Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence

Ashurst, Wm. T.; Kerstein, Alan R.; Kerr, Robert M.; Gibson, Carl H.

doi:10.1063/1.866513

Cited by 732 publications

(715 citation statements)

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“…Recall that, in turbulence, the vorticity tends to be aligned withê 2 (Ashurst et al 1987). It would then be expected that the conditional average of the tumbling rate on p ·ê 2 (figure 11(b)) would share some similarity with the conditional average on p ·ω (figure 9).…”

Section: Resultsmentioning

confidence: 99%

“…Intuitively, one would expect that the vorticityω would tend to align with the most extensional eigenvector,ê 1 . But, in general, vorticity is preferentially aligned with the intermediate eigenvectorê 2 (Ashurst et al 1987). We show the PDFs of the cosine of the angle betweenω and theê i in figure 7 for our measured velocity gradients and for the direct numerical simulation.…”

Section: Alignment Between Vorticity and Strain Rate Tensormentioning

confidence: 99%

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Measurements of the coupling between the tumbling of rods and the velocity gradient tensor in turbulence

Kramel

Ouellette

et al. 2015

J. Fluid Mech.

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We present simultaneous experimental measurements of the dynamics of anisotropic particles transported by a turbulent flow and the velocity gradient tensor of the flow surrounding them. We track both rod-shaped particles and small spherical flow tracers using stereoscopic particle tracking. By using scanned illumination, we are able to obtain a high enough seeding density of tracers to measure the full velocity gradient tensor near the rod. The alignment of rods with the vorticity and the eigenvectors of the strain rate show agreement with numerical simulations. A full description of the tumbling of rods in turbulence requires specifying a seven-dimensional joint probability density function (PDF) of five scalars characterizing the velocity gradient tensor and two scalars describing the relative orientation of the rod. If these seven parameters are known, then Jeffery's equation specifies the rod tumbling rate and any statistic of rod rotations can be obtained as a weighted average over the joint PDF. To look for a lower-dimensional projection to simplify the problem, we explore conditional averages of the mean-squared tumbling rate. The conditional dependence of the mean-squared tumbling rate on the magnitude of both the vorticity and the strain rate is strong, as expected, and similar. There is also a strong dependence on the orientation between the rod and the vorticity, since a rod aligned with the vorticity vector tumbles due to strain but not vorticity. When conditioned on the alignment of the rod with the eigenvectors of the strain rate, the largest tumbling rate is obtained when the rod is oriented at a certain angle to the eigenvector that corresponds to the smallest eigenvalue, because this particular orientation maximizes the contribution from both the vorticity and strain.

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Section: Resultsmentioning

confidence: 99%

Section: Alignment Between Vorticity and Strain Rate Tensormentioning

confidence: 99%

Measurements of the coupling between the tumbling of rods and the velocity gradient tensor in turbulence

Kramel

Ouellette

et al. 2015

J. Fluid Mech.

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“…See f i g u r e 1 . The r e s u l t i n g mean temperature (chemical product) p r o f i l e t h a t peaks i n t h e i n t e r i o r of the r e a c t i o n zone is more a consequence of the v a r i a t i o n of the f r a c t i o n of t h e time a given f i x e d point is v i s i t e d by t h e h o t l a r g e s c a l e c o r e s (duty c y c l e ) , r a t h e r than t h e v a r i a t i o n of the temperature f i e l d w i t h i n a core.…”

Section: N O T H E R Words While Having T H E C O R R E C T F L U mentioning

confidence: 99%

Turbulent Shear Layer Mixing With Fast Chemical Reactions

Dimotakis

1989

Lecture Notes in Engineering

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I n v i t e d l e c t u r e a t t h e United S t a t e s -France J o i n t Workshop onTurbulent Reacting Flows, 6-10 J u l y 1987, Rouen, FRANCE ABSTRACT A model is proposed f o r c a l c u l a t i n g mixing and chemical r e a c t i o n s i n t h e l i m i t of i n f i n i t e l y f a s t chemical k i n e t i c s and n e g l i g i b l e heat r e l e a s e , i n f u l l y developed t u r b u l e n t shear l a y e r s . The model is based on t h e assumption t h a t t h e topology of t h e i n t e r f a c e between t h e two e n t r a i n e d r e a c t a n t s i n t h e l a y e r , a s well a s t h e s t r a i n f i e l d a s s o c i a t e d with i t , can be described by t h e s i m i l a r i t y laws of the Kolmogorov cascade. The c a l c u l a t i o n y i e l d s the i n t e g r a t e d volume f r a c t i o n a c r o s s t h e l a y e r occupied by t h e chemical product, a s a function of the s t o i c h i o m e t r i c mixture r a t i o of t h e r e a c t a n t s c a r r i e d by the free streams, t h e v e l o c i t y r a t i o of the shear l a y e r , t h e l o c a l Reynolds number, and t h e Schmidt number of t h e flow.The r e s u l t s a r e i n good agreement with measurements of the volume f r a c t i o n occupied by t h e molecularly mixed f l u i d i n a t u r b u l e n t shear l a y e r and t h e amount of chemical product, i n both gas phase and l i q u i d phase chemically r e a c t i n g shear l a y e r s .

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“…In reality they are pseudo-3D in nature as they are composed of 2D flows superimposed on a 3D vorticity free strain field, a fact exploited by Lundgren in his transformation [2]. Depending on whether a tube or shear layer symmetry has been chosen, corresponding to uni-axial or bi-axial strain [3], they have the properties that the vorticity ω ω ω firstly lies respectively either along the axis of the tube or in the plane of the layer and secondly that it aligns with an eigenvector of the strain matrix S. While numerical simulations [10,11] and experiments [12] have shown that, in a spatially averaged sense, alignment of the vorticity vector ω ω ω with the intermediate eigenvector of S is favoured (for a list of references see [13]), it is clear that local vorticity accumulation and alignment processes are more complicated than this [14,15]. For instance, the solution for the Burgers vortex has the drawback that it is stretched by a strain field that is decoupled from the flow around it and that its vorticity is unidirectional [1][2][3].…”

Section: Introductionmentioning

confidence: 99%

Dynamically stretched vortices as solutions of the 3D Navier–Stokes equations

Gibbon

Fokas

Doering

1999

Physica D: Nonlinear Phenomena

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A well known limitation with stretched vortex solutions of the 3D Navier-Stokes (and Euler) equations, such as those of Burgers type, is that they possess uni-directional vorticity which is stretched by a strain field that is decoupled from them. It is shown here that these drawbacks can be partially circumvented by considering a class of velocity fields of the type u u u = (u 1 (x, y, t), u 2 (x, y, t), γ (x, y, t)z + W (x, y, t)) where u 1 , u 2 , γ and W are functions of x, y and t but not z. It turns out that the equations for the third component of vorticity ω 3 and W decouple. More specifically, solutions of Burgers type can be constructed by introducing a strain field into u u u such that u u u = (−(γ /2)x − (γ /2)y, γ z) + −ψ y , ψ x , W . The strain rate, γ (t), is solely a function of time and is related to the pressure via a Riccati equationγ + γ 2 + p zz (t) = 0. A constraint on p zz (t) is that it must be spatially uniform. The decoupling of ω 3 and W allows the equation for ω 3 to be mapped to the usual general 2D problem through the use of Lundgren's transformation, while that for W can be mapped to the equation of a 2D passive scalar. When ω 3 stretches then W compresses and vice versa. Various solutions for W are discussed and some 2π -periodic θ -dependent solutions for W are presented which take the form of a convergent power series in a similarity variable. Hence the vorticity ω ω ω = r −1 W θ , −W r , ω 3 has nonzero components in the azimuthal and radial as well as the axial directions. For the Euler problem, the equation for W can sustain a vortex sheet type of solution where jumps in W occur when θ passes through multiples of 2π .

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Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence

Abstract: Articles you may be interested inA framework for epistemic uncertainty quantification of turbulent scalar flux models for Reynolds-averaged Navier-Stokes simulations Phys. Fluids 25, 055105 (2013);

Cited by 732 publications

References 14 publications

Measurements of the coupling between the tumbling of rods and the velocity gradient tensor in turbulence

Measurements of the coupling between the tumbling of rods and the velocity gradient tensor in turbulence

Turbulent Shear Layer Mixing With Fast Chemical Reactions

Dynamically stretched vortices as solutions of the 3D Navier–Stokes equations

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