Linear Stability Analysis of Rotating Baroclinic Annulus with Localized Heating Using Floquet-BiGlobal Methods
Researchers have developed a Floquet-BiGlobal stability analysis method to study convective flows in a rotating fluid annulus with localized peripheral heating and uniform inner-wall cooling. Classical stability methods break down in this configuration because the localized heating creates a non-axisymmetric base state, requiring a more complex mathematical treatment. The work advances understanding of baroclinic instability mechanisms relevant to geophysical and engineering fluid dynamics.
A new study submitted to the InnoVEST 2026 conference proceedings presents a rigorous linear stability framework for analyzing convective flows in a rotating baroclinic annulus subjected to localized heating at the outer bottom periphery and uniform cooling at the inner cylindrical wall. Because the localized forcing breaks axial symmetry, conventional normal-mode decomposition is invalid, prompting the authors to combine Floquet-Bloch theory in the azimuthal direction with a BiGlobal eigenvalue formulation in the meridional plane. The non-axisymmetric base state is expanded in azimuthal Fourier harmonics, and perturbations are expressed as quasi-periodic Bloch modes that couple all azimuthal wavenumbers through base-state harmonics. The analysis derives full linearized perturbation equations, a BiGlobal block-operator structure, pressure elimination, solenoidal projection, and a modal energy budget. Key findings indicate that instability is driven by cross-modal baroclinic energy release and shear production — mechanisms that are absent in classical axisymmetric theory. The paper is currently under review and has been revised once since its initial submission in early June 2026.
What's missing
The preprint is under review and has not yet been peer-reviewed or published; numerical validation, experimental comparison, and convergence tests for the BiGlobal eigenvalue solver are not described in the abstract. The scope of parameter regimes explored (e.g., rotation rates, heating intensities, fluid properties) and any quantitative stability thresholds are not reported. Open questions include whether the framework extends to nonlinear regimes and how results compare with existing laboratory annulus experiments.
What different sources said
- arXiv physicsCenter
Linear Stability Analysis of convective flows in Rotating Baroclinic Annulus with Localized Peripheral Heating: A Floquet-BiGlobal Approach
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