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

Authors

Prabakaran Rajamanickam, University of ManchesterFollow
Joel Daou, University of ManchesterFollow

Abstract

A tricritical point as a crossover between (stationary finite-wavelength) type-I_s and (stationary longwave) type-II_s 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.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

DOI

https://doi.org/10.13023/psmij.2023.04-01-02

Recommended Citation

Rajamanickam, Prabakaran and Daou, Joel (2023) "Tricritical point as a crossover between type-Is and type-IIs bifurcations," Progress in Scale Modeling, an International Journal: Vol. 4: Iss. 1, Article 2.
DOI: https://doi.org/10.13023/psmij.2023.04-01-02
Available at: https://uknowledge.uky.edu/psmij/vol4/iss1/2