Maximum Penetration Height and Intrusion Speed of Weak Symmetric Plane Fountains in Linearly Stratified Fluids

Abstract

The flow behavior of weak symmetric plane fountains in linearly stratified fluids is studied numerically with three-dimensional simulations over a range of the Froude (Fr), Reynolds (Re), and stratification numbers (s). The two main parameters describing the fountain characterization are the dimensionless maximum fountain penetration height (zm) and intrusion velocity (uint), which differ significantly at different flow development stages. It was found that the stratification stabilizes the symmetry of the weak fountains, which makes the fountain become asymmetric at a larger Fr value, and zm at the fully developed stage continues to increase as a result of the intrusion, which continually changes the ambient fluid stratification features, thus the buoyant force. The evolution of intrusion experiences three distinct stages. Both Fr and s have effects on zm and uint, with the effect of Fr usually larger than that of s. The overall impacts of Fr and s can be quantified in terms of Frasb, with a and b varying for different parameters. With numerical results, empirical correlations are produced in terms of Frasb for each relevant parameter, which generally predict the results very well.