Classical and quantum turbulence

The reconnection of two singularities in 2D, 3D, and 4D classical and quantum turbulence is examined. Singularity reconnection plays an essential role in the dissipation of the incompressible part of kinetic energy. A reconnection condition 2(ds+1)≥d+12(ds+1)≥d+1 is derived, which crucially depends on the dimension dsds of the singular structure in relation to the spatial dimension dd of the system. The feasibility of this condition is examined using direct numerical simulations of the Navier–Stokes and Gross–Pitaevskii equations for the classical and quantum turbulence, respectively. We observed that the condition was satisfied for d=3d=3 and 4, in agreement with the occurrence of energy cascades in both classical and quantum turbulence in those dimensions.