European Journal of Applied Mathematics· 2026Q2
On fire whirls and Popov’s equation
- 0citations
- Q2SCImago
- 2026year
Short summary
A new linear second-order elliptic PDE for stream function models fire whirls, incorporating thermal effects that prevent variable separation and yielding first-order PDEs via approximations.
AI-generated from the title and abstract; the full text is not read.
Key points
- A new linear second-order elliptic PDE is proposed for modeling fire whirls with thermal effects.
- Thermal effects prevent the standard variable separation method for solving the PDE.
- Large parameter A allows for parabolic approximations, similar to high-frequency diffraction problems.
- Two methods are developed to solve the PDE, both resulting in first-order PDEs.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract A fire whirl is a swirling flow with a burning core. A very simple model of a fire whirl is used, consisting of a linear second-order elliptic partial differential equation (PDE) for a stream function, extending established models for axisymmetric swirling flow of an incompressible inviscid fluid. The introduction of thermal effects means that the PDE cannot be solved by separating variables. The PDE contains a dimensionless parameter upper A A $A$ . When upper A A $A$ is large, parabolic approximations can be obtained, in much the same way that high-frequency approximations for diffraction problems are derived. The new PDE has similarities with Popov’s equation, which arises when a whispering gallery wave encounters a boundary inflection. To solve it, two approaches are developed, both leading to first-order PDEs. The simpler assumes that a second parameter in the PDE is also large. If this assumption is not made, progress can be made by using a Laplace transform with respect to a radial coordinate, but the result is seen to be much more complicated.
The authors' abstract, as published at the source. European Journal of Applied Mathematics, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Numerical Analysis
Numerical AnalysisMathematics