The concentration of solute undergoing advection and local dispersion
in a random hydraulic conductivity held is analyzed to quantify its va
riability and dilution. Detailed numerical evaluations of the concentr
ation variance sigma(c)(2) are compared to an approximate analytical d
escription, which is based on a characteristic variance residence time
(VRT), over which local dispersion destroys concentration fluctuation
s, and effective dispersion coefficients that quantify solute spreadin
g rates. Key features of the analytical description for a finite size
impulse input df solute are (1) initially, the concentration fields be
come more irregular with time, i.e., coefficient of variation, CV = si
gma(c)/[c], increases with time ([c] being the mean concentration); (2
) owing to the action of local dispersion, at large times (t > VRT), s
igma(c)(2) is a linear combination of [c](2) and (partial derivative[c
]/partial derivative x(i))(2), and the CV decreases with time (at the
center, CV congruent to (N)(1/2) VRT/t, N being the macroscopic dimens
ionality of the plume); (3) at early time, dilution and spreading can
be severely disconnected; however, at large time the volume occupied b
y solute approaches that apparent from its spatial second moments; and
(4) in contrast to the advection-local dispersion case, under advecti
on alone, the CV grows unboundedly with time (at the center, CV propor
tional to t(N/4)), and spatial second moment is increasingly disconnec
ted from dilution, as time progresses. The predicted large time evolut
ion of dilution and concentration fluctuation measures is observed in
the numerical simulations.