Abstract
Analyses have disagreed on whether the velocity $$u_T$$ of bulk advancement of a Huygens front in turbulence vanishes or remains finite in the limit of vanishing local front propagation speed $$u_0$$ . Here, a connection to the large-deviation statistics of log-correlated random processes enables a definitive determination of the correct small- $$u_0$$ asymptotics. This result reconciles several theoretical and phenomenological perspectives with the conclusion that $$u_T$$ remains finite for vanishing $$u_0$$ , which implies a propagation anomaly akin to the energy-dissipation anomaly in the limit of vanishing viscosity. Various leading-order structural properties such as a novel $$u_0$$ dependence of a bulk length scale associated with front geometry are predicted in this limit. The analysis involves a formal analogy to random advection of diffusive scalars.
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