  Bose-Einstein condensates with their superfluidity property provide an
interesting parallel to classical fluids. Due to the Kolmogorov spectrum of
homogeneous turbulence the statistics of the incompressible velocity field is
of great interest, but in superfluids the velocity field is quite complicated
therefore most of the work done has been numerical in nature. We leveraged the
Weak Wave Turbulence (WWT) theory to obtain the statistics of the velocity
field which allowed us to produce a semi-analytical procedure for extracting
the incompressible energy spectrum in the WWT regime. We also showed that this
spectrum is directly induced by the wave spectrum, showing that the two
phenomena are closely related.
