0cddb7c06f1cd518e1efdc0e20b70c31-Supplemental.pdf

The 2048 mesh point high-resolution solution is generated using the Fourier-Galerkin spectral method [41] with the 4th order Runge-Kutta method for time stepping. From the box-filtered initial condition, the 32-point low-resolution solution is conducted using central differencing for the spatial derivatives. This choice does not introduce additional artificial viscosity; thus, the solution without closure is naturally unstable. In this setting, u can be regarded as fully resolved, thus the numerical residual r(u), defined in Eq.(10),iszero. Forthereacting flow simulation task, the different variables in the input q are normalized to the same order of magnitude.