Proper orthogonal decomposition analysis of coherent structures in a transient buoyant jet

Abstract

The spatial evolution of a circular buoyant jet at moderate Reynolds number (Re = 103) and density ratio (ρ* = 2) has been investigated using large-eddy simulation (LES). The Smagorinsky subgrid-scale model is used for the unresolved small-scale turbulence. Dynamic puffing phenomena is observed and corresponds to the formation of large-scale vortex structures near the plume base with an axisymmetric mode of instability. These toroidal vortical structures break down into smaller, disorganized eddies with increasing distance downstream. Two-point correlation variances of temperature and velocities generated from LES are analysed using the proper orthogonal decomposition (POD) method. The POD analysis yields a set of numerical eigenfunctions which provide a reduced-order description of the flow. The energy of the flow is found to be well represented by a finite number of eigenmodes. For example, our results indicate that the first 20 modes capture over 70% of the total energy in the transitional region. Furthermore, the corresponding eigenfunctions accurately capture the large-scale coherent structures, namely, the vortex rings in the laminar region and a large-scale strong helical motion in the turbulent region. In the near-field region, the dominant vortex-shedding frequency obtained from Fourier analysis agrees well with experimental data of Cetegen. Low-order POD analysis in the transitional and turbulent regions reveals the persistence of the vortex shedding frequencies in the downstream flow that cannot be detected from Fourier analysis of raw LES data.