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Transition from Euclidean to fractal forms within a scale-covariant process: a turbulent combustion study

Multiscale flame fronts are generated by the combustion of turbulent flows. Whereas most wrinkled fronts look fractal in a classical scale analysis, the evolution of their geometry in scale space reveals that they definitely stand part-way between the Euclidean and the fractal regimes. This intermediate domain is studied by exploiting the scale-covariance of geometry formation. An iterative evolution of front roughness from scale to scale is derived. It corresponds to a deterministic evolution of geometry from the Euclidean to the fractal regime which reveals a universal feature of this transition.