Direct numerical simulation of buoyantly driven turbulence

Numerical simulations of homogeneous turbulence subject to buoyant forcing were performed. The presence of a mean temperature gradient combined with a gravitational field results in a forcing term in the momentum equation. The development of the turbulence was studied and compared to the decay of similar fields in the absence of gravity. In the buoyantly driven fields, the vorticity is preferentially aligned with the intermediate eigenvector of the strain-rate tensor and the local temperature gradient is more likely to be aligned with the most compressive eigenvector. These relationships are qualitatively similar to those observed in previous shear flow results studied by Ashurst et al. (1987). A tensor diffusivity model for passive scalar transport developed from shear flow results in Rogers, Moin & Reynolds (1986) also predicts this buoyant scalar transport, indicating that the relationship between the scalar flux and the Reynolds stress is similar in both flows. Discussion During the workshop period, calculations were made with 64 by 322 grids in order to examine the effect of forcing the velocity field with scalar fluctuations. With the Boussinesq assumption of a zero divergent velocity field, the modifications to the Rogallo (1981) code were simple. The buoyant forcing develops flow patterns at large length scales in the gravity direction. Because of this, a grid which is longer in the gravitational direction is used. The flow is analyzed at a time before the large scales feel the effect, of the periodic boundary conditions. Calculations were made with and without gravity, that. is forcing and no forcing. The Rayleigh number based on the Taylor microscale of the velocity field, _, is defined as Ra_ = (g/To)l -Tl 'Pr/v 2, where z is the gravitational direction and g is the gravitational acceleration. The Prandtl number, Pr, was taken to be 0.7 and the Taylor-nficroscale Reynolds number was 7.4. In the field analyzed here Ra_ = 93 and the ratio Rax/(Re2Pr) is 2.4. Previous work by Ashurst et al. (1987) indicated a coupling between the vorticity field and the eigenvectors of the strain-rate tensor (ordered so that o >/3 > 3') as determined from single point analysis of the alignment between the vorticity vector and the strain-rate directions. This analysis was repeated for the buoyantly driven fields and similar results were found in that vorticity has a large probability to 1 Sandia National Laboratories 2 NASA-Ames Research Center 118 Ashurst and Rogers