Scaling properties of nonstationary wind fields based on time-varying mean wind speed models

This paper introduces an approach designed to address an inadequacy of Taylor's frozen hypothesis in determining the scaling exponent of structure functions for nonstationary wind speeds. The key step of this approach is to substitute the time-varying mean (TVM) components U¯(t) for the constant mean U¯ in the calculation of structure functions of nonstationary wind speed fields. In this approach, TVM components of nonstationary wind speeds were first determined based on the advanced wavelet transform and empirical mode decomposition. Subsequently, a comprehensive comparison was conducted for the calculation of scaling exponents of nonstationary wind speed records measured during Typhoon and Downburst events, utilizing different approaches. Our analysis results reveal that various models, including the K41 model [A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluid for very large Reynolds' numbers,” Proc. USSR Acad. Sci. 30, 301–305 (1941), available at https://scispace.com/papers/the-local-structure-of-turbulence-in-incompressible-viscous-25te3acxv9], K62 model [A. Kolmogorov, “A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number,” J. Fluid Mech. 13(1), 82–85 (1962)], β model [Frisch et al., “A simple dynamical model of intermittent fully developed turbulence,” J. Fluid Mech. 87(4), 719–736 (1978)], and SL model [She and Leveque, Universal scaling laws in fully developed turbulence,” Phys. Rev. Lett. 72(3), 336–339 (1994)], have their own respective strengths and limitations in describing the relationship between the scaling exponent ξp and the order p. Significant differences in scaling exponents were observed between the original and new versions of Taylor's hypothesis, particularly at higher orders of p or for wind speed with strong nonstationarity such as the downburst. It is suggested that the Taylor's frozen hypothesis needs to be adjusted when computing the scaling exponents ξp of nonstationary wind speed fields in future studies.