  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 obtaining quantities such as the
statistics of the velocity field from the macroscopic wavefunction turns out be
a complicated task; therefore, most of the work up to now has been numerical in
nature. We made use of the Weak Wave Turbulence (WWT) theory, which provides
the statistics of the macroscopic wavefunction, 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. This is done
by introducing an auxiliary wavefunction that preserves the relevant
statistical and hydrodynamical properties of the condensate but with a
homogeneous density thus allowing for a simpler description of the velocity
field.
