Numerical investigation of the structure of a randomly advected Huygens front using a minimal stochastic model

Theoretical predictions (J. R. Mayo and A. R. Kerstein, J. Stat. Phys. 176:456-477, 2019) of structural features of a Huygens front randomly advected by turbulence, in the limit of vanishing local front propagation speed, are confirmed using an adaptation of the linear-eddy model (LEM). In particular, the 1D numerical simulations confirm that the mean streamwise extent of the advectively dispersed front diverges as the logarithm of the advective fluctuation intensity normalized by the front propagation speed, while the root-mean-square streamwise dispersion of front surface density diverges as the square root of that logarithm. These results support the 3D theoretical framework, which additionally predicted that the bulk front-advancement velocity is finite in the considered limit, implying a propagation anomaly analogous to the turbulent dissipation anomaly. The mean streamwise profiles of the progress variable and its turbulent flux in LEM are found to resemble those of propagating fronts advected by 3D turbulence. This suggests that the present results, focusing on a particular limit of the narrowband advection regime, are relevant to the physically important 3D case. [SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.]