<abstract xmlns="http://www.w3.org/1999/xhtml">

It is proved analytically that the complex growth rate <italic>σ</italic>= <italic>σr</italic>+<italic>iσi</italic> (<italic>σr</italic> and <italic>σi</italic> are the real and imaginary parts of <italic>σ</italic>, 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 <italic>σrσi</italic>-plane, whose center is at the origin and 
<disp-formula id="j_sgem-2022-0005_ueq_001">
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_sgem-2022-0005_ueq_001.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mtext>radius</mtext><mo> </mo><mo>=</mo><mo> </mo><msqrt><mrow><mfrac><mrow><msub><mi>R</mi><mi>s</mi></msub><mrow><mo>[</mo><mrow><mn>1</mn><mo>−</mo><msubsup><mi>M</mi><mn>1</mn><mo>′</mo></msubsup><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><mfrac><mn>1</mn><mrow><msub><mi>M</mi><mn>5</mn></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mo>]</mo></mrow></mrow><mrow><msubsup><mi>P</mi><mi>r</mi><mo>′</mo></msubsup></mrow></mfrac></mrow></msqrt><mo>,</mo></mrow></math>
<tex-math>{\rm{radius}}\, = \,\sqrt {{{{R_s}\left[{1 - M_1^{'}\left({1 - {1 \over {{M_5}}}} \right)} \right]} \over {P_r^{'}}}},</tex-math>
</alternatives>
</disp-formula>
where <italic>Rs</italic> is the concentration Rayleigh number, <italic>Pr</italic>′ is the solutal Prandtl number, <italic>M</italic>1′ is the ratio of magnetic flux due to concentration fluctuation to the gravitational force, and <italic>M</italic>5 is the ratio of concentration effect on magnetic field to pyromagnetic coefficient. Further, bounds for the case of rigid boundaries are also derived separately.
</abstract>

It is proved analytically that the complex growth rate σ= σr+iσi (σr and σi 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 σrσi-plane, whose center is at the origin and 



radius = Rs[1−M1′(1−1M5)]Pr′,
{\rm{radius}}\, = \,\sqrt {{{{R_s}\left[{1 - M_1^{'}\left({1 - {1 \over {{M_5}}}} \right)} \right]} \over {P_r^{'}}}},


where Rs is the concentration Rayleigh number, Pr′ 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.

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

Studia Geotechnica et Mechanica

This work is licensed under the Creative Commons Attribution 4.0 International License.

It is proved analytically that the complex growth rate σ= σr+iσi (σr and σi are the real and imaginary parts of σ, respectively) of an arbitrary oscillatory...

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

Article Category: Original Study

Published Online: Mar 10, 2022

Page range: 114 - 122

Received: Jun 13, 2020

Accepted: Dec 29, 2021

DOI: https://doi.org/10.2478/sgem-2022-0005

Keywords
Linear stability, Ferrofluid, Oscillatory motions, Ferrothermohaline convection

© 2022 Kaka Ram et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

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

Article Category: Original Study

Published Online: Mar 10, 2022

Page range: 114 - 122

Received: Jun 13, 2020

Accepted: Dec 29, 2021

DOI: https://doi.org/10.2478/sgem-2022-0005

KeywordsLinear stability, Ferrofluid, Oscillatory motions, Ferrothermohaline convection

© 2022 Kaka Ram et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

Keywords
Linear stability, Ferrofluid, Oscillatory motions, Ferrothermohaline convection