Kavli Affiliate: Shmuel M. Rubinstein
| First 5 Authors: Rodolfo Ostilla-Mónico, Ryan McKeown, Michael P. Brenner, Shmuel M. Rubinstein, Alain Pumir
| Summary:
At high Reynolds number, the interaction between two vortex tubes leads to
intense velocity gradients, which are at the heart of fluid turbulence. This
vorticity amplification comes about through two different instability
mechanisms of the initial vortex tubes, assumed anti-parallel and with a mirror
plane of symmetry. At moderate Reynolds number, the tubes destabilize via a
Crow instability, with the nonlinear development leading to strong flattening
of the cores into thin sheets. These sheets then break down into filaments
which can repeat the process. At higher Reynolds number, the instability
proceeds via the elliptical instability, producing vortex tubes that are
perpendicular to the original tube directions. In this work, we demonstrate
that these same transition between Crow and Elliptical instability occurs at
moderate Reynolds number when we vary the initial angle $beta$ between two
straight vortex tubes. We demonstrate that when the angle between the two tubes
is close to $pi/2$, the interaction between tubes leads to the formation of
thin vortex sheets. The subsequent breakdown of these sheets involves a
twisting of the paired sheets, followed by the appearance of a localized cloud
of small scale vortex structures. At smaller values of the angle $beta$
between the two tubes, the breakdown mechanism changes to an elliptic
cascade-like mechanism. Whereas the interaction of two vortices depends on the
initial condition, the rapid formation of fine-scales vortex structures appears
to be a robust feature, possibly universal at very high Reynolds numbers.
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