  This paper explores the application of SPH to a Direct Numerical Simulation
(DNS) of decaying turbulence in a two-dimensional no-slip wall-bounded domain.
In this bounded domain, the inverse energy cascade, and a net torque exerted by
the boundary, result in a spontaneous spin up of the fluid, leading to a
typical end state of a large monopole vortex that fills the domain. The SPH
simulations were compared against published results using a high accuracy
pseudo-spectral code. Ensemble averages of the kinetic energy, enstrophy and
average vortex wavenumber compared well against the pseudo-spectral results, as
did the evolution of the total angular momentum of the fluid. However, while
the pseudo-spectral results emphasised the importance of the no-slip boundaries
as generators of long lived coherent vortices in the flow, no such generation
was seen in the SPH results. Vorticity filaments produced at the boundary were
always dissipated by the flow shortly after separating from the boundary layer.
The kinetic energy spectrum of the SPH results was calculated using a SPH
Fourier transform that operates directly on the disordered particles. The
ensemble kinetic energy spectrum showed the expected k-3 scaling over most of
the inertial range. However, the spectrum flattened at smaller length scales
(initially less than 7.5 particle spacings and growing in size over time),
indicating an excess of small-scale kinetic energy.
