Nonlinear convection of binary liquids in a porous medium

Rameshwar, Y.; Anuradha, V.; Srinivas, G.; Pérez, Laura M.; Laroze, David; Pleiner, Harald

doi:10.1063/1.5027468

Cited by 4 publications

(2 citation statements)

References 32 publications

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“…the last equality of which defines the Eckhaus threshold predicted by cubic-quintic GL equation. From the comparison between existence (35) and Eckhaus thresholds (38), it is possible to identify which bifurcating branch may undergo EI as:…”

Section: Cubic-quintic Ginzburg-landau Equationmentioning

confidence: 99%

Eckhaus instability of stationary patterns in hyperbolic reaction–diffusion models on large finite domains

Consolo

Grifó

2022

Partial Differ. Equ. Appl.

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We have theoretically investigated the phenomenon of Eckhaus instability of stationary patterns arising in hyperbolic reaction–diffusion models on large finite domains, in both supercritical and subcritical regime. Adopting multiple-scale weakly-nonlinear analysis, we have deduced the cubic and cubic–quintic real Ginzburg–Landau equations ruling the evolution of pattern amplitude close to criticality. Starting from these envelope equations, we have provided the explicit expressions of the most relevant dynamical features characterizing primary and secondary quantized branches of any order: stationary amplitude, existence and stability thresholds and linear growth rate. Particular emphasis is given on the subcritical regime, where cubic and cubic–quintic Ginzburg–Landau equations predict qualitatively different dynamical pictures. As an illustrative example, we have compared the above-mentioned analytical predictions to numerical simulations carried out on the hyperbolic modified Klausmeier model, a conceptual tool used to describe the generation of stationary vegetation stripes over flat arid environments. Our analysis has also allowed to elucidate the role played by inertia during the transient regime, where an unstable patterned state evolves towards a more favorable stable configuration through sequences of phase-slips. In particular, we have inspected the functional dependence of time and location at which wavelength adjustment takes place as well as the possibility to control these quantities, independently of each other.

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Section: Cubic-quintic Ginzburg-landau Equationmentioning

confidence: 99%

Eckhaus instability of stationary patterns in hyperbolic reaction–diffusion models on large finite domains

Consolo

Grifó

2022

Partial Differ. Equ. Appl.

View full text Add to dashboard Cite

show abstract

“…Finally, the article by Rameshwar et al (2018) deals with the thermal convection of binary liquids in a porous medium. Since this system exhibits stationary and oscillatory instabilities leading to transitions from supercritical to subcritical dynamics the authors have derived corresponding cubic-quintic Ginzburg-Landau equations.…”

Section: Introductionmentioning

confidence: 99%