Anomalous roughness of turbulent interfaces with system size dependent local roughness exponent

In a system far from equilibrium the system size can play the role of control parameter that governs the spatiotemporal dynamics of the system. Accordingly, the kinetic roughness of interfaces in systems far from equilibrium may depend on the system size. To get an insight into this problem, we performed a detailed study of rough interfaces formed in paper combustion experiments. Using paper sheets of different width λ, we found that the turbulent flame fronts display anomalous multi-scaling characterized by non-universal global roughness exponent α and by the system size dependent spectrum of local roughness exponents, ζ_q(λ) = ζ₁(1)q^-ωλ^φ<α, whereas the burning fronts possess conventional multi-affine scaling characterized by the universal spectrum of roughness exponent ζ_q = 0.93q^-0.15. The structure factor of turbulent flame fronts also exhibits unconventional scaling dependence on λ. These results are expected to apply to a broad range of far from equilibrium systems when the kinetic energy fluctuations exceed a certain critical value.