Theses Doctoral

Multiscale Turbulence in the Atmospheric Boundary Layer

Cheng, Yu

Turbulent flows are widely observed in nature and man-made systems. The understanding of turbulence is important since the air motion in the atmospheric boundary layer is essentially turbulent at high Reynolds numbers with spatial scales ranging from millimeters to kilometers. In particular, the Earth's energy, water and carbon budgets are constrained by turbulent fluxes of momentum, heat, water vapor and CO2 in the atmospheric surface layer, which are key for improved hydrological, weather, climate and carbon cycle prediction. Moreover, climate models are highly sensitive to the representation of turbulence in the atmospheric boundary layer, which is thus important for the projections of future climate. Some few exact and nontrivial hypotheses or theories form the basis of the understanding of turbulence, which are then applied in the modeling and parameterization, and field observations of turbulence. However, these hypotheses or theories do not always apply in the atmospheric boundary layer since some prerequisites are not always met. The main objective of this dissertation is thus to improve the understanding of turbulence in the atmospheric boundary layer and to correct key assumptions in observation and modeling of atmospheric turbulence through novel high-resolution field measurements, theoretical derivation and numerical simulations.

Chapter 2 describes the study that challenges the frozen turbulence hypothesis that was proposed by Geoffrey Ingram Taylor in 1938. Taylor's hypothesis suggests that turbulent eddy properties do not change during advection and all eddies are advected at the same mean flow velocity. The high-resolution distributed temperature sensing measurements of air temperature in both space and time together with a large eddy simulation of the atmospheric boundary layer and derivation from simplified Navier-Stokes equations show that small eddies lose their coherent properties due to turbulent diffusion and are advected at smaller velocities than large eddies, i.e., Taylor's hypothesis does not work for small eddies. The study also proposes a correction for flux measurements in a global network of eddy-covariance towers.

Chapter 3 introduces the proposed model for turbulence spectra in the strongly stratified atmospheric boundary layer at high Reynolds numbers. Through high-quality eddy-covariance and distributed temperature sensing measurements, a direct numerical simulation and theoretical derivation, the study demonstrates that three regimes: the buoyancy subrange, transition region and isotropic inertial subrange exist in turbulent kinetic energy and temperature spectra in horizontal wavenumber of the equilibrium range in the stable atmospheric boundary layer. The study suggests that Monin-Obukhov similarity theory does not apply in the very stable atmospheric boundary layer as it does not consider the buoyancy scale that characterizes the transition region.

Chapter 4 describes a close examination of the power-law scaling of turbulence cospectra in high wavenumbers of the inertial subrange that can be used for high-frequency spectral corrections in eddy-covariance measurements in the stably stratified conditions. The study shows that a -2 power-law scaling for turbulence cospectra is valid within dimensional analysis and appears to be a better approximation than the -7/3 power-law scaling across various field measurements including eddy-covariance systems and the sonic and hot-film anemometer dyad sampling at 2000 Hz at Taylor-microscale-based Reynolds number up to 3236 in the stably stratified atmospheric boundary layer.

Chapter 5 introduces the proposed the logarithmic profiles of potential temperature in the near-wall region of convective boundary layers. The coexistence of the temperature log law and constant heat flux is reported in the near-wall region through direct numerical simulations of the convective boundary layers ranging from the weakly convective condition to free convection. In contrast, velocity does not follow a log law at highly convective conditions. The temperature log law is derived from the transport equation for heat flux by applying previous theories and the results of the numerical experiments, and is then supported by field observations of the convective atmospheric boundary layer. The slope of the proposed temperature log law varies with buoyancy as compared to the universal slope of von K\'arm\'an' velocity log law. The proposed temperature log profile can thus serve as an alternative to Monin-Obukhov similarity theory that is widely applied in climate models and wall models for large eddy simulations.

In the last chapter the findings of the dissertation are summarized. Future work on developing new representation of stratified turbulence in numerical weather prediction and climate models and investigating the surface energy imbalance problem in convective conditions are discussed.


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More About This Work

Academic Units
Earth and Environmental Engineering
Thesis Advisors
Gentine, Pierre
Ph.D., Columbia University
Published Here
February 28, 2020