Roughness effects on fine-scale anisotropy and anomalous scaling in atmospheric flows
The effects of surface roughness on various measures of fine-scale intermittency within the inertial subrange were analyzed using two data sets that span the roughness "extremes" encountered in atmospheric flows, an ice sheet and a tall rough forest, and supplemented by a large number of existing literature data. Three inter-related problems pertaining to surface roughness effects on (i) anomalous scaling in higher-order structure functions, (ii) generalized dimensions and singularity spectra of the componentwise turbulent kinetic energy, and (iii) scalewise measures such local flatness factors and stretching exponents were addressed. It was demonstrated that surface roughness effects do not impact the fine-scale intermittency in u (the longitudinal velocity component), consistent with previous laboratory experiments. However, fine-scale intermittency in w (the vertical velocity component) increased with decreasing roughness. The consequence of this external intermittency (i.e., surface roughness induced) is that the singularity spectra of the scaling exponents are much broader for w when compared u in the context of the multifractal formalism for the local kinetic energy (instead of the usual conservative cascade studied for the dissipation rate). The scalewise evolution of the flatness factors and stretching exponents collapse when normalized using a global Reynolds number Rt = σLI/ν, where σ is the velocity standard deviation, LI is the integral length scale, and ν is the fluid viscosity. © 2009 American Institute of Physics.
Katul, GG; Porporato, A; Poggi, D
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