  The influence of viscosity contrast on buoyantly unstable miscible fluids in
a porous medium is investigated through a linear stability analysis (LSA) as
well as direct numerical simulations (DNS). The linear stability method
implemented in this paper is based on an initial value approach, which helps to
capture the onset of instability more accurately than the quasi-steady state
analysis. In the absence of displacement, we show that viscosity contrast
delays the onset of instability in buoyantly unstable miscible fluids. Further,
it is observed that suitably choosing the viscosity contrast and injection
velocity a gravitationally unstable miscible interface can be stabilized
completely. Through LSA we draw a phase diagram, which shows three distinct
stability regions in a parameter space spanned by the displacement velocity and
the viscosity contrast. DNS are performed corresponding to parameters from each
regime and the results obtained are in accordance with the linear stability
results. Moreover, the conversion from a dimensionless formulation to the other
and its essence to compare between two different type of flow problems
associated with each dimensionless formulation are discussed.
