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

Mathematics And Statistics

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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.

Original language	English
Article number	2
Journal	Progress in Scale Modeling, an International Journal
Volume	4
Issue number	1
DOIs	https://doi.org/10.13023/psmij.2023.04-01-02
Publication status	Published - 31 Oct 2023

Funding

This research was supported by the UK EPSRC through grant EP/V004840/1

Keywords

tricritical point
sixth-order PDEs
Kuramoto–Sivashinsky equation
Weakly nonlinear analysis

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10.13023/psmij.2023.04-01-02Licence: CC BY 4.0

Rajamanickam-and-Daou-Tricritical-point-as-a-crossover-between-type-Is-and-type-IIs-bifurcationsFinal published version, 1.28 MBLicence: CC BY 4.0

https://arxiv.org/abs/2407.00109

Cite this

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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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KW - sixth-order PDEs

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M3 - Article

SN - 2693-969X

VL - 4

JO - Progress in Scale Modeling, an International Journal

JF - Progress in Scale Modeling, an International Journal

IS - 1

M1 - 2

ER -

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

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