Universal interface scaling: from isothermal flames to supernovae and population dynamics

Abstract The propagation of a self-sustaining interface through a turbulent medium is a fundamental problem spanning combustion, astrophysics, and population dynamics. While the governing equations – the Level-Set and Fisher-KPP equations – are mathematically isomorphic in the pulled-front limit, scaling laws for interface speed are often derived in isolation within each discipline. This study argues that the specific scaling regimes identified for isothermal premixed flames, recently clarified by high-fidelity level-set simulations, provide a unifying predictive framework for non-combustion systems. We specifically examine the transition from a quadratic scaling regime at low turbulence intensities to a 4/3 power law at intermediate intensities and finally a linear scaling regime at high intensities. By comparing scaling exponents and regime boundaries from Type Ia supernova deflagrations and KPP population-dynamics models against these combustion-derived correlations – and presenting the cross-domain comparison on master-scaling and stabilization-time correlation plots – we present evidence that the three-regime scaling architecture (quadratic → 4/3 → linear) is a common feature of pulled-front propagation across physically disparate systems. Furthermore, we show that the unbounded transient growth phase identified in isothermal flame theory offers a novel explanation for the rapid, early-stage acceleration of invasive species fronts in coastal currents. These findings suggest that subgrid models developed for isothermal combustion may, within well-defined physical limits, be portable to astrophysical and ecological simulations.