## 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

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 language | English |
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Title of host publication | Book of abstracts |

Subtitle of host publication | The 65th British Applied Mathematics Colloquium |

Place of Publication | Newcastle Upon Tyne |

Publisher | Newcastle University |

Pages | 96-96 |

Number of pages | 1 |

Publication status | Published - 9 Apr 2024 |

Event | British Applied Mathematics Colloquium - Newcastle, United Kingdom Duration: 9 Apr 2024 → 11 Apr 2024 https://conferences.ncl.ac.uk/bamc2024/ |

### Conference

Conference | British Applied Mathematics Colloquium |
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Country/Territory | United Kingdom |

City | Newcastle |

Period | 9/04/24 → 11/04/24 |

Internet address |

## Keywords

- Rotating flows
- magnetohydrodynamcs (MHD)
- stratified flows
- lenticular vortices
- thermal gradient
- instabilities
- WKB