Validation of A One Dimensional Model for Volumetrically Forced Jets Using Large Eddy Simulations

Volumetrically forced jets are often considered as idealized models for atmospheric clouds. In this work, we use an existing energy-consistent approach for dynamically expressing the entrainment rate constant, $\alpha$, in terms of radial integrals of the velocity field, Reynolds stress field and bouyancy field. We use a mixing length model to relate the Reynolds stress to the velocity gradient. We then construct a one-dimensional (1-D) model for evolving volumetrically forced jets, in which we assume that the radial variation of the axial velocity has a Gaussian shape. The imposed external forcing, with a Gaussian radial profile, is applied within a certain height range, far from the jet inlet. Large Eddy Simulations of forced jets are conducted to validate this 1-D model. We find that the axial velocity deviates significantly from a Gaussian profile if the forcing is confined to a radius that is much smaller than the jet radius; this in turn can lead to discrepancy between the LES and the 1-D model. On the other hand, if the forcing radius is comparable to the jet radius, then the 1-D model agrees well with the LES, even at high forcing Richardson number. The bouyancy flux within the forcing zone is predicted well by the 1-D model for all the cases.