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

Shaymaa M. Shraida; Graeme C. Hocking

doi:10.1007/s10665-025-10429-8

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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

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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

Shaymaa M. Shraida and Graeme C. Hocking

Journal of engineering mathematics, Vol.150(1), 21

2025

DOI: https://doi.org/10.1007/s10665-025-10429-8

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Abstract

Applications of Mathematics

Article

Computational Mathematics and Numerical Analysis

Mathematical and Computational Engineering

Mathematical Modeling and Industrial Mathematics

Mathematics

Mathematics and Statistics

Theoretical and Applied Mechanics

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.

Details

Title: The behaviour of a flow from an elevated source into a less dense fluid
Authors/Creators: Shaymaa M. Shraida - University of Baghdad
Graeme C. Hocking - Murdoch University, Centre for Animal Production and Health
Publication Details: Journal of engineering mathematics, Vol.150(1), 21
Publisher: Springer Netherlands
Number of pages: 19
Grant note: PhD scholarship to Australia / Iraqi Ministry of Education Murdoch University
Identifiers: 991005743944207891
Murdoch Affiliation: School of Mathematics, Statistics, Chemistry and Physics
Language: English
Resource Type: Journal article

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Collaboration types: Domestic collaboration; International collaboration
Citation topics: 7 Engineering & Materials Science; 7.177 Combustion; 7.177.1573 Fire Dynamics
Web Of Science research areas: Engineering, Multidisciplinary; Mathematics, Interdisciplinary Applications
ESI research areas: Engineering