Data-driven large-eddy simulation with stochastic surrogate closure for capturing intermittency in generalized stochastic Burgers turbulence

Turbulence is ubiquitous in scientific and engineering flows, yet resolving its multiscale dynamics remains challenging due to the prohibitively high computational cost of direct numerical simulation (DNS) and the limited availability of complete experimental datasets. Although the Fokker–Planck equation (as a second-order truncation of the Kramers–Moyal expansion) can partially characterize the spatial Markovianity of turbulent velocity fluctuations, it fails to effectively capture the more complex intermittency features inherent in the turbulent energy cascade. To address this, this paper proposes a data-driven computational method for large eddy simulation (LES) that effectively captures the phenomenon of velocity fluctuations with intermittency evolved by the generalized stochastic Burgers equation. By estimating higher-order Kramers–Moyal coefficients tailored to the energy cascade process, a stochastic surrogate model is constructed that captures the non-Gaussian statistical behavior associated with intermittency. This surrogate model is then embedded as a subgrid-scale closure within the LES framework. Validation against DNS benchmarks demonstrates that our framework achieves an order-of-magnitude reduction in computational cost while capturing small-scale turbulent intermittency more accurately than several existing LES methods. This approach integrates stochastic modeling with LES to establish a universal framework capable of accommodating the vast majority of turbulence models, providing an efficient, physically consistent, and scalable prediction tool for more complex flows.