Phenomenological approach to 3D spinning combustion waves: numerical experiments with a rectangular rod

The spinning waves occur in solid flames and detonation when the plane uniformly propagating reaction front loses stability. As a result, the front breaks into localized zones of intensive reaction. We study a 3D phenomenological model aimed at modeling such phenomena. The model constitutes a nonlinear partial differential equation. This work contains preliminary results demonstrating the capacity of the model to reproduce basic experimental features of the unstable front: metastability of the uniform state and formation of self-sustained regime with predominantly lateral propagation of the front curvature.