Applicability of Taylor's frozen hypothesis and elliptic model in the atmospheric surface layer

Based on the synchronous multi-point temperature data measured at different streamwise positions with the application of distributed temperature sensing, a field investigation on the applicability of Taylor's frozen hypothesis and elliptic model was performed in the atmospheric surface layer (ASL). In this work, several important spatial statistical functions of temperature field, such as longitudinal space–time correlation [CTT(r, t)], space correlation [RTT(r)], normalized second-order structure function [ ⟨ Δ T + 2 ( r ) ⟩], and wavenumber spectrum [ΦTT(k)] of temperature fluctuations, were directly measured in the ASL. By comparing the directly measured spatial statistical functions with the predicted results, our study indicates that both Taylor's frozen hypothesis and elliptic model are applicable in the near-neutral and stable ASLs when the turbulence level is low. However, only the elliptic model is substantially accurate in the unstable ASL when the turbulence level is high. The elliptic model can relate CTT(r, t) to RTT(rE), where rE = [(r−Ueτ)2+(Veτ)2]1/2, Ue is the convection velocity, and Ve is the sweeping velocity. With the application of Ue and Ve, RTT(r) and ⟨ Δ T + 2 ( r ) ⟩ can be estimated by the elliptic model in the near-neutral, unstable, and stable ASLs.