A global linearized framework for modelling shear dispersion and turbulent diffusion of passive scalar fluctuations

2021 ◽  
Vol 915 ◽  
Author(s):  
Thomas Ludwig Kaiser ◽  
Kilian Oberleithner
Keyword(s):  
Turbulent Diffusion ◽  
Passive Scalar ◽  
Shear Dispersion

Abstract

Spatially varying mixing of a passive scalar in a buoyancy-driven turbulent flow

2014 ◽  
Vol 742 ◽  
pp. 701-719
Author(s):  
Daan D. J. A. van Sommeren ◽  
C. P. Caulfield ◽  
Andrew W. Woods
Keyword(s):  
Diffusion Coefficient ◽  
Turbulent Flow ◽  
Turbulent Diffusion ◽  
Saline Solution ◽  
Passive Scalar ◽  
Eddy Diffusion ◽  
Turbulent Diffusion Coefficient ◽  
Advection Diffusion Equation ◽  
Eddy Diffusion Coefficient ◽  
Spatially Varying

AbstractWe perform experiments to study the mixing of passive scalar by a buoyancy-induced turbulent flow in a long narrow vertical tank. The turbulent flow is associated with the downward mixing of a small flux of dense aqueous saline solution into a relatively large upward flux of fresh water. In steady state, the mixing region is of finite extent, and the intensity of the buoyancy-driven mixing is described by a spatially varying turbulent diffusion coefficient $\kappa _v(z)$ which decreases linearly with distance $z$ from the top of the tank. We release a pulse of passive scalar into either the fresh water at the base of the tank, or the saline solution at the top of the tank, and we measure the subsequent mixing of the passive scalar by the flow using image analysis. In both cases, the mixing of the passive scalar (the dye) is well-described by an advection–diffusion equation, using the same turbulent diffusion coefficient $\kappa _v(z)$ associated with the buoyancy-driven mixing of the dynamic scalar. Using this advection–diffusion equation with spatially varying turbulent diffusion coefficient $\kappa _v(z)$, we calculate the residence time distribution (RTD) of a unit mass of passive scalar released as a pulse at the bottom of the tank. The variance in this RTD is equivalent to that produced by a uniform eddy diffusion coefficient with value $\kappa _e= 0.88 \langle \kappa _v \rangle $, where $\langle \kappa _v \rangle $ is the vertically averaged eddy diffusivity. The structure of the RTD is also qualitatively different from that produced by a flow with uniform eddy diffusion coefficient. The RTD using $\kappa _v$ has a larger peak value and smaller values at early times, associated with the reduced diffusivity at the bottom of the tank, and manifested mathematically by a skewness $\gamma _1\approx 1.60$ and an excess kurtosis $\gamma _2\approx 4.19 $ compared to the skewness and excess kurtosis of $\gamma _1\approx 1.46$, $\gamma _2 \approx 3.50$ of the RTD produced by a constant eddy diffusion coefficient with the same variance.

Horizontal turbulent diffusion in a convective mixed layer

2014 ◽  
Vol 758 ◽  
pp. 553-564 ◽  
Author(s):  
Junshi Ito ◽  
Hiroshi Niino ◽  
Mikio Nakanishi
Keyword(s):  
Scalar Field ◽  
Mixed Layer ◽  
Turbulent Diffusion ◽  
Passive Scalar ◽  
Rate Of Change ◽  
Horizontal Gradient ◽  
Scalar Flux ◽  
Turbulent Diffusion Coefficient ◽  
Convective Mixed Layer ◽  
Convergence Zones

AbstractA large eddy simulation (LES) is used to estimate a reliable horizontal turbulent diffusion coefficient, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}K_{{h}}$, in a convective mixed layer (CML). The introduction of a passive scalar field with a fixed horizontal gradient at a given time enables $K_{{h}}$ estimation as a function of height, based on the simulated turbulent horizontal scalar flux. Here $K_{{h}}$ is found to be of the order of $100\ {\mathrm{m}}^2\ {\mathrm{s}}^{-1}$ for a typical terrestrial atmospheric CML. It is shown to scale by the product of the CML convective velocity, $w_{*}$, and its depth, $h$. Here $K_{{h}}$ is characterized by a vertical profile in the CML: it is large near both the bottom and top of the CML, where horizontal flows associated with convection are large. The equation pertaining to the temporal rate of change of a horizontal scalar flux suggests that $K_{{h}}$ is determined by a balance between production and pressure correlation at a fully developed stage. Pressure correlation near the bottom of the CML is localized in convergence zones near the boundaries of convective cells and becomes large within an eddy turnover time, $h/w_{*}$, after the introduction of the passive scalar field.

Effects of a fluctuating sheared flow on cross phase in passive-scalar turbulent diffusion

2006 ◽  
Vol 13 (11) ◽  
pp. 112301 ◽  
Author(s):  
M. Leconte ◽  
P. Beyer ◽  
S. Benkadda ◽  
X. Garbet
Keyword(s):  
Turbulent Diffusion ◽  
Passive Scalar ◽  
Sheared Flow

scholarly journals Anomalous diffusion in geophysical and laboratory turbulence

1994 ◽  
Vol 1 (2/3) ◽  
pp. 80-94 ◽  
Author(s):  
A. Tsinober
Keyword(s):  
Boundary Layer ◽  
Atmospheric Boundary Layer ◽  
Turbulent Flows ◽  
Anomalous Diffusion ◽  
Turbulent Diffusion ◽  
Scaling Laws ◽  
Rotational Symmetry ◽  
Scaling Law ◽  
Passive Scalar ◽  
Spontaneous Breaking

Abstract. We present an overview and some new results on anomalous diffusion of passive scalar in turbulent flows (including those used by Richardson in his famous paper in 1926). The obtained results are based on the analysis of the properties of invariant quantities (energy, enstrophy, dissipation, enstrophy generation, helicity density, etc.) - i.e. independent of the choice of the system of reference as the most appropriate to describe physical processes - in three different turbulent laboratory flows (grid-flow, jet and boundary layer, see Tsinober et al. (1992) and Kit et al. (1993). The emphasis is made on the relations between the asymptotic properties of the intermittency exponents of higher order moments of different turbulent fields (energy, dissipation, helicity, spontaneous breaking of isotropy and reflexional symmetry) and the variability of turbulent diffusion in the atmospheric boundary layer, in the troposphere and in the stratosphere. It is argued that local spontaneous breaking of isotropy of turbulent flow results in anomalous scaling laws for turbulent diffusion (as compared to the scaling law of Richardson) which are observed, as a rule, in different atmospheric layers from the atmospheric boundary layer (ABL) to the stratosphere. Breaking of rotational symmetry is important in the ABL, whereas reflexional symmetry breaking is dominating in the troposphere locally and in the stratosphere globally. The results are of speculative nature and further analysis is necessary to validate or disprove the claims made, since the correspondence with the experimental results may occur for the wrong reasons as happens from time to time in the field of turbulence.

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