Study of anisotropic scaling and intermittency of aerosols using airborne lidar.

摘要

Nonlinear processes, such as passive scalar fluctuation, driven by the turbulent wind field, exhibit extreme variability over a wide range of Space-time scales and intensities. As a result of the complexity of those fields, the theoretical treat merit of turbulence is a long-standing challenge of fluid mechanics. An empirical study of stochastic fluctuations in atmospheric aerosol concentration using state of the art lidar data is the subject of this thesis. The statistics of the fluctuations in the scalar field are closely related to those of the turbulent wind field. Initially, a detailed review of the treatments of such turbulent atmospheric fields that is commonly found in the litterature is given. The main strands of research relevant to a statistical understanding of atmospheric dynamics are (1) isotropic hydrodynamic turbulence in 2D and 3D (with extensions), (2) buoyancy driven flows, (3) gravity wave theories, (4) closures, (5) direct numerical simulations. It is argued that all current approaches treat the anisotropy of the dynamics and the characteristic intermittency inappropriately. Already existing—albeit—empirical evidence is then used to motivate the relevance of Generalized Scale Invariance and the Unified Scaling Model (e.g. [Schertzer and Lovejoy, 1983, 1984, 1985]) which models turbulent atmospheric fields as anisotropic multifractal cascade processes. This model implies the anisotropic multiscaling of the fields over the entire range of spatial scales and that variability increases algebraically downscale leading to a highly intermittent field.;For each individual data set as well as for the ensemble average, excellent agreement was found with the theoretical predictions of the model. In Fourier space, scalar fluctuations as a function of horizontal wavenumber scale with the Kolmogorov exponent βh = -5/3 [Kolmogorov, 1941] corresponding to the real space exponent Hh = 1/3 which was itself also obtained from the first order structure function with a very good degree of agreement with the theory. Scalar fluctuations as a function of vertical wavenumber scale with the Bolgiano-Obukhov exponent β v -11/5 [Bolgiano, 1959] corresponding to the real space exponent Hv = 3/5 also verified with the first order structure function. The ratio Hz = 5/9 of those exponents corresponds to a measure of the anisotropy of the dynamics and implies an effective fractal elliptical dimension Del = 23/9. The single scale of isotropy throughout the scaling range is the sphero-scale ℓ s and corresponds to the scale at which the amplitude of the dynamics in the vertical equals that of those in the horizontal. This amplitude can be quite variable depending on atmospheric conditions. It was found that ℓ s varied between 3 cm and 80 cm, implying flattened structures almost all the way to the dissipation scale. Usina TRM and DTM, it was found that the Universal Multifractal parameters α and C 1 are equal to 1.8 and 0.037 (in the horizontal) or 0.053 (in the vertical) respectively. These values are comparable to those found in the literature. Overall, very good consistency was obtained between the predictions of the Unified Scaling Model, throughout the analyses, and with existing results.;Recognizing the necessity for an improved, systematic and thorough empirical test of the Unified Scaling Model, we analyzed high resolution aircraft lidar atmospheric aerosol backscatter ratio data, verified to be a good surrogate of the aerosol concentration, and taken to be a very good approximation for a passive scalar. Fourier analysis and structure function analysis were used to test the anisotropie scaling and multi-scaling properties exhibited by the scalar fluctuations. Trace Moment (TRM) and Double Trace Moment (DTM) analyses (e.g. [Schertzer and Lovejoy, 1993], [Lavallée et al., 1993]) were used to determine the Universal Multifractal critical exponents of the underlying energy fluxes (e .g. Schertzer and Lovejoy, 1993]). The analyses were conducted on nine data sets with a horizontal range of scales between 100 m and 100 km, and with a vertical range of scales between 3 m and 4.5 km.