Elementary Vortex Processes in Thermal Superfluid Turbulence

Abstract

By solving pertinent mathematical models with numerical and computational methods, we analyze the formation of superfluid vorticity structures in a turbulent normal fluid with an inertial range exhibiting Kolmogorov scaling. We demonstrate that mutual friction forcing causes quantum vortex instabilities whose signature is spiral vortical configurations. The spirals expand until they accidentally meet metastable, intense normal fluid vorticity tubes of similar curvature and vorticity orientation that trap them by driving them towards low mutual friction sites where superfluid bundles are formed. The bundle formation sites are located within the tube cores, but, due to tube curvature and many-tube interaction effects, are displaced by variable distances from the tube centerlines as they follow the contours of the latter. We analyze possible implications of these processes in fully developed thermal superfluid turbulence dynamics.

Spreading of superfluid vorticity clouds in normal-fluid turbulence

“…Indeed, the initial ring becomes unstable and, remarkably, the newly added length is folded back onto the original ring creating a new ring of double circulation strength (figure 3a). Subsequent instabilities (figure 3b) do not follow this pattern, and subsequent tangle configurations (figure 3c) do not show, within the cloud, the superfluid bundles observed in the kinematic computations of Kivotides (2006) and Kivotides & Wilkin (2009). This could be the case because, as discussed above and in Kivotides (2007a), the generated superfluid vorticity damps the normal-fluid structure responsible for its generation and subsequent coherence.…”

“…This damping action is much weaker than viscous dissipation effects in a corresponding pure normal-fluid turbulence. The energy spectrum of superfluid turbulence presents the k −3 scaling of Kivotides & Wilkin (2009) that characterizes the spiral superfluid vorticity patterns of normal vortex tube-superfluid vortex interactions. The corresponding k −2 pressure spectrum indicates (in the fashion of Kivotides et al 2001c) the singular nature of superfluid vorticity.…”

“…Since this asymmetry is induced by the reaction of the superfluid vortices on the normal-fluid flow, the power-law growth rate is an artefact of the kinematic approximation that cannot be observed experimentally. On the other hand, the linear growth of R c in the steady-state fully coupled case can be explained as follows: the tangle grows via the spiral vortex forming mechanism of normal vortex tube-superfluid vortex interaction (Kivotides & Wilkin 2009) that continuously takes place in the interface layer. Indeed, the superfluid energy spectrum of figure 5 (lower curve) shows the characteristic k −3 scaling of this mechanism.…”

“…Indeed, the superfluid energy spectrum of figure 5 (lower curve) shows the characteristic k −3 scaling of this mechanism. Since, the intensity of the spiral-forming mechanism scales with the normal-fluid velocity (Kivotides & Wilkin 2009), it is plausible to expect (on dimensional analysis grounds) that dR c /dt should scale with the intensity of turbulence ahead of the cloud V n . The fact that the Kolmogorov spectrum of the latter (figure 1a) and the k −3 scaling of the superfluid energy spectrum (figure 5) have the same support in k space is also consistent with this suggestion (i.e.…”

“…In this formulation, vortices are discrete, potential, quantized and unconditionally stable due to their topological defect nature. Since, at macroscopic scales, their apparent core size is zero, they cannot be stretched and produce a Kolmogorov-type turbulence cascade (Kivotides 2007a,b;Kivotides & Wilkin 2009). These characteristics are in sharp contrast with the continuous viscous finite-core size vortices of Navier-Stokes turbulence that can be either vortex filaments or sheets and can become unstable and merge with the background fluctuating vorticity field.…”