  In this paper we model the gravitational wave emission of a freely precessing
neutron star. The aim is to estimate likely source strengths, as a guide for
gravitational wave astronomers searching for such signals. We model the star as
a partly elastic, partly fluid body with quadrupolar deformations of its moment
of inertia tensor. The angular amplitude of the free precession is limited by
the finite breaking strain of the star's crust. The effect of internal
dissipation on the star is important, with the precession angle being rapidly
damped in the case of a star with an oblate deformation. We then go on to study
detailed scenarios where free precession is created and/or maintained by some
astrophysical mechanism. We consider the effects of accretion torques,
electromagnetic torques, glitches and stellar encounters. We find that the
mechanisms considered are either too weak to lead to a signal detectable by an
Advanced LIGO interferometer, or occur too infrequently to give a reasonable
event rate. We therefore conclude that, using our stellar model at least, free
precession is not a good candidate for detection by the forthcoming laser
interferometers.
