External Intermittency Research Articles

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.

Large Eddy Simulation of Evolution of a Passive Scalar in Plane Jet

Large-eddy simulation (LES) is performed to investigate the passive scalar development in a plane jet. This is a follow-up of our previous simulation of the jet e owe eld. The LES results are compared to both experiments and direct numerical simulation (DNS). Two subgrid models are investigated: the dynamic Smagorinsky model and the dynamic mixed model. It is found that the evolution of mean scalar and turbulent scalar intensity is well represented. Some properties of the LES models such as the evolution of the dynamic constant and the subgrid viscosity are also discussed. Proe les of higher scalar moments show non-Gaussianity near the jet boundaries that is associated with external intermittency. Finally, the probability density function (PDF) of the passive scalar computed with LES is obtained and compared with the true PDF obtained with DNS. The LES approach is found able to represent the main characteristics of the PDF including qualitative changes during its initial evolution.

Dynamic stochastic estimation of physical variables

A fundamental problem facing the physical sciences today is analysis of natural variations and mapping of spatiotemporal processes. Detailed maps describing the space/time distribution of groundwater contaminants, atmospheric pollutant deposition processes, rainfall intensity variables, external intermittency functions, etc. are tools whose importance in practical applications cannot be overestimated. Such maps are valuable inputs for numerous applications including, for example, solute transport, storm modeling, turbulent-nonturbulent flow characterization, weather prediction, and human exposure to hazardous substances. The approach considered here uses the spatiotemporal random field theory to study natural space/time variations and derive dynamic stochastic estimates of physical variables. The random field model is constructed in a space/time continuum that explicitly involves both spatial and temporal aspects and provides a rigorous representation of spatiotemporal variabilities and uncertainties. This has considerable advantages as regards analytical investigations of natural processes. The model is used to study natural space/time variations of springwater calcium ion data from the Dyle River catchment area, Belgium. This dataset is characterized by a spatially nonhomogeneous and temporally nonstationary variability that is quantified by random field parameters, such as orders of space/time continuity and random field increments. A rich class of covariance models is determined from the properties of the random field increments. The analysis leads to maps of continuity orders and covariances reflecting space/time calcium ion correlations and trends. Calcium ion estimates and the associated statistical errors are calculated at unmeasured locations/instants over the Dyle region using a space/time kriging algorithm. In practice, the interpretation of the results of the dynamic stochastic analysis should take into consideration the scale effects.

Fractal properties of isovelocity surfaces in high Reynolds number laboratory shear flows

The fractal properties of isovelocity surfaces are studied in three high Reynolds number (Rλ≊2.0×102–3.2×103) laboratory shear flows using the standard box-counting method. The fractal dimension D=−d(log Nr)/d(log r) was estimated within the range of box sizes r from several Kolmogorov scales up to several integral scales (Nr is the number of boxes with size r required to cover the line intersection of an isovelocity surface). The inertial subrange was of particular interest in this investigation. Measurements were carried out for external intermittency factors γ≊0.6–1.0. The data were processed using threshold levels U±2.5u′ (U and u′ denote mean and rms values of longitudinal velocity). Over the parameters studied, no wide range of constant fractal dimension was found. On the other hand, the accuracy of constant fractal dimension approximation with D≊0.4 over the inertial subranges was shown to be similar to that of the Kolmogorov [Dokl. Akad. Nauk SSSR 30, 301 (1941)] ‘‘two-thirds law.’’

Fine-scale turbulence structure of intermittent hear flows

An experimental investigation of the fine-scale structure of turbulence was carried out. Five different shear flows were studied: three in a wind tunnel with an open working section and an elliptical nozzle and two in a wind tunnel of closed working section and square cross-section. The experiments tested two approaches to the theory of fine-scale turbulence structure: one based on the Navier-Stokes equations and the other on some similarity hypotheses. The variability of all fine-scale constants (including exponents in inertial-subrange power laws and the Kolmogorov constant) is revealed. A correlation between all fine-scale constants and the external intermittency coefficient is established.

Local structure of turbulence in flows with large Reynolds numbers.

Results are reported on an experimental investigation of the characteristics of fine-scale pulsations of the velocity in several shear flows (mixing layer, boundary layer, planar, axially symmetric, and spatial wakes, and in the return channel of a large wind tunnel) in an interval of definite Reynolds numbers R(lambda) [approximately-equal-to] 70-3000 with respect to the Taylor microscale lambda. The characteristic scales of most of the studied flows are quite large, and the integral scale of the turbulence reaches 5 m. The apparatus had a high resolving power-the ratio of the hot-wire length to the Kolmogorov scale was varied in the range 0.8-2.5. It is shown that the Kolmogorov constant C in the "two thirds" law and the constants C(epsilon) and &mgr; in the energy-dissipation correlation function are not universal and have a systematic dependence on the coefficient of external intermittency. The same constants determined in a completely turbulent fluid are universal within the errors of the measurements.