ZhETF, Vol. 142,
p. 1284 (December 2012)
(English translation - JETP,
Vol. 115, No. 6,
available online at www.springer.com
SCALE-INVARIANT STREAMLINE EQUATIONS AND STRINGS OF SINGULAR VORTICITY FOR PERTURBED ANISOTROPIC SOLUTIONS OF THE NAVIER-STOKES EQUATION
Received: May 23, 2012
A linear combination of a pair of dual anisotropic decaying Beltrami flows with spatially constant amplitudes (the Trkal solutions) with the same eigenvalue of the curl operator and of a constant velocity orthogonal vector to the Beltrami pair yields a triplet solution of the force-free Navier-Stokes equation. The amplitudes slightly variable in space (large scale perturbations) yield the emergence of a time-dependent phase between the dual Beltrami flows and of the upward velocity, which are unstable at large values of the Reynolds number. They also lead to the formation of large-scale curved prisms of streamlines with edges being the strings of singular vorticity.