Smallest scale of wrinkles of a Huygens front in extremely strong turbulence

By analyzing the statistically stationary stage of propagation of a Huygens front in homogeneous, isotropic, constant-density turbulence, a length scale $l_0$ is introduced to characterize the smallest wrinkles on the front surface in the case of a low constant speed $u_0$ of the front when compared to the Kolmogorov velocity $u_K$. The length scale is derived following a hypothesis of dynamical similarity that highlights a balance between (i) creation of a front area due to advection and (ii) destruction of the front area due to propagation. Consequently, the front speed is compared with the magnitude of the fluid velocity difference in two points separated by a distance smaller than the Kolmogorov length scale. Appropriateness of the smallest wrinkle scale is demonstrated by applying a fractal approach to evaluating the mean area of the instantaneous front surface. Since the scales of the smallest and larger wrinkles belong to different subranges (dissipation and inertial, respectively) of the Kolmogorov turbulence spectrum, the front is hypothesized to be a bifractal characterized by two different fractal dimensions in the two subranges. Both fractal dimensions are evaluated adapting the aforementioned hypothesis of dynamical similarity. Such a bifractal model yields a linear relation between the mean fluid consumption velocity, which is equal to the front speed $u_0$ multiplied with a ratio of the mean area of the instantaneous front surface to the transverse projected area, and the rms turbulent velocity $u^{\prime }$ even if a ratio of $u_0/u^{\prime }$ tends to zero.