  Presented is a prediction, based on the Frenet-Serret differential geometry
of space curves, that the wave number dependence of the average kinetic energy
per unit length of two mutually interacting highly curved quantum vortex scales
as k^-3. The interacting quantum vortices are helical in shape, supporting
circularly polarized counter-propagating waves, with arbitrary curvature and
torsion. This power-law spectrum agrees with the high-k spectrum found in
precise quantum simulations of turbulent superfluidity with tangle of highly
curved and excited quantum vortices.
