Turbulence, entrainment and low-order description of a transitional variable-density jet

Geophysical flows occur over a large range of scales, with Reynolds numbers and Richardson numbers varying over several orders of magnitude. For this study, jets of different densities were ejected vertically into a large ambient region, considering conditions relevant to some geophysical phenomena. Using particle image velocimetry, the velocity fields were measured for three different gases exhausting into air – specifically helium, air and argon. Measurements focused on both the jet core and the entrained ambient. Experiments considered relatively low Reynolds numbers from approximately 1500 to 10 000 with Richardson numbers near 0.001 in magnitude. These included a variety of flow responses, notably a nearly laminar jet, turbulent jets and a transitioning jet in between. Several features were studied, including the jet development, the local entrainment ratio, the turbulent Reynolds stresses and the eddy strength. Compared to a fully turbulent jet, the transitioning jet showed up to 50 % higher local entrainment and more significant turbulent fluctuations. For this condition, the eddies were non-axisymmetric and larger than the exit radius. For turbulent jets, the eddies were initially smaller and axisymmetric while growing with the shear layer. At lower turbulent Reynolds number, the turbulent stresses were more than 50 % higher than at higher turbulent Reynolds number. In either case, the low-density jet developed faster than a comparable non-buoyant jet. Quadrant analysis and proper orthogonal decomposition were also utilized for insight into the entrainment of the jet, as well as to assess the energy distribution with respect to the number of eigenmodes. Reynolds shear stresses were dominant in Q1 and Q3 and exhibited negligible contributions from the remaining two quadrants. Both analysis techniques showed that the development of stresses downstream was dependent on the Reynolds number while the spanwise location of the stresses depended on the Richardson number.