A large eddy simulation study of the applicability of Taylor's frozen turbulence hypothesis in the atmospheric boundary layer

Taylor’s frozen turbulence hypothesis (TFTH) posits all turbulent eddies are advected by the mean wind, without changes in their spatial characteristics. In this framework turbulence is ‘frozen’ and eddies of all scales are advected similarly by the mean flow. This hypothesis allows one to use fast response sensors to measure turbulence in the temporal domain at higher frequencies and translate them to infer the spatial statistics. This assumption and approach is critical in micrometeorology, where the surface turbulent fluxes are measured using stationary, tower-mounted, fast-response sensors.

To address the validity of TFTH, Chowdhuri et al. (under review) calculated the scale-dependent convective velocities of turbulent eddies using Distributed Temperature Sensing measurements in a heterogeneous forest clear-cut. By using observations at a single height, their results demonstrated that in buoyancy-dominated high-Reynolds number atmospheric flows, the convective speeds of turbulent eddies in the inertial subrange scales are dependent on the wavenumbers in a power-law fashion. They hypothesized that this scale-dependency is sensitive to the underlying surface characteristics, stability conditions, height above the surface, and flow anisotropy. To test their hypotheses, we build on their approach and investigate the validity of TFTH in large eddy simulations of the atmospheric boundary layer (ABL) using the PALM model system. We calculate the scale-dependent convective speeds (uc(k), where k is the streamwise wavenumber) and investigate their dependence with wavenumbers over a suite of different surface conditions (homogeneous to heterogeneous), dynamic stabilities (convective to stable), and heights within the surface layer. These results are used to examine the conversion of turbulence (co) spectra between temporal and spatial domains.