Plot of the energy of helical structures with vs time for . For , NSe’s are in a linear regime. Growth rates obtained from the linear instability theory are for the and for the experimental profile . For , nonlinearities are important. Vortex breakdown occurs for (see the text for its definition).
Plot of the enstrophy against time. Vortex breakdown occurs for , relaxing the increase of the enstrophy.
The breakdown with . Three-dimensional representation of the vorticity field evolution (the 30 000 vectors with the highest vorticity norms are presented in each frame). Time runs from left to right, then from top to bottom. The fourth frame corresponds to the time of the beginning of the linear instability saturation . The sixth one corresponds to the time of the maximum enstrophy .
Plot of the minimum value of the axial velocity (evaluated at ) against time. For almost all the values of , vortex breakdown occurs without a stagnation point in the flow.
Plot of the vorticity averaged radius against time. A lateral expansion of the vorticity is associated with the vortex breakdown.
Plot of the momentum thickness (normalized by its initial value) against time. Vortex breakdown of the experimental profile leads to a more efficient mixing than that in the .
Plot of the axial strain rate against the axial coordinate at a time . The natural strain is far from being uniform.
Energy spectra when the Batchelor profile is used as initial condition. Until , no breakdown is observed for and for this profile. Before, the breakdown corresponds to a time . After, the breakdown corresponds to .
Energy spectra when the experimental profile is used as initial condition.
Plot of the spectrum exponent against time.
Inviscid computation. (Top) Plot of the energy spectra for and . (Bottom) Plot of the spectrum exponent against time.
Comparison between Navier–Stokes equations and truncated Euler equations for using the experimental profile and a resolution.
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