THE CONCENTRATION DISTRIBUTION NEAR A CONTINUOUS POINT-SOURCE IN STEADY HOMOGENEOUS SHEAR

The concentration distribution resulting from a continuous point sourc e in a fluid with a steady linear variation in velocity is distorted b y the flow at distances greater than (kappa/E(b))1/2, where kappa is t he molecular diffusion coefficient and E(b) 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 flo ws a single expansive principal axis of strain results in a tube-like distribution, while two expansive axes results in a disk-like distribu tion. Approximate analytical solutions, derived by neglecting diffusio n 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 a way from the principal axes of strain and to reduce the asymmetry of t he concentration distribution. Aside from reorientation, the concentra tion distribution varies little until the vorticity approaches a criti cal 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 simulation s of isotropic turbulence suggests that tubes are more common than dis ks and that vorticity exceeds the critical value in at least 25% of th e fluid.