The concentration distribution near a continuous point source in steady homogeneous shear
Journal of Fluid Mechanics, 236 (-1):
95--110 (1992)DOI: 10.1017/s0022112092001356
Abstract
The concentration distribution resulting from a continuous point source in a fluid with a steady linear variation in velocity is distorted by the flow at distances greater than (K/Eb)½, where K is the molecular diffusion coefficient and Eb is a characteristic shear rate. The distribution has two distinct shapes depending on the number of principal axes of fluid strain that are expansive and the relative magnitude of irrotational and rotational shears. For irrotational flows a single expansive principal axis of strain results in a tube-like distribution, while two expansive axes results in a disk-like distribution. Approximate analytical solutions, derived by neglecting diffusion along the expansive axes, agree well with concentrations calculated by numerically convolving the exact instantaneous source solution. The effect of fluid vorticity is generally to reorient the distribution away from the principal axes of strain and to reduce the asymmetry of the concentration distribution. Aside from reorientation, the concentration distribution varies little until the vorticity approaches a critical value defined by a kinematic condition for equilibrium orientation in the presence of rotation. For vorticity greater than the critical value, the concentration distribution becomes axisymmetric around the axis of rotation. Application of these results to numerical simulations of isotropic turbulence suggests that tubes are more common than disks and that vorticity exceeds the critical value in at least 25\% of the fluid.