abstract

With the development of measuring instruments and the study of turbulence theory, the field measurement of wind field has become increasingly accurate and refined. Thus, these improvements provide us with a new perspective on the old problem, which is how to solve problems through the physical mechanism of objective phenomena rather than relying on phenomenological experience and statistical results. In the present paper, an observation array was built up to measure the near-surface strong winds in Southeast of China. Based on extensive observation data, the stochastic Fourier spectrum model of fluctuating wind is verified. Then, under the assumption that the flow is stationary and homogeneous, a theoretical model of lateral coherence with solid physical basis is derived, which is a segmentation function corresponding to the different energy ranges in energy spectrum. This model portrays the correlation between the stochastic Fourier spectrum of two spatial points. It is revealed that how the probabilistic evolution of the fundamental physical quantities affects the spatial coherence of the wind field, when the wave number is small or the lateral separation is short. The theoretical results accord with the measured results well.