Upper Bounds for the Complex Growth Rate of a Disturbance in Ferrothermohaline Convection
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...
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| Format: | Article |
| Language: | English |
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Sciendo
2022-03-01
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| Series: | Studia Geotechnica et Mechanica |
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| Online Access: | https://doi.org/10.2478/sgem-2022-0005 |
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| author | Ram Kaka Prakash Jyoti Kumari Kultaran Kumar Pankaj |
| author_facet | Ram Kaka Prakash Jyoti Kumari Kultaran Kumar Pankaj |
| author_sort | Ram Kaka |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T15:45:26Z |
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| institution | Directory Open Access Journal |
| issn | 2083-831X |
| language | English |
| last_indexed | 2024-04-13T15:45:26Z |
| publishDate | 2022-03-01 |
| publisher | Sciendo |
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| spelling | doaj.art-7fbfd78119a4405db67ac68cf0f58da72022-12-22T02:41:00ZengSciendoStudia Geotechnica et Mechanica2083-831X2022-03-0144211412210.2478/sgem-2022-0005Upper Bounds for the Complex Growth Rate of a Disturbance in Ferrothermohaline ConvectionRam Kaka0Prakash Jyoti1Kumari Kultaran2Kumar Pankaj3Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla171005, IndiaDepartment of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla171005, IndiaDepartment of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla171005, IndiaPankaj Kumar, Department of Mathematics, Central University of Himachal Pradesh, Dharamshala, District Kangra-176215, IndiaIt 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.https://doi.org/10.2478/sgem-2022-0005linear stabilityferrofluidoscillatory motionsferrothermohaline convection |
| spellingShingle | Ram Kaka Prakash Jyoti Kumari Kultaran Kumar Pankaj Upper Bounds for the Complex Growth Rate of a Disturbance in Ferrothermohaline Convection Studia Geotechnica et Mechanica linear stability ferrofluid oscillatory motions ferrothermohaline convection |
| title | Upper Bounds for the Complex Growth Rate of a Disturbance in Ferrothermohaline Convection |
| title_full | Upper Bounds for the Complex Growth Rate of a Disturbance in Ferrothermohaline Convection |
| title_fullStr | Upper Bounds for the Complex Growth Rate of a Disturbance in Ferrothermohaline Convection |
| title_full_unstemmed | Upper Bounds for the Complex Growth Rate of a Disturbance in Ferrothermohaline Convection |
| title_short | Upper Bounds for the Complex Growth Rate of a Disturbance in Ferrothermohaline Convection |
| title_sort | upper bounds for the complex growth rate of a disturbance in ferrothermohaline convection |
| topic | linear stability ferrofluid oscillatory motions ferrothermohaline convection |
| url | https://doi.org/10.2478/sgem-2022-0005 |
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