The behaviour of a flow from an elevated source into a less dense fluid: The behaviour of a flow from an elevated source into a less dense fluid - Shraida, Shaymaa M.; Hocking, Graeme C. (Journal of engineering mathematics, 2025)
The viscous Boussinesq equations are used to simulate the unsteady flow from an elevated source of a plume of heavier fluid into a lighter fluid. The solution is obtained with a spectral method. The source is located at some height above the bottom of a vertically confined layer and the flow is two dimensional. Results indicate that the small, initially circular bubble of heavier fluid expands until the top reaches some height above the source, after which it levels off and starts to flow downwards in a vertical plume before spreading horizontally. We discuss the results for different values of Reynolds number, flow rate, and density differential. It is found that there are several different plume types, the behaviours of which depend on the flow rate. At low flows, the plume forms an inverted mushroom shape, some parts of which may separate as it falls downward. At moderate flow rates, the inverted mushroom plume remains connected until it reaches the base, after which it spreads horizontally as a gravity current. Finally, at large flow rates, the central blob expands outward until it hits the bottom, after which it spreads horizontally. When the Reynolds number is small and viscosity is relatively high, the interface between the expanding region and the ambient fluid is very stable and exhibits few deviations and very little mixing, but as the Reynolds number increases, spirals begin to form around the edges, thus, enhancing the mixing.