Nonstationary aspects of passive scalar gradient behaviour

García, A.; Gonzalez, M.; Paranthoën, Pierre

doi:10.1016/j.euromechflu.2007.09.002

Cited by 6 publications

(14 citation statements)

References 14 publications

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“…14): for y(0)/d = 1 ζ eq almost retrieves its initial value, ζ c , at σ 0 t = 100; for y(0)/d = 10 ζ c − ζ eq is still greater than 0.2π. Now, the local, instantaneous orientation of the scalar gradient coincides with ζ eq only if its response time scale is short enough as compared to the time scale of r variations (Garcia et al , 2005(Garcia et al , , 2008. Figure 15 shows that after σ 0 t = 2 this condition is realized and ζ varies as ζ eq no matter the value of y(0)/d.…”

Section: Consequences For Alignment and Stirring Propertiesmentioning

confidence: 95%

Effect of density step on stirring properties of a strain flow

Gonzalez¹,

Paranthoën

2009

Fluid Dyn. Res.

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The influence of steep density gradient upon stirring properties of a strain flow is addressed by considering the problem in which an interface separating two regions with different constant densities is stabilised within a stagnation-point flow. The existence of an analytic solution for the two-dimensional incompressible flow field allows the exact derivation of the velocity gradient tensor and of parameters describing the local flow topology. Stirring properties are affected not only through vorticity production and jump of strain intensity at the interface, but also through rotation of strain principal axes resulting from anisotropy of pressure Hessian. The strain persistence parameter, which measures the respective effects of strain and effective rotation (vorticity plus rotation rate of strain basis), reveals a complex structure. In particular, for large values of the density ratio it indicates dominating effective rotation in a restricted area past the interface. Information on flow structure derived from the Okubo-Weiss parameter, by contrast, is less detailed.The influence of the density step on stirring properties is assessed through the Lagrangian evolution of the gradient of a passive scalar. Even for a moderate density ratio, alignment of the scalar gradient and growth rate of its norm are deeply altered. Past the interface effective rotation indeed drives the scalar gradient to align with a direction determined by the local strain persistence parameter, away from the compressional strain direction. The jump of strain intensity at the interface, however, opposes the lessening effect of the latter mechanism on the growth rate of the scalar gradient norm and promotes the rise of the gradient.

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Section: Consequences For Alignment and Stirring Propertiesmentioning

confidence: 95%

Effect of density step on stirring properties of a strain flow

Gonzalez¹,

Paranthoën

2009

Fluid Dyn. Res.

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“…Moreover, better alignment of scalar gradient with equilibrium orientation when / /e 2 may result from values of strain time scale, ͑ 1 − 3 ͒ −1 , smaller than in the case / /e 1 where this time scale is ͑ 2 − 3 ͒ −1 . Garcia et al 30,31 showed that in the two-dimensional case alignment of the scalar gradient is in fact determined by the gradient response to strain persistence fluctuations; more precisely, good alignment with the equilibrium direction needs that the variations of strain persistence occur on a time scale larger than the response time scale of the scalar gradient-which is roughly given by strain intensity. It is interesting to see that in this turbulent, three-dimensional case alignment with the equilibrium direction-computed for / /e 1 and / /e 2 -is strong which is reminiscent of the results of Lapeyre et al 25 in turbulent, two-dimensional flows.…”

Section: -5mentioning

confidence: 99%

Kinematic properties of passive scalar gradient predicted by a stochastic Lagrangian model

Gonzalez

2009

Physics of Fluids

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A modeled equation for the gradient of a passive scalar is derived consistently with the approach of Chevillard and Meneveau for the velocity gradient tensor ͓Phys. Rev. Lett. 97, 174501 ͑2006͔͒ and its predictions are analyzed in three-dimensional, isotropic turbulence. General features of scalar gradient kinematics, namely, production of scalar gradient norm and alignment with respect to strain principal axes and vorticity are rather well described. A strain persistence parameter defined for tight alignment of vorticity with a strain eigenvector is used to bring further insight into geometric properties of the scalar gradient. In particular, the model results lend support to the existence of special alignments of the scalar gradient which are determined by local strain persistence and are different from the directions of strain principal axes as already shown in two-dimensional turbulence.

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“…Recently, it has also been shown that in two-dimensional flow -more specifically in the laminar Bénard -von Kármán street [16,17] -forcing through Lagrangian variations of strain persistence may deeply affect tracer gradient behaviour in terms of alignment properties and norm growth rate. In particular, local orientation of the tracer gradient appears to be strongly dependent on whether or not the gradient responds to this kind of forcing.…”

Section: Introductionmentioning

confidence: 99%

On the role of unsteady forcing of tracer gradient in local stirring

Gonzalez¹,

Paranthoën²

2010

European Journal of Mechanics - B/Fluids

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Gonzalez, M. Paranthoen, P.Local stirring properties in two basic mixing flows - namely, the blinking vortex and the sine flow are studied through the tracer gradient approach. The velocity gradient tensor and related quantities such as the strain persistence parameter are derived from the analytical velocity fields. Numerical Lagrangian tracking of the gradient of a tracer shows how local stirring is affected by forcing experienced through strain persistence. In both flows Lagrangian variations of strain persistence occuring on a time scale shorter than the response time scale of the tracer gradient lead the latter to align close to the direction determined by the mean strain persistence. It is the special alternating behaviour of strain persistence resulting from flow operation that makes this direction coincide with the local compressional strain direction for both the sine flow and the clockwise/counterclockwise blinking vortex. The rise of the tracer gradient and thus local stirring are in turn promoted by this statistical alignment. (C) 2009 Elsevier Masson SAS. All rights reserved

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Nonstationary aspects of passive scalar gradient behaviour

Cited by 6 publications

References 14 publications

Effect of density step on stirring properties of a strain flow

Effect of density step on stirring properties of a strain flow

Kinematic properties of passive scalar gradient predicted by a stochastic Lagrangian model

On the role of unsteady forcing of tracer gradient in local stirring

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