  Gravitational waves can be emitted by accretion discs if they undergo
instabilities that generate a time varying mass quadrupole. In this work we
investigate the gravitational signal generated by a thick accretion disc of $1
M_{\odot}$ around a static super-massive black hole of $10^{6}M_{\odot}$,
assumed to be formed after the tidal disruption of a solar type star. This
torus has been shown to be unstable to a global non-axisymmetric hydrodynamic
instability, the Papaloizou-Pringle instability, in the case where it is not
already accreting and has a weak magnetic field. We start by deriving
analytical estimates of the maximum amplitude of the gravitational wave signal,
with the aim to establish its detectability by the Laser Interferometer Space
Antenna (LISA). Then, we compare these estimates with those obtained through a
numerical simulation of the torus, made with a 3D smoothed particle
hydrodynamics code. Our numerical analysis shows that the measured strain is
two orders of magnitude lower than the maximum value obtained analytically.
However, accretion discs affected by the Papaloizou-Pringle instability may
still be interesting sources for LISA, if we consider discs generated after
deeply penetrating tidal disruptions of main sequence stars of higher mass.
