Vortex stretching

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Vortex stretching is associated with a particular term in the vorticity equation. For example, vorticity transport in an incompressible inviscid flow is governed by

${\displaystyle {D{\vec {\omega }} \over Dt}=\left({\vec {\omega }}\cdot {\vec {\nabla }}\right){\vec {v}},}$

where D/Dt is the material derivative. The source term on the right hand side is the vortex stretching term. It amplifies the vorticity ${\displaystyle {\vec {\omega }}}$ when the velocity is diverging in the direction parallel to ${\displaystyle {\vec {\omega }}}$.

A simple example of vortex stretching in a viscous flow is provided by the Burgers vortex.

Vortex stretching is at the core of the description of the turbulence

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