Overturning a Long-held Hypothesis About Turbulence
Novel observational results provide improved understanding of turbulent fluxes; may resolve a long-standing issue regarding measurements of the surface energy balance
Observations of turbulent fluxes of momentum, heat, water vapor, and carbon dioxides are important constraints on land-surface, weather forecast, and earth system models. Scientists have relied on a theory known as Taylor’s frozen turbulence hypothesis to calculate these fluxes from single-point measurements using a technique known as the eddy-covariance method. Taylor’s hypothesis assumes that time averages can replace spatial averages in characterizing turbulences. The turbulent eddies are considered to be “frozen”, or unchanging as they move with the wind past the sensor. In this study, scientists reexamine Taylor’s hypothesis using temperature data obtained from a relatively new measurement technique known as distributed temperature sensing (DTS) that uses scattering within an optical fiber to measure temperature at high spatial and temporal resolution. In this experiment, DTS fibers were set up at four heights within the atmospheric surface layer along a 230-m transect. The very high resolution measurements of temperature along the length of the DTS fiber allow scientists to examine the detailed characteristics of the turbulent eddies.
The study finds that Taylor’s hypothesis holds for larger eddies, but fails for smaller eddies because they lose their coherence due to turbulent diffusion as they are transported with the wind. Thus the smaller eddies are no longer ‘frozen’, one of the key assumptions of the hypothesis. The authors propose a correction that can be applied to existing high-frequency eddy-covariance data measured at flux towers. The results should improve estimates of surface turbulent energy and carbon dioxide fluxes, which can in turn be used to improve model projections. The results may also resolve a long-standing issue in which measurements of the various components of the surface energy budget at flux tower sites, which should balance each other, disagree by 10-20%.
Taylors’ frozen turbulence hypothesis suggests that all turbulent eddies are advected by the mean streamwise velocity, without changes in their properties. This hypothesis has been widely invoked to compute Reynolds’ averaging using temporal turbulence data measured at a single point in space. However, in the atmospheric surface layer, the exact relationship between convection velocity and wavenumber (k) has not been fully revealed since previous observations were limited by either their spatial resolution or by the sampling length. Using Distributed Temperature Sensing (DTS), acquiring turbulent temperature fluctuations at high temporal and spatial frequencies, we computed convection velocities across wavenumbers using a phase spectrum method. We found that convection velocity decreases as k-1/3 at the higher wavenumbers of the inertial subrange instead of being independent of wavenumber as suggested by Taylor’s hypothesis. We further corroborated this result using large eddy simulations. Applying Taylor’s hypothesis thus systematically underestimates turbulent spectrum in the inertial subrange. A correction is proposed for point-based eddy-covariance measurements, which can improve surface energy budget closure and estimates of CO2 fluxes.
PG would like to acknowledge funding from the National Science Foundation (NSF CAREER, EAR- 1552304), and from the Department of Energy (DOE Early Career, DE-SC00142013). Dr. Selker’s contributions to this work were made possible the Center for Transformative Environmental Monitoring Programs (CTEMPs) funded by the National Science Foundation, award EAR 1440506.
Cheng, Y., C. Sayde, Q. Li, J. Basara, J. Selker, E. Tanner, and P. Gentine (2017), Failure of Taylor’s hypothesis in the atmospheric surface layer and its correction for eddy-covariance measurements, Geophys. Res. Lett., 44, doi:10.1002/2017GL073499.