A low-dimensional model of large-scale convective flow in an elongated rectangular cavity

The work focuses on studying the large-scale circulation (LSC) of turbulent convective flow in the case of a free upper boundary. LSC is characterized by complex temporal dynamics and significantly influences heat and mass transfer processes. A large number of studies have analyzed LSC in cylindrical cavities, detailing the features of its formation and various changes in the direction of its rotation. The novelty of this work lies in considering turbulent convective flow in an elongated rectangular domain, where the lower boundary is uniformly heated, and the upper boundary is free, allowing for quasi-stationary heat outflow. Numerical simulations revealed the formation of LSC with pronounced oscillatory behavior in three planes. Direct numerical simulations and large-eddy simulations performed using the OpenFOAM package demonstrated similar LSC behavior. Using a proper orthogonal decomposition, the most energy-containing modes were identified, each of which was found to contribute primarily to the corresponding projection of the angular momentum of the LSC. The evolution of these modes is described by a system of ordinary differential equations derived by projecting the governing equations of thermogravitational convection onto the basis of spatial modes using the Galerkin approach. As a result, a low-dimensional nonlinear model was formulated, including only three modes and capable of reproducing the observed LSC oscillations. From a physical perspective, the observed LSC oscillations can be interpreted as weakly nonlinear triadic interactions of large-scale modes.