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Determine whether finite-time singularities can spontaneously emerge in three-dimensional inviscid, incompressible fluid flows.

Spontaneous Singularity in Three-Dimensional Inviscid, Incompressible Flow

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Determine whether finite-time singularities can spontaneously emerge in three-dimensional inviscid, incompressible fluid flows.
Applied series-analysis techniques to evaluate the temporal evolution of the three-dimensional inviscid Taylor-Green vortex.
Demonstrated that vortex lines can undergo infinite stretching within a finite period of time.
Provided analytical evidence supporting the spontaneous formation of finite-time singularities in idealized incompressible fluids.

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Series analysis demonstrates finite-time infinite vortex stretching in Taylor-Green vortices, suggesting spontaneous singularity formation.

Morf et al. (1980) studied this question.

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Series analysis demonstrates finite-time infinite vortex stretching in Taylor-Green vortices, suggesting spontaneous singularity formation.