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A data-driven, model-free framework is introduced for calculatingReduced-Order Models (ROMs) capable of accurately predicting time-meanresponses to external forcings, or forcings needed for specified responses,e.g., for control, in fully turbulent flows. The framework is based on usingthe Fluctuation-Dissipation Theorem (FDT) in the space of a limited number ofmodes obtained from Dynamic Mode Decomposition (DMD). Using the DMD modes asthe basis functions, rather than the commonly used Proper OrthogonalDecomposition (POD) modes, resolves a previously identified problem in applyingFDT to high-dimensional, non-normal turbulent flows. Employing thisDMD-enhanced FDT method (FDT$_\mathrm{DMD}$), a 1D linear ROM with horizontallyaveraged temperature as state vector, is calculated for a 3D Rayleigh-B\'enardconvection system at the Rayleigh number of $10^6$ using data obtained fromDirect Numerical Simulation (DNS). The calculated ROM performs well in varioustests for this turbulent flow, suggesting FDT$_\mathrm{DMD}$ as a promisingmethod for developing ROMs for high-dimensional, turbulent systems.

Data-driven reduced modelling of turbulent Rayleigh-Benard convection using DMD-enhanced Fluctuation-Dissipation Theorem