TY - JOUR

T1 - Stability of a rotating liquid heated from below with respect to periodic perturbations

AU - Shliomis, M. I.

PY - 1962/1/1

Y1 - 1962/1/1

N2 - The coupling of a system of ordinary equations for convection [1] leads to the conclusion that a perturbation occurring due to the heating of a liquid from below always varies monotonically with time [2]. Presence of magnetic field (in a conducting liquid) or of a rotation render the equations of motion uncoupled and therefore the stability of an initially balanced system and the nature of perturbations causing its collapse should be investigated separately. Chandrasekhar has considered the effect of magnetic field [3] and of rotation [4,5] on the convection in a horizontal plane layer. The consideration of a layer of infinite length which ordinarily admits the analysis of a phenomenon in a "pure form" in this particular case would only obscure the physical nature of the problem. In a finite strip, however, (all dimensions of which are of the same order) these basically new effects which are occasioned by the magnetic field or by rotation, are discernible in a distinct fashion. Below, using a simple example, one considers the effect of rotation on the stability of a liquid heated from below which occupies a closed space whose linear dimensions are of the same order in all directions. As will be shown in Section 6, the magnetic field in a conducting liquid is equivalent to the rotation of liquid with regard to all aspects concerning its stability.

AB - The coupling of a system of ordinary equations for convection [1] leads to the conclusion that a perturbation occurring due to the heating of a liquid from below always varies monotonically with time [2]. Presence of magnetic field (in a conducting liquid) or of a rotation render the equations of motion uncoupled and therefore the stability of an initially balanced system and the nature of perturbations causing its collapse should be investigated separately. Chandrasekhar has considered the effect of magnetic field [3] and of rotation [4,5] on the convection in a horizontal plane layer. The consideration of a layer of infinite length which ordinarily admits the analysis of a phenomenon in a "pure form" in this particular case would only obscure the physical nature of the problem. In a finite strip, however, (all dimensions of which are of the same order) these basically new effects which are occasioned by the magnetic field or by rotation, are discernible in a distinct fashion. Below, using a simple example, one considers the effect of rotation on the stability of a liquid heated from below which occupies a closed space whose linear dimensions are of the same order in all directions. As will be shown in Section 6, the magnetic field in a conducting liquid is equivalent to the rotation of liquid with regard to all aspects concerning its stability.

UR - http://www.scopus.com/inward/record.url?scp=49749205315&partnerID=8YFLogxK

U2 - 10.1016/0021-8928(62)90068-0

DO - 10.1016/0021-8928(62)90068-0

M3 - Article

AN - SCOPUS:49749205315

VL - 26

SP - 384

EP - 391

JO - Journal of Applied Mathematics and Mechanics

JF - Journal of Applied Mathematics and Mechanics

SN - 0021-8928

IS - 2

ER -