Infulence of atmospheric stability on the spatial structure of turbulence

This thesis consists of three chapters. In the first chapter, the cross-spectral phases between velocity components at two heights are analyzed from observations at the Høvsøre test site under diabatic conditions. These phases represent the degree to which turbulence sensed at one height leads (or lags) in time the turbulence sensed at the other height. The phase angle of the cross-wind component is observed to be significantly greater than the phase for the along-wind component, which in turn is greater than the phase for the vertical component. The cross-wind and along-wind phases increase with stream-wise wavenumber and vertical separation distance, but there is no significant change in the phase angle of vertical velocity. The phase angles for all atmospheric stabilities show similar order in phasing. The phase angles from the Høvsøre observations under neutral conditions are compared with a rapid distortion theory model, which shows similar order in phase shift. In the second chapter, a velocity spectral tensor model was evaluated using single point measurements of wind speed. The model contains three parameters, representing the dissipation rate of specific turbulent kinetic energy, a turbulence length scale and the turbulence anisotropy, respectively. Sonic anemometer measurements taken over a forested and an agricultural landscape were used to calculate the model parameters for neutral, slightly stable and slightly unstable atmospheric conditions over a selected wind speed interval. The dissipation rate above the forest was 9 times that at the agricultural site. No significant differences were observed in the turbulence length scales between the forested and agricultural areas. A small difference was observed in the turbulence anisotropy at the two sites, except near the surface, where the forest turbulence was more isotropic. The turbulence anisotropy remained more or less constant with height at the forest site, whereas the turbulence became more isotropic with height for the agricultural site. Using the three parameters as inputs, we quantified the performance of the model in coherence predictions for vertical separations. The model coherences of all the three velocity components were overestimated for the analyzed stability classes at both the sites. The model performed better at both sites for neutral stability than slightly stable and unstable conditions. The model predictions of coherence of the along-wind and vertical components were better than that of the cross-wind component. No significant difference was found between the performance of the model at the forested and the agricultural areas. The last chapter summarizes the present state of the theory, in which an attempt is made to investigate the spectral tensor model of both wind velocity and temperature fluctuations, which treats the effects of mean uniform vertical shear and mean uniform temperature gradient. The model is based on rapid distortion theory, which gives the linearized Navier-Stokes equations in Fourier space. We incorporate the general concept of an eddy life time in order to make the model stationary. The parameterized eddy life time from Mann (1994) is used. In addition to the three parameters from the spectral tensor model of Mann (1994), the model contains two extra parameters as a result of introducing a mean uniform temperature gradient. These parameters are: a stability parameter in the form of the Richardson number, and a measure of the rate of destruction of temperature variance. The model seems to work better for stable than unstable conditions. The model is able to predict well the length scales (corresponding to the peaks of (co-) spectra) of the temperature spectrum and temperature-velocity co-spectra. In the intertial subrange, the model shows that the velocity-temperature co-spectra are proportional to the −7/3 power of streamwise wavenumber, which is consistent with the measurements. The model is able to predict the temperature-coherence, moreso in the stable case than in the unstable case. We compare the model predictions against those of Mann (1994) in the coherence estimations, where the new model seems to give slightly improved results. The thesis is submitted to the Danish Technical University in partial fulfilment of the requirements for the PhD degree. Risø-PhD-XX(EN) May 2013 ISBN XXXXXXXXXXXXXXXXX