Upper Bounds for the Complex Growth Rate of a Disturbance in Ferrothermohaline Convection

Kaka Ram; Jyoti Prakash; Kultaran Kumari; Pankaj Kumar

doi:10.2478/sgem-2022-0005

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Upper Bounds for the Complex Growth Rate of a Disturbance in Ferrothermohaline Convection

Studia Geotechnica et Mechanica

Volume 44 (2022): Issue 2 (June 2022)

By: Kaka Ram, Jyoti Prakash, Kultaran Kumari and Pankaj Kumar

Open Access

|Mar 2022

Abstract

It is proved analytically that the complex growth rate σ= σ_r+iσ_i (σ_r and σ_i are the real and imaginary parts of σ, respectively) of an arbitrary oscillatory motion of neutral or growing amplitude in ferrothermohaline convection in a ferrofluid layer for the case of free boundaries is located inside a semicircle in the right half of the σ_rσ_i-plane, whose center is at the origin and $radius = \sqrt{\frac{R_{s} [1 - M_{1}^{'} (1 - \frac{1}{M_{5}})]}{P_{r}^{'}}},$ {\rm{radius}}\, = \,\sqrt {{{{R_s}\left[{1 - M_1^{'}\left({1 - {1 \over {{M_5}}}} \right)} \right]} \over {P_r^{'}}}}, where R_s is the concentration Rayleigh number, P_r^′ is the solutal Prandtl number, M₁^′ is the ratio of magnetic flux due to concentration fluctuation to the gravitational force, and M₅ is the ratio of concentration effect on magnetic field to pyromagnetic coefficient. Further, bounds for the case of rigid boundaries are also derived separately.

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Articles in this issue

DOI: https://doi.org/10.2478/sgem-2022-0005 | Journal eISSN: 2083-831X | Journal ISSN: 0137-6365

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Language: English

Page range: 114 - 122

Submitted on: Jun 13, 2020

Accepted on: Dec 29, 2021

Published on: Mar 10, 2022

Published by: Wroclaw University of Science and Technology

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

Linear stability,

Ferrofluid,

Oscillatory motions,

Ferrothermohaline convection

Related subjects:

Physics,

Mechanics and fluid dynamics

© 2022 Kaka Ram, Jyoti Prakash, Kultaran Kumari, Pankaj Kumar, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 44 (2022): Issue 2 (June 2022)