Smoothed particle hydrodynamics simulations of turbulence in fixed and rotating boxes in two dimensions with no-slip boundaries

Abstract

In this paper we study decaying turbulence in fixed and rotating boxes in two dimensions using the particle method smoothed particle hydrodynamics (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 Monaghan [Eur. J. Mech. – B/Fluids 30, 360370 (2011)] and Robinson and Monaghan [Int. J. Numer. Methods Fluids (in press)] 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 of ∼500 smaller than in 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.