Unsteady turbulent buoyant plumes
Mark J. Woodhouse, Jeremy C. Phillips, Andrew J. Hogg

TL;DR
This paper develops a hyperbolic integral model for unsteady turbulent buoyant plumes that accounts for non-uniform radial profiles, ensuring well-posedness and capturing transient dynamics after source changes.
Contribution
It introduces a hyperbolic integral model incorporating shape factors for radial profiles, resolving mathematical issues in previous models and analyzing transient plume behavior.
Findings
The model remains well-posed with shape factors different from unity.
A stability threshold for the shape factor is identified.
Transient responses include pulse propagation with distinct regimes.
Abstract
We model the unsteady evolution of turbulent buoyant plumes following temporal changes to the source conditions. The integral model is derived from radial integration of the governing equations expressing the conservation of mass, axial momentum and buoyancy. The non-uniform radial profiles of the axial velocity and density deficit in the plume are explicitly described by shape factors in the integral equations; the commonly-assumed top-hat profiles lead to shape factors equal to unity. The resultant model is hyperbolic when the momentum shape factor, determined from the radial profile of the mean axial velocity, differs from unity. The solutions of the model when source conditions are maintained at constant values retain the form of the well-established steady plume solutions. We demonstrate that the inclusion of a momentum shape factor that differs from unity leads to a well-posed…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
