12 Notations

C solute concentration (M/L3)
c and cs specific heat capacities of the groundwater and rock, respectively (ML2/(T2Θ))
C0 initial concentration of the groundwater (M/L3)
Ci concentration species i (M/L3)
Ci,0 reference concentration of species i (M/L3)
cP volumetric heat capacity (M/(LT2Θ))
Css concentration associated with a source (M/L3)
D diffusion coefficient (L2/T); for solutes, D=DC the molecular diffusion coefficient; for heat, D=DT the thermal diffusion coefficient
\overline{D_{h,C}} solute dispersion tensor (L2/T) which includes the effect of both molecular diffusion and mechanical dispersion
DC solute diffusion coefficient in the bulk medium which is decreased from the diffusion coefficient in open water by the factors of connected porosity (n) and tortuosity (τ) (L2/T)
ΔC concentration difference (M/L3)
Δρ density difference (M/L3)
∆T temperature difference (Θ)
DT thermal diffusivity (L2/T)
\overline{D_{C}} dispersion tensor which includes the combined effects of thermal conduction and mechanical dispersion (L2/T)
g gravitational acceleration (L/T2)
\vec{g} gravitational acceleration vector (L/T2)
H thickness of the layer (L)
hp pressure head (L)
hp,i pressure head for a piezometer at location i containing a fluid column with density ρi (L)
\vec{J}_{C} solute mass flux (M/(L2T))
\vec{J}_{e} heat flux (M/T3)
k intrinsic permeability (L2)
Kd distribution coefficient (L3/M)
kT thermal conductivity (ML/(T3Θ))
μ dynamic viscosity (M/(LT))
n porosity (dimensionless)
gradient operator which represents the rate of change of a variable per unit of distance in the x, y and z direction
NS total number of solutes that contribute to the fluid density
p pressure (M/(LT2))
p0 initial fluid pressure (M/(LT2))
\displaystyle \left ( \frac{\partial \rho }{\partial C} \right )_{i} slope of the density-concentration relationship for species i
\vec{q} specific discharge (L/T)
Qh heat flow across the source boundary (M/T3)
Qm mass flux across the source boundary (M/(TL2))
qss discharge rate per unit of volume of water source, or sink (1/T)
ρ groundwater density (M/L3)
ρ0 density of the fluid at initial concentration, temperature and pressure (M/L3)
ρb dry bulk density of the rock (M/L3)
ρr density of the rock (M/L3)
ρss density of water source, or sink (M/L3)
t time (T)
T temperature (Θ)
T0 initial temperature of the groundwater (Θ)
Tss temperature associated with a source (Θ)
z elevation relative to a datum (L)

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Variable-Density Groundwater Flow Copyright © 2022 by Vincent E.A. Post and Craig T. Simmons. All Rights Reserved.