Micro structure and Lagrangian statistcs of the scalar field with a mean gradient in isotropic turbulence

This paper presents an analysis and numerical study of the relations between the small-scale velocity and scalar fields in fully developed isotropic turbulence with random forcing of the large scales and with an imposed constant mean scalar gradient. Simulations have been performed for a range of Reynolds numbers from Reλ = 22 to 130 and Schmidt numbers from Sc = 1/25 to 144. The simulations show that for all values of Sc [gt-or-equal, slanted] 0.1 steep scalar gradients are concentrated in intermittently distributed sheet-like structures with a thickness approximately equal to the Batchelor length scale η/Sc[fraction one-half] with η the Kolmogorov length scale. We observe that these sheets or cliffs are preferentially aligned perpendicular to the direction of the mean scalar gradient. Due to this preferential orientation of the cliffs the small-scale scalar field is anisotropic and this is an example of direct coupling between the large- and small-scale fluctuations in a turbulent field. The numerical simulations also show that the steep cliffs are formed by straining motions that compress the scalar field along the imposed mean scalar gradient in a very short time period, proportional to the Kolmogorov time scale. This is valid for the whole range of Sc. The generation of these concentration gradients is amplified by rotation of the scalar gradient in the direction of compressive strain. The combination of high strain rate and the alignment results in a large increase of the scalar gradient and therefore in a large scalar dissipation rate. These results of our numerical study are discussed in the context of experimental results (Warhaft 2000) and kinematic simulations (Holzer & Siggia 1994). The theoretical arguments developed here follow from earlier work of Batchelor & Townsend (1956), Betchov (1956) and Dresselhaus & Tabor (1991)

Recurrent bursts via linear processes in turbulent environments

Large-scale instabilities occurring in the presence of small-scale turbulent fluctuations are frequently observed in geophysical or astrophysical contexts but are difficult to reproduce in the laboratory. Using extensive numerical simulations, we report here on intense recurrent bursts of turbulence in plane Poiseuille flow rotating about a spanwise axis. A simple model based on the linear instability of the mean flow can predict the structure and time scale of the nearly-periodic and self-sustained burst cycles. Rotating Poiseuille flow is suggested as a prototype for future studies of low-dimensional dynamics embedded in strongly turbulent environments

Scaling analysis and simulation of strongly stratified turbulent flows

International audienceDirect numerical simulations of stably and strongly stratified turbulent flows with Reynolds number Re " 1 and horizontal Froude number Fh Gt; 1 are presented. The results are interpreted on the basis of a scaling analysis of the governing equations. The analysis suggests that there are two different strongly stratified regimes according to the parameter R = ReFh2. When R " 1, viscous forces are nimportant and lv scales as lv ~ U/N (U is a characteristic horizontal velocity and N is the Brunt - Väis¨alä frequency) so that the dynamics of the flow is inherently three-dimensional but strongly anisotropic. When R " 1, vertical viscous shearing is important so that lv ~ lh/Re1/2 (lh is a characteristic horizontal length scale). The parameter R is further shown to be related to the buoyancy Reynolds number and proportional to (lO/?) 4/3, where lO is the Ozmidov length scale and ? the Kolmogorov length scale. This implies that there are simultaneously two distinct ranges in strongly stratified turbulence when R " 1: the scales larger than lO are strongly influenced by the stratification while those between lO and ? are weakly affected by stratification. The direct numerical simulations with forced large-scale horizontal two-dimensional motions and uniform stratification cover a wide Re and Fh range and support the main parameter controlling strongly stratified turbulence being R. The numerical results are in good agreement with the scaling laws for the vertical length scale. Thin horizontal layers are observed independently of the value of R but they tend to be smooth for R > 1, while for R > 1 small-scale three-dimensional turbulent disturbances are increasingly superimposed. The dissipation of kinetic energy is mostly due to vertical shearing for R > 1 but tends to isotropy as R increases above unity. When R > 1, the horizontal and vertical energy spectra are very steep while, when R > 1, the horizontal spectra of kinetic and potential energy exhibit an pproximate kh-5/3-power-law range and a clear forward energy cascade is observed. © 2007 Cambridge University Press

Passive scalars in stratified turbulence

The statistics of a passive scalar in randomly forced and strongly stratified turbulence is investigated by numerical simulations including a horizontal passive scalar mean gradient. We observe that horizontal isotropy of the passive scalar spectrum is satisfied in the inertial range. The spectrum has the form E_theta(k_h) = C_theta*epsilon_theta*epsilon_K^{-1/3}* k_h^{-5/3}, where epsilon_theta, epsilon_K are the dissipation of scalar variance and kinetic energy respectively, and C_theta about 0.5 is a constant. This spectrum is consistent with atmospheric measurements in the mesoscale range. The calculated passive scalar structure functions show that intermittency effects are significant

Analysis of Equilibria for Generalized Market Sharing Games

We analyze the quality of several equilibria for generalized market sharing games. Generalized market sharing games model n selfish players selecting subsets of a finite set of items, where the payoff of an item is divided among all players choosing that item. Market sharing games are a special case of this, where the available subsets are restricted by budget constraints

Modelling extreme concentration from a source in a turbulent flow over rough wall

The concentration fluctuations in passive plumes from an elevated and a groundlevel source in a turbulent boundary layer over a rough wall were studied using large eddy simulation and wind tunnel experiment. The predictions of statistics up to second order moments were thereby validated. In addition, the trend of relative fluctuations far downstream for a ground level source was estimated using dimensional analysis. The techniques of extreme value theory were then applied to predict extreme concentrations by modelling the upper tail of the probability density function of the concentration time series by the Generalised Pareto Distribution. Data obtained from both the simulations and experiments were analysed in this manner. The predicted maximum concentration (?0) normalized by the local mean concentration (Cm) or by the local r.m.s of concentration fluctuation (crms), was extensively investigated. Values for ?0/Cm and ?0/crms as large as 50 and 20 respectively were found for the elevated source and 10 and 15 respectively for the ground-level source