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

Studia Geotechnica et Mechanica

article

Kaka Ram¹  Jyoti Prakash¹  Kultaran Kumari¹  Pankaj Kumar² 

[1] Department of Mathematics and Statistics, Himachal Pradesh University;Department of Mathematics, Central University of Himachal Pradesh

关键词: Linear stability;    Ferrofluid;    Oscillatory motions;    Ferrothermohaline convection;   

DOI  :  10.2478/sgem-2022-0005

学科分类：社会科学、人文和艺术（综合）

来源: Walter de Gruyter GmbH

【 摘 要 】

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.

【 授权许可】

CC BY