Tricritical point as a crossover between type-Is and type-IIs bifurcations

Prabakaran Rajamanickam; Joel Daou

doi:10.13023/psmij.2023.04-01-02

Tricritical point as a crossover between type-Is and type-IIs bifurcations

Prabakaran Rajamanickam, Joel Daou

Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A tricritical point as a crossover between (stationary finite-wavelength) type-Is and (stationary longwave) type-IIs bifurcations is identified in the study of diffusive-thermal (Turing) instability of flames propagating in a Hele-Shaw channel in a direction transverse to a shear flow. Three regimes exhibiting different scaling laws are identified in the neighbourhood of the tricritical point. For these three regimes, sixth-order partial differential equations are obtained governing the weakly nonlinear evolution of unstable solutions near the onset of instability. These sixth-order PDES may be regarded as the substitute for the classical fourth-order Kuramoto–Sivashinsky equation which is not applicable near the tricritical point.

Original language	English
Article number	2
Journal	Progress in Scale Modeling, an International Journal
Volume	4
Issue number	1
Early online date	1 Oct 2023
DOIs	https://doi.org/10.13023/psmij.2023.04-01-02
Publication status	E-pub ahead of print - 1 Oct 2023

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abstract = "A tricritical point as a crossover between (stationary finite-wavelength) type-Is and (stationary longwave) type-IIs bifurcations is identified in the study of diffusive-thermal (Turing) instability of flames propagating in a Hele-Shaw channel in a direction transverse to a shear flow. Three regimes exhibiting different scaling laws are identified in the neighbourhood of the tricritical point. For these three regimes, sixth-order partial differential equations are obtained governing the weakly nonlinear evolution of unstable solutions near the onset of instability. These sixth-order PDES may be regarded as the substitute for the classical fourth-order Kuramoto–Sivashinsky equation which is not applicable near the tricritical point.",

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N2 - A tricritical point as a crossover between (stationary finite-wavelength) type-Is and (stationary longwave) type-IIs bifurcations is identified in the study of diffusive-thermal (Turing) instability of flames propagating in a Hele-Shaw channel in a direction transverse to a shear flow. Three regimes exhibiting different scaling laws are identified in the neighbourhood of the tricritical point. For these three regimes, sixth-order partial differential equations are obtained governing the weakly nonlinear evolution of unstable solutions near the onset of instability. These sixth-order PDES may be regarded as the substitute for the classical fourth-order Kuramoto–Sivashinsky equation which is not applicable near the tricritical point.

AB - A tricritical point as a crossover between (stationary finite-wavelength) type-Is and (stationary longwave) type-IIs bifurcations is identified in the study of diffusive-thermal (Turing) instability of flames propagating in a Hele-Shaw channel in a direction transverse to a shear flow. Three regimes exhibiting different scaling laws are identified in the neighbourhood of the tricritical point. For these three regimes, sixth-order partial differential equations are obtained governing the weakly nonlinear evolution of unstable solutions near the onset of instability. These sixth-order PDES may be regarded as the substitute for the classical fourth-order Kuramoto–Sivashinsky equation which is not applicable near the tricritical point.

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Tricritical point as a crossover between type-Is and type-IIs bifurcations

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