Spectrally optimal SGS closures of Burgers turbulence

The wavelet-based modeling framework developed by Nabavi & Kim (J. Fluid Mech., 2024) is extended to discover functional forms of spectrally optimal subgrid-scale (SGS) models. High-fidelity data are generated using direct numerical simulation (DNS) of the one-dimensional forced Burgers equation. The resulting dataset is used to construct SGS models for Burgers turbulence. The residual stress is represented as a truncated series expansion in terms of resolved-scale gradients, with unknown constants determined by solving an optimization problem for spectral optimality. A priori analysis is performed to analyze the discovered SGS models. A posteriori tests are conducted across a range of grid cutoff scales for validation. The resulting SGS models are examined in terms of their ability to support energy backscatter in the large-eddy simulation (LES) of Burgers turbulence.