CONVECTIVE STABILITY OF GRAVITY-MODULATED DOUBLY CROSS-DIFFUSIVE FLUID LAYERS

Citation
G. Terrones et Cf. Chen, CONVECTIVE STABILITY OF GRAVITY-MODULATED DOUBLY CROSS-DIFFUSIVE FLUID LAYERS, Journal of Fluid Mechanics, 255, 1993, pp. 301-321
Citations number
26
Categorie Soggetti
Mechanics,"Phsycs, Fluid & Plasmas
Journal title
ISSN journal
00221120
Volume
255
Year of publication
1993
Pages
301 - 321
Database
ISI
SICI code
0022-1120(1993)255:<301:CSOGDC>2.0.ZU;2-B
Abstract
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.