Vorticity-based modeling of stratified flows
Within the present investigation, the broad span of applications of the vorticity-based modeling concept for stratified flows, based on the simultaneous use of horizontal and vertical momenta equations in the form of vorticity balance principle, is studied in detail. Towards this objective, this approach, originally introduced by Borden and Meiburg [Z. Borden and E. Meiburg, Phys. Fluids 25 (10), 101301 (2013); Z. Borden and E. Meiburg, J. Fluid Mech. 726, R1 (2013)], for gravity currents propagating into unstratified ambients and internal bores traveling at the interface of two-layer fluids, respectively, is extended to various well known stratified flow problems, in the following. These flows normally involve several fronts which can be analyzed according to the quasisteady conservation laws of mass and momentum by appropriate shift in the reference frame, or possibly unsteady sections for which the flow cannot be rendered quasisteady by any finite number of changes in the reference frames. The analyses of various flow components are then superimposed and matched to obtain the whole flow field. It is also demonstrated that under certain conditions the propagation of gravity currents (or intrusions) can lead to the formation of interfacial perturbations in the form of rarefaction waves or internal bores, which are a source of unsteadiness, and can substantially impact the flow dynamics as well as its energy budget.
Enforcing the conservation laws for horizontal and vertical momenta concurrently, enables us to avoid employing energy-based closure assumptions invoked by previous peer models. Consequently, the assessment of flow energetics becomes plausible, which can be utilized to investigate the validity of the energy-related arguments made by other authors. Furthermore, the predictions of the current study obtained by detailed parametric studies are compared to the results of our two-dimensional direct numerical simulations as well as the theoretical and experimental findings of earlier investigations, where very good agreement is observed with regard to all flow properties.