  In this paper we study decaying turbulence in fixed and rotating boxes in two
dimen- sions using the particle method SPH. The boundaries are specified by
boundary force particles, and the turbulence is initiated by a set of gaussian
vortices. In the case of fixed boxes we recover the results of Clercx and his
colleagues obtained using both a high accuracy spectral method and experiments.
Our results for fixed boxes are also in close agreement with those of Monaghan1
and Robinson and Monaghan2 obtained using SPH. A feature of decaying turbulence
in no-slip, square, fixed boundaries is that the angular momentum of the fluid
varies with time because of the reaction on the fluid of the viscous stresses
on the boundary. We find that when the box is allowed to rotate freely, so that
the total angular momentum of box and fluid is constant, the change in the
angular momentum of the fluid is a factor ~ 500 smaller than is the case for
the fixed box, and the final vorticity distribution is different. We also
simulate the behaviour of the turbulence when the box is forced to rotate with
small and large Rossby number, and the turbulence is initiated by gaussian
vortices as before. If the rotation of the box is maintained after the
turbulence is initiated we find that in the rotating frame the decay of kinetic
energy, enstrophy and the vortex structure is insensitive to the angular
velocity of the box. On the other hand, If the box is allowed to rotate freely
after the turbulence is initiated, the evolved vortex structure is completely
different.
