Proper orthogonal decomposition of a fully confined cubical differentially heated cavity flow at Rayleigh number Ra = 109

Abstract

Proper orthogonal decomposition is used to educe fundamental velocity and temperature coherent structures in the fully confined cubical three-dimensional differentially heated cavity (DHC) flow. Among other linear decompositions, the POD is optimal in the sense that it provides a set of modes that captures the largest amount of energy contained in the snapshot ensemble. We present here preliminary results of the first empirical eigenfunctions that account up to 95% of the total energy of the ensemble. The database is made of 200 snapshots obtained by means of Direct Numerical Simulation (DNS) at Rayleigh Ra=109. The results are in good agreement with previous observations of coherent structures identified with λ2 criterion, confirming the importance of the elongated spanwise structures (located downstream the break up of the laminar vertical boundary layers) for the description/modeling of the turbulent heat flux. The basis functions that account for the largest part of the turbulent heat flux are not made of the most energetic POD empirical eigenfunctions. In appears that the spatial structures which contain the largest fraction of the turbulent heat transfer correspond to the POD modes characterized by the presence of spanwise elongated vortices at the vertical active walls where temperature and velocity eigenfunctions are spatially strongly correlated.