Superfluid turbulence, often referred to as quantum turbulence, is a
fascinating phenomenon for which a satisfactory theoretical framework is
lacking. Holographic duality provides a systematic new approach to studying
quantum turbulence by mapping the dynamics of certain quantum theories onto the
dynamics of classical gravity. We use this gravitational description to
numerically construct turbulent flows in a holographic superfluid in two
spatial dimensions. We find that the superfluid kinetic energy spectrum obeys
the Kolmogorov -5/3 scaling law, as it does for turbulent flows in normal
fluids. We trace this scaling to a direct energy cascade by injecting energy at
long wavelengths and watching it flow to a short-distance scale set by the
vortex core size, where dissipation by vortex annihilation and vortex drag
becomes efficient. This is in sharp contrast with the inverse energy cascade of
normal fluid turbulence in two dimensions. We also demonstrate that the
microscopic dissipation spectrum has a simple geometric interpretation.Comment: 23 pages, 7 figures. Minor corrections made. Movies and supplementary
material available at http://turbulent.lns.mit.edu/Superflui
