Geometrical optics stability analysis of rotating visco-diffusive flows

Oleg Kirillov*

*Corresponding author for this work

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Abstract

The geometrical optics stability analysis has proved successful in solving problems of ideal hydrodynamics and magnetohydrodynamics related to the stability of 3D flows of both compressible and incompressible fluids [1-3]. The method is based on perturbations of a background flow in a small parameter, representing a short wavelength. These perturbations are localized wave envelopes moving along the trajectories of fluid elements. Thus, detecting instabilities localized near a particular fluid element location, moving with the flow, reduces to solving a system of ODEs for the wave vector and amplitude, along particle paths in the underlying flow, with coefficients depending on the unperturbed velocity field [1-3]. Inclusion of viscosity or diffusivity in the analysis was long-time believed to be only stabilizing. However, starting with the works [4,5] that considered both viscosity and magnetic diffusivity in the geometrical optics analysis of helical magnetorotational instability it became possible to extend the method to visco-diffusive [6] and multiple-diffusive [7] flows for a wide range of Prandtl, Schmidt and magnetic Prandtl numbers. In the talk we review these works and discuss new applications.

References:
[1] K.S. Eckhoff (1981) J. Differ. Equ. 40 (1), 94–115.
[2] A. Lifschitz, E. Hameiri (1991) Phys. Fluids 3, 2644–2651.
[3] S. Friedlander, M.M. Vishik (1991) Phys. Rev. Lett. 66, 2204–2206.
[4] O.N. Kirillov, F. Stefani, Y. Fukumoto (2014) JFM, 760: 591- 633.
[5] O.N. Kirillov (2017) Proc. A, 473(2205): 20170344.
[6] O.N. Kirillov, I. Mutabazi (2017) JFM, 818: 319-343.
[7] J. Labarbe, O.N. Kirillov (2021). Phys. Fluids, 33(10): 104108
Original languageEnglish
Title of host publicationBook of abstracts
Subtitle of host publicationThe 65th British Applied Mathematics Colloquium
Place of PublicationNewcastle Upon Tyne
PublisherNewcastle University
Pages96-96
Number of pages1
Publication statusPublished - 9 Apr 2024
EventBritish Applied Mathematics Colloquium - Newcastle, United Kingdom
Duration: 9 Apr 202411 Apr 2024
https://conferences.ncl.ac.uk/bamc2024/

Conference

ConferenceBritish Applied Mathematics Colloquium
Country/TerritoryUnited Kingdom
CityNewcastle
Period9/04/2411/04/24
Internet address

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