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Concentrated beams in differentially rotating and stratified fluids and their reflection at a turning point.

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Title: Concentrated beams in differentially rotating and stratified fluids and their reflection at a turning point.
Authors: Le Dizès, Stéphane1 stephane.ledizes@univ-amu.fr, Favier, Benjamin1
Source: Journal of Fluid Mechanics. 3/10/2026, Vol. 1030, p1-24. 24p.
Subjects: Gravity waves, Wave packets, Computer simulation, Rotating fluid, Fluids, Buoyancy-driven flow, Asymptotic analysis
Abstract: Concentrated wave beams are analysed both theoretically and numerically in a general rotating and stratified axisymmetric medium, where both the rotation rate and the Brunt-Väisälä frequency vary with position. The fluid is assumed to be incompressible, weakly diffusive and weakly viscous. The analysis is conducted within the Boussinesq approximation and a linear framework, with a prescribed frequency. An asymptotic solution is derived in the limit of weak viscosity and diffusivity, describing a harmonic beam of inertia gravity waves localised around a characteristic (or ray path), similar to those generated by boundary singularities or critical points. This solution is shown to break down when the characteristic reaches a turning point which corresponds to the transition from oscillatory to evanescent behaviour. A local asymptotic analysis near the turning point demonstrates that the wave beam reflects, preserving its transverse structure while acquiring a phase shift of ±π/2. These theoretical predictions are validated through numerical simulations, which show that the wave beam structure, both near and far from the turning point, is accurately reproduced. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:Concentrated wave beams are analysed both theoretically and numerically in a general rotating and stratified axisymmetric medium, where both the rotation rate and the Brunt-Väisälä frequency vary with position. The fluid is assumed to be incompressible, weakly diffusive and weakly viscous. The analysis is conducted within the Boussinesq approximation and a linear framework, with a prescribed frequency. An asymptotic solution is derived in the limit of weak viscosity and diffusivity, describing a harmonic beam of inertia gravity waves localised around a characteristic (or ray path), similar to those generated by boundary singularities or critical points. This solution is shown to break down when the characteristic reaches a turning point which corresponds to the transition from oscillatory to evanescent behaviour. A local asymptotic analysis near the turning point demonstrates that the wave beam reflects, preserving its transverse structure while acquiring a phase shift of ±π/2. These theoretical predictions are validated through numerical simulations, which show that the wave beam structure, both near and far from the turning point, is accurately reproduced. [ABSTRACT FROM AUTHOR]
ISSN:00221120
DOI:10.1017/jfm.2026.11219