| Summary: | The effect of odd viscosity on the instability of liquid film along a wavy inclined bottom with linear temperature variation is investigated. By utilizing the long-wave approximation, the non-linear evolution equation of the free surface is derived. By applying the normal mode method, the linear instability of thin film flow is investigated. With the help of multi-scale analysis methods, the weakly non-linear instability of thin film flow is also investigated. The results reveal that the Marangoni effect caused by non-uniform temperature distribution promotes the instability of the liquid film, while the odd viscosity has a stabilizing effect. In addition, for a positive local inclination angle <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula>, an increase in bottom steepness <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ζ</mi></semantics></math></inline-formula> inhibits the instability of the liquid film flow. In contrast, with a negative local inclination angle <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>θ</mi></semantics></math></inline-formula>, increased bottom steepness <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ζ</mi></semantics></math></inline-formula> promotes the instability of the liquid film flow. The results of the temporal linear instability analysis and the weakly non-linear instability analysis have been substantiated through numerical simulations of the non-linear evolution equations.
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