Convection on a non-uniformly heated, rotating plane

Abstract

This investigation is concerned with the convective motions in a shallow layer of silicone oil on a plane, circular copper plate which is heated at the rim and cooled at the centre and at the same time rotated around a vertical axis. The oil is in touch with a glass lid, which is cooled uniformly. With sufficient heating axially symmetric concentric rings develop. The details of the motion can be described as a superposition of a circulation due to the horizontal temperature gradient and a circulation of opposite sense due to the centrifugal force, with the motions due to the vertical instability. There seems to be a conversion into rolls whose axes point radially, if the centrifugal circulation becomes too strong.

The effect of centrifugal convection on the stability of a rotating fluid heated from below

“…If these disturbance velocities are taken to be an adequate indication of what would be observed in a rotating cylinder at or slightly above the critical Rayleigh number, the instability should set in at the outer edge of the container. This seems to be in agreement with the observations of Koschmieder [12,13,14]. § 6.…”

“…Furthermore, in making the Galerkin expansion below it is assumed that the disturbance fields are also axisymmetric. This assumption ean be justified by noting that the difference between critical Rayleigh numbers for various azimuthal waves numbers decreases as the Taylor number is increased [8] and also by noting Koschmieder's experimental observation that at the onset of instability in a cylindrical container the initial disturbances take the form of axisymmetric roll cells [12,13,14]. It is assumed that the fluid is incompressible except in the gravitational and centrifugal terms where it is…”

A Numerical Study of Three-Dimensional Benard Convection

“…The three-dimensional convection in the initial developing stage changes into two-dimensional rolls in the later stage. Such a transformation from a three-dimensional cell into a two-dimensional roll was observed in experiments by Koschmieder (1966) and Krishnamurti (1968). Krishnamurti (1970) have also found the final steady rolls at rather low Rayleigh number regardless of Prandtl number in her laboratory experiments.…”

“…There is some information from experimental studies. Koschmieder (1966) found a system of concentric round rolls with round wall and rectangular patterns, which transformed into rolls and combinations of rolls and rectangular cells with a rectangular frame. Krishnamurti (1970Krishnamurti ( , 1973 showed that steady rolls are realized just above the critical Rayleigh number Rc and the three-dimensional cellular motions are obtained at higher Rayleigh numbers for several Prandtl numbers from 0.02 to 104.…”

Generation of continental rifts, basins, and swells by lithosphere instabilities

“…Different planforms are generated depending on the thermal boundary conditions at the side walls. For conducting walls with horizontal temperature gradients in the radial direction, convection develops as a set of concentric circular upwellings and downwellings [Koschmieder, 1966]. For insulating boundary conditions, Croquette et al [1983] found that disordered planforms prevail.…”