Cascades and reconnection in interacting vortex filaments

Abstract

The reconnection of two interacting vortex tubes is a fundamental process in fluid mechanics, which, at very high Reynolds numbers, is associated with the formation of intense velocity gradients. Reconnection is usually studied using two antiparallel tubes which are destabilized via the long-wavelength Crow instability, leading to a very symmetric configuration and to a strong flattening of the cores into thin sheets. Here, we consider the interaction of two initially straight tubes at an angle of β and show that by relaxing some symmetries of the problem, a rich phenomenology appears. When the angle between the two tubes is close to β=90∘, their interaction leads to pairing of small portions of antiparallel tubes, followed by the formation of thin and localized vortex sheets as a precursor of reconnection. 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. By decreasing β, we show that reconnection involves increasingly larger portions of tubes, whose cores are subsequently destabilizing, leaving behind more small-scale vortices. At the smallest values of the angle β studied, the two vortices break down through a mechanism, which leads to a cascadelike process of energy conveyance across length scales similar to what was found for previous studies of antiparallel vortex tubes (β=0) which imposed no symmetries. While, in all cases, the interaction of two vortices depends on the initial condition, the rapid formation of fine-scale vortex structures appears to be a robust feature, possibly universal at very high Reynolds numbers.