On the Upper Bound for Growth Rate of Hydromagnetic Swirling- flows

CHANDRASHEKHAR GANGIPELLI, Ganesh V

Abstract


We consider stability of inviscid, incompressible, hydromagnetic swirling flows. We obtained supremum for the growth rates. Growth rate has been illustrated with three standard examples. Growth rate depends up on vorticity function, velocity profile and wave number. Furthermore, we obtained upper and lower bound for neutral phase speed. Also, we derived an instability regions depending on Rayleigh-Synge-Michael discriminant, velocity profile and radii.

Keywords


Swirling flow; Co-axial Cylinders; Incompressible; Inviscid

Full Text:

PDF

References


G. K. Batchelor and A. E. Gill, "On the

hydrodynamic and hydromagnetic stability of

swirling flows," J. Fluid. Mech., vol. 14,

pp. 529-551, 1962.

S. Chandrasekhar, "Hydrodynamic and

hydromagnetic instability", Clarendon Oxford,

G. Chandrashekhar and A. Venkatalaxmi, "Note

on the Circular Rayleigh Problem", Nonlinear

Dynamics and Applications, Springer

Proceedings in Complexity,

pp.366-376, 2022,

https://doi.org/10.1007/978-3-030-99792- 2_31.

G. Chandrashekhar and A. Venkatalaxmi, "On the

improved instability region for the circular Rayleigh

problem of Hydrodynamic stability", J. Appl. Math.

& Informatics, Vol. 41, No. 1 pp. 155-165, 2023,

https://doi.org/10.14317/jami.2023.155 .

Chandrashekhar Gangipelli, Venkatalaxmi

Akavaram,

and Ganesh Venkataraman, "On the Condition for

Wave Number in the Stability of Hydromagnetic

Swirling- flows", Published by AIP Publishing, Vol.

, No. 1, 030001-1–030001-8, 1-9, 2023,

https://doi.org/10.1063/5 .

M. S. A. Iype and M. Subbiah, "On the

hydrodynamic and hydromagnetic stability of

inviscid flows between coaxial cylinders",

Inter. J. Fluid. Mech. Res., vol. 37, 146, pp. 1-15,

P. Pavithra and M. Subbiah, "Note on instability

regions in the circular Raleigh problem of

hydrodynamic stability", Proc. Natl. Aca. Sci.,

Section A:Physical Sciences, vol. 91, pp. 49–54,

S. Prakash and M. Subbiah, "Bounds on complex

eigen values in a hydromagnetic stability problem",

The Journal of Analysis, vol. 29, pp.1137–

, 2021,

https://doi.org/10.1007/s41478-020-00301-6.

S. Parthi and G. Nath, "Stability of

Magnetohydrodynamic Stratified Shear Flows",

IL NUOVO CIMENTO, Giugno, Vol. 13, 765-778,

Y. Sasakura, "Semi-Ellipse Theorem for the

Heterogeneous Swirling Flow in an Azimuthal

Magnetic Field with Respect to Axisymmetric

Disturbances", J. Phys. Soc. Jpn. 53, 2012-2017,

V. Srinivasan, P. Kandaswamy and L. Debnath,

"Hydromagnetic stability of rotating stratified

compressible fluid flows", Zeitschrift fur Angewandte

Mathematik und Physik (ZAMP), Vol. 35 728-738,




DOI: http://dx.doi.org/10.21533/scjournal.v13i1.302

Refbacks

  • There are currently no refbacks.


Copyright (c) 2024 CHANDRASHEKHAR GANGIPELLI, Ganesh V

ISSN 2233 -1859

Digital Object Identifier DOI: 10.21533/scjournal

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License