Vortex Stretching
A mechanism in three-dimensional fluids in which vortex tubes are stretched, causing vorticity to intensify. It is a key process in the turbulent energy cascade and vorticity dynamics.
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In three-dimensional fluids, the vorticity equation contains a term \( (\boldsymbol{\omega} \cdot \nabla) \mathbf{u} \), indicating that vorticity strengthens when a vortex tube is stretched by the velocity field, analogous to conservation of angular momentum.
The vortex constructed in the AI-assisted proof thins through three-dimensional stretching, with the vortex radius continuously shrinking and energy remaining finite, while the local vorticity tends to infinity, achieving blow-up.
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In three-dimensional fluids, the vorticity equation contains a term \( (\boldsymbol{\omega} \cdot \nabla) \mathbf{u} \), indicating that vorticity strengthens when a vortex tube is stretched by the velocity field, analogous to conservation of angular momentum.
50%UnverifiedThe vortex constructed in the AI-assisted proof thins through three-dimensional stretching, with the vortex radius continuously shrinking and energy remaining finite, while the local vorticity tends to infinity, achieving blow-up.
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