Resolving the cascade bottleneck in vortex-line turbulence
Seminar Room 1, Newton Institute
Both in many superfluid experimental situations and simulations of a 3D hard-core interaction model, it is found that the vortex line length in superfluid turbulence decays in a manner consistent with classical turbulence. Two decay mechanisms have been proposed, Kelvin wave emission along lines and phonon radiation at small scales. It has been suggested that both would require a Kelvin wave cascade, which theory says cannot reach the smallest scales due to a bottleneck. In this presentation we will discuss a new approach using a recent quaterionic formulation of the Euler equations, coupled with the local induction approximation. Without the extra quaterionic terms It can be shown that if there are sharp reconnections, the above scenario occurs. But with the extra terms, the direction of propagation of nonlinear waves is reversed, there is a cascade to the smallest scales that could create phonons, and the paradox can be resolved.