# Relation between vorticity and turbulence intensity in streamtube contraction

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 September 22, 2020, 03:50 Relation between vorticity and turbulence intensity in streamtube contraction #1 New Member   Join Date: Jan 2019 Posts: 7 Rep Power: 6 Currently, I am investigating the effect of streamtube contraction on a given turbulence field. In literature, I find mathematical descriptions of the problem. However, I fail to understand the physics behind the process. Take for example figure 1 in 'The alignment of vortical structures in turbulent flow through a contraction' by Mugundhan et al ( https://doi.org/10.1017/jfm.2019.887). Clearly when a vortex tube is stretched, the combination of Stokes' and Helmoltz' theorems say that the vorticity is increased. Subsequently, the axial turbulent velocity fluctuations decrease. This last step I fail to understand, and the authors do not explain why this is. Can somebody give a physical interpretation of this effect.

September 22, 2020, 05:38
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Filippo Maria Denaro
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 Originally Posted by Lmath Currently, I am investigating the effect of streamtube contraction on a given turbulence field. In literature, I find mathematical descriptions of the problem. However, I fail to understand the physics behind the process. Take for example figure 1 in 'The alignment of vortical structures in turbulent flow through a contraction' by Mugundhan et al ( https://doi.org/10.1017/jfm.2019.887). Clearly when a vortex tube is stretched, the combination of Stokes' and Helmoltz' theorems say that the vorticity is increased. Subsequently, the axial turbulent velocity fluctuations decrease. This last step I fail to understand, and the authors do not explain why this is. Can somebody give a physical interpretation of this effect.

Actually, it seems to me that the authors produced some explanation in Sec. 3.3 and 3.4. But, as you can read, the general according between different authors is not reported. The contraction C seems to determine the action on the rms of the fluctuations. The increasing of vorticity intencity is simply due to conservation of angular momentum. The vorticity field is divergence-free like the velocity field.

 September 22, 2020, 06:02 #3 New Member   Join Date: Jan 2019 Posts: 7 Rep Power: 6 I see, but I still miss the physical explanation behind it. I have read that it seems that the intensity scales with the contraction, however why does an increase of the vorticity of a axial vortex tube/element lead to a decrease in the axial velocity fluctuations. I am thinking about induced velocities i.e. the axial elongation leads to compression in the two other directions hence decreasing the vorticity. Only these two vortex tube directions influence the velocity in the axial direction. The vorticity in the axial direction only affects velocities in the plane perpendicular to the axial direction. But I am not sure at all if this makes any sense and even if it makes sense to try to visualize it as vorticity is not something we can see.

 October 2, 2020, 05:19 #4 Member   EM Join Date: Sep 2019 Posts: 52 Rep Power: 5 vortex stretching is an inviscid process. to explain the experiment u need to add pressure and viscosity effects. the basics: most vortices in turbulence have relatively short lives. they originate from the rolling-up of shear layers. they are more like a rolled-up vortex sheets where vortex-line reconnection (a viscous effect) is unlikely and hence the closed streamline patterns of the theoretical models is an approximation. according to one experiment (i forgot where i saw it) in a boundary layer, the life time of its vortices are comparable with the time it takes for each to complete one turn. also note that the experiment you quoted shows results for large-scale vortices meaning that their results are more likely to be about early in their lifetimes. all the above has one purpose: most vortices in turbulent flows have internal shear layers (very far from solid body rotation) and are highly dissipative. as vortices go thru the contraction, the ones quasi-aligned with the imposed strain get stretched and inviscidly increase the axial vorticity meaning that the off-axial derivatives of the off-axial velocity components increase and hence the relevant component of the dissipation goes up. this is reflected in the increase in the rms of the axial vorticity while it goes thru the contraction. as the two non-axial velocity components lose energy, the 'isotropizing' effect of pressure is continually acting against the increasing anisotropy and hence the axial velocity losses part of its energy to the other two components; hence the loss of u_rms. -- Last edited by gnwt4a; October 4, 2020 at 08:07.

 Tags distortion, turbulence, vorticity