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