Abstract
A one-dimensional (1D) reduced-order model (ROM) is developed for a 3D Rayleigh-Bénard convection system in the turbulent regime with Rayleigh number . The state vector of the 1D ROM is horizontally averaged temperature. Using the Green's function (GRF) method, which involves applying many localized weak forcings to the system one at a time and calculating the responses using long-time averaged direct numerical simulations (DNSs), the system's linear response function (LRF) is computed. Another matrix, called the eddy flux matrix (EFM), which relates changes in the divergence of vertical eddy heat fluxes to changes in the state vector, is also calculated. Using various tests, it is shown that the LRF and EFM can accurately predict the time-mean responses of temperature and eddy heat flux to external forcings and that the LRF can predict well the forcing needed to change the mean flow in a specified way (inverse problem). The non-normality of the LRF is discussed and its eigenvectors or singular vectors are compared with the leading proper orthogonal decomposition modes of the DNS data. Furthermore, it is shown that if the LRF and EFM are simply scaled by the square root of the Rayleigh number, they perform equally well for flows at other , at least in the investigated range of . The GRF method can be applied to develop 1D or 3D ROMs for any turbulent flow, and the calculated LRF and EFM can help with better analyzing and controlling the nonlinear system.
4 More- Received 8 May 2018
DOI:https://doi.org/10.1103/PhysRevFluids.4.013801
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