Saltwater intrusion in Southern Eyre Peninsula, December 2009

conditions expected in field settings – a ”flux-controlled case”, and a ”head-controlled
case”. Head-controlled boundaries may arise in situations where, for instance, an
inland water body (e.g. a canal, lake or wetland) of constant head occurs at the
inland boundary of the model (e.g. in the case considered by Dausman and
Langevin, 2005), or where pumping occurs such that the inland head is constant
despite sea-level rise. In Ward et al. (In Prep.), both flux-controlled and headcontrolled
settings are investigated further, however for the present study the fluxcontrolled
boundary is considered to be the only relevant inland boundary condition.
4.2.2 Dimensionless Formulation
Naji et al. (1998) presented (1) in dimensionless form, and we adopt a similar form.
The dimensionless clusters used below are slightly different to those of Naji et al.
(1998) because they allow the physical processes to be described in terms of
meaningful ratios of the different flow types (as described below). The dimensionless
seawater intrusion extent is defined as
x
T
x
T
(3)
xi
2
such that: x T
F 1 F 1 M F 1
(4)
where:
q
Rx
i
F ,
i
M
K
x
i
1
q
i
B
Rx
i
2
(5)
Here x
T
is the seawater intrusion extent, expressed as a proportion of the inland
distance x i . F and M are two dimensionless ratios describing the governing physical
controls. F is the ratio of lateral inflow to coastal rainfall-recharge (which we term
“mixed inflow ratio” from herein). M is a ratio of free-convective components to
forced-convective (advective) components that we term a “mixed convection ratio”, in
a similar fashion to Massmann et al. (2006) and Ward et al. (2007). In M, the
numerator lumps together those parameters which we know contribute to increasing
seawater intrusion (most significantly K and B, as the density ratio is relatively
constant for freshwater/seawater interactions). The denominator in M contains the
summed inflows, i.e. the discharge to the sea (which leads to the retardation of
seawater intrusion). The reason for using a dimensionless formulation is to reduce
the number of critical parameters, so as to allow different systems to be more rapidly
compared against each other. In this case, all of the hydrogeological variables have
been reduced to just two parameters (M and F), and as a result the idealised
seawater intrusion extent can be rapidly compared across multiple unconfined
coastal aquifer systems which vary widely in terms of recharge and inland inflows,
hydraulic conductivity, thickness and inland extent, by simply comparing their
respective M and F values.
Mathematically, x
T
is defined over the interval 0 M F 1 . What this means in
practical terms is that when M > F + 1 it implies that the toe of the wedge has
intruded inland of the point of maximum hydraulic head (the peak of the coastal
groundwater mound), and the situation becomes unstable (Strack, 1989).
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