Density-driven instabilities between miscible fluids in a vertical Hele-Shaw cell are
investigated by means of experimental measurements, as well as two- and three-dimensional
numerical simulations. The experiments focus on the early stages of the
instability growth, and they provide detailed information regarding the growth rates
and most amplified wavenumbers as a function of the governing Rayleigh number Ra.
They identify two clearly distinct parameter regimes: a low-Ra, ‘Hele-Shaw’ regime
in which the dominant wavelength scales as Ra−1, and a high-Ra ‘gap’ regime in
which the length scale of the instability is 5±1 times the gap width. The experiments
are compared to a recent linear stability analysis based on the Brinkman equation.
The analytical dispersion relationship for a step-like density profile reproduces the
experimentally observed trend across the entire Ra range. Nonlinear simulations
based on the two- and three-dimensional Stokes equations indicate that the high-Ra
regime is characterized by an instability across the gap, wheras in the low-Ra regime
a spanwise Hele-Shaw mode dominates.
Harmonic to subharmonic transition of the Faraday instability in miscible fluids
