  The meltwater mixing line (MML) model provides a theoretical prediction of
near-ice water mass properties that is useful to compare with observations. If
oceanographic measurements reported in a temperature-salinity diagram overlap
with the MML prediction, then it is usually concluded that the local dynamics
are dominated by the turbulent mixing of an ambient water mass with nearby
melting ice. While the MML model is consistent with numerous observations, it
is built on an assumption that is difficult to test with field measurements,
especially near the ice boundary, namely that the effective (turbulent and
molecular) salt and temperature diffusivities are equal. In this paper, this
assumption is tested via direct numerical simulations of a canonical model for
externally-forced ice-ocean boundary layers in a uniform ambient. We focus on
the well-mixed regime by considering an ambient temperature close to freezing
and run the simulations until a statistical steady state is reached. The
results validate the assumption of equal effective diffusivities across most of
the boundary layer. Importantly, the validity of the MML model implies a linear
correlation between the mean salinity and temperature profiles normal to the
interface that can be leveraged to construct a reduced ice-ocean boundary layer
model based on a single scalar variable called thermal driving. We demonstrate
that the bulk dynamics predicted by the reduced thermal driving model are in
good agreement with the bulk dynamics predicted by the full
temperature-salinity model. Then, we show how the results from the thermal
driving model can be used to estimate the interfacial heat and salt fluxes, and
the melt rate.
