Jd. Bowen et Kd. Stolzenbach, THE CONCENTRATION DISTRIBUTION NEAR A CONTINUOUS POINT-SOURCE IN STEADY HOMOGENEOUS SHEAR, Journal of Fluid Mechanics, 236, 1992, pp. 95-110
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.