  We study and elucidate the mechanism of spiral density wave excitation in a
differentially rotating turbulent flow. We formulate a set of wave equations
with sources that are only non-zero in the presence of turbulent fluctuations.
We solve these in a shearing box domain using a WKBJ method. It is found that,
for a particular azimuthal wave length, the wave excitation occurs through a
sequence of regularly spaced swings during which the wave changes from leading
to trailing form. This is a generic process that is expected to occur in
shearing discs with turbulence. Trailing waves of equal amplitude propagating
in opposite directions are produced, both of which produce an outward angular
momentum flux that we give expressions for as functions of the disc parameters
and azimuthal wave length.
  By solving the wave amplitude equations numerically we justify the WKBJ
approach for a Keplerian rotation law for all parameter regimes of interest. In
order to quantify the wave excitation completely the important wave source
terms need to be specified. Assuming conditions of weak nonlinearity, these can
be identified and are associated with a quantity related to the potential
vorticity, being the only survivors in the linear regime. Under the additional
assumption that the source has a flat power spectrum at long azimuthal wave
lengths, the optimal azimuthal wave length produced is found to be determined
solely by the WKBJ response and is estimated to be 2 pi H, with H being the
nominal disc scale height.
