G. Terrones et Cf. Chen, CONVECTIVE STABILITY OF GRAVITY-MODULATED DOUBLY CROSS-DIFFUSIVE FLUID LAYERS, Journal of Fluid Mechanics, 255, 1993, pp. 301-321
A stability analysis is undertaken to theoretically study the effects
of gravity modulation and cross-diffusion on the onset of convection i
n horizontally unbounded doubly diffusive fluid layers. We investigate
the stability of doubly stratified incompressible Boussinesq fluid la
yers with stress-free and rigid boundaries when the stratification is
either imposed or induced by Soret separation. The stability criteria
are established by way of Floquet multipliers of the amplitude equatio
ns. The topology of neutral curves and stability boundaries exhibits f
eatures not found in modulated singly diffusive or unmodulated multipl
y diffusive fluid layers. A striking feature in gravity-modulated doub
ly cross-diffusive layers is the existence of bifurcating neutral curv
es with double minima, one of which corresponds to a quasi-periodic as
ymptotically stable branch and the other to a subharmonic neutral solu
tion. As a consequence, a temporally and spatially quasi-periodic bifu
rcation from the basic state is possible, in which case there are two
incommensurate critical wavenumbers at two incommensurate onset freque
ncies at the same Rayleigh number. In some instances, the minimum of t
he subharmonic branch is more sensitive to small parameter variations
than that of the quasi-periodic branch, thus affecting the stability c
riteria in a way that differs substantially from that of unmodulated l
ayers.