Why do vortices 'stretch'?
Why do vortices undergo stretching, i.e. what causes vortices to stretch?
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Nothing but the conservation laws. It falls right out when you write down (i.e derive) the vorticity transport equation.
Let us presume that there is a 3D flowfield with some vorticity in it, which implies some form of velocity gradient. Velocity gradients means (there are differences in velocity) and different layers of fluid will tend to move at different speeds. However, angular momentum must be conserved. The conservation of angular momentum as the fluid in different speed-layers move automatically yields the longitudinal vortex stretching. |
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Have you seen this?
https://en.m.wikipedia.org/wiki/Vortex_stretching I think it is pretty clear about it |
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If you read the fluid dynamics texbook of Chorin you understand you need to think about a vortical tube, that is a tube having the vorticity vector field tangent to the surface. Then you have the conservation of vorticity as same as the conservation of mass. Action of the stretching of vorticity on the vortical tube can be identified. Note: the stretching term can be analysed in term of matrix operator on a vector. You have the matrix in the velocity gradient acting on the vector that is the vorticity. Express in terms of eigenvectors problem. |
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You have to think that a vortical tube is the envelope of the vorticity field, therefore the stretching of the vorticity affects the vortical tube. This is the link you missed. Not only conservation of angular moment but also the fact that the vorticity field is divergence-free is useful. |
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Assume a vortical tube of characteristic diameter d. Now only if d is comparable to the Taylor microscale the viscosity starts to have effects until d is of the order of the Kolmogorov lenght when the vortical structures disappear. Only in this range the energy dissipation takes place. You understand that the stretching is responsible of deformation of the structures in an inviscid-like manner until d is small enough. That means you have an inviscid energy transfer also in viscous flows. |
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