Description
Geometrical optics stability analysis has proven effective in deriving analytical instability criteria for 3D flows in ideal hydrodynamics and magnetohydrodynamics, for both compressible and incompressible fluids. This method models perturbations as high-frequency wavelets evolving along fluid trajectories. Detecting local instabilities reduces to solving ODEs for the wave vector and wavelet amplitude, with coefficients derived from the background flow. While viscosity and diffusivity were traditionally seen as stabilizing, recent extensions of this framework reveal their destabilizing potential in visco-diffusive and multi-diffusive flows. Encouraged by these findings, this talk examines the visco-thermodiffusive McIntyre instability of spiral Poiseuille flow with a radial temperature gradient (SPFRT) using the generalized geometrical optics approach. SPFRT combines circular Couette flow and annular Poiseuille flow driven by an axial pressure gradient, while the temperature gradient induces centrifugal buoyancy. Neglecting vertical Archimedean buoyancy simplifies the derivation of analytical thresholds for both oscillatory and monotonic McIntyre instability. A key advancement in this study lies in the relationship between parametric optimization and the construction of envelopes of curve families. This enables the derivation of universal stability criteria by computing the envelopes of neutral stability curves, parameterized by the axial (or azimuthal) wavenumber. Treating the equations for neutral stability as polynomials in the wavenumber, we identify their discriminant set, which includes the equation for the envelope and provides explicit instability criteria. These new analytical criteria apply across a wide range of Prandtl numbers, extending beyond the reach of numerical methods in many critical physical and industrial applications.| Period | 23 Jun 2025 → 26 Jun 2025 |
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| Event title | BMC-BAMC 2025: British Mathematical Colloquium and British Applied Mathematics Colloquium |
| Event type | Conference |
| Location | Exeter, United KingdomShow on map |
| Degree of Recognition | National |