Instabilities in flows of viscous, heatconducting media
Abstract
Some basic relations between different instabilities of fluid dynamics are considered, taking into account theoretical and experimental investigations. A state of flow is regarded as unstable if a slight disturbance has an effect which leads to an unlimited temporal increase of the amplitude of the flow parameters. The limiting case at which such a temporal increase does not yet occur is called neutral state. The various possible forms of flow in the case of the Benard convection are examined. The instable density distribution in a vertical direction for the Benard convection corresponds to the unstable centrifugal force distribution in a radial direction in the case of the Taylor instability. A complete analogy between the Benard convection and Taylor vortices is obtained on the basis of the linear theory. Attention is given to the Benard convection in the case of an inhomogeneous heating of the base area, Taylor instabilities between two rotating spheres, and aspects of unsteady cellular convection.
 Publication:

Zeitschrift fur Flugwissenschaften und Weltraumforschung
 Pub Date:
 June 1978
 Bibcode:
 1978ZFlWe...2..143Z
 Keywords:

 Benard Cells;
 Conductive Heat Transfer;
 Convection Currents;
 Rotating Spheres;
 Taylor Instability;
 Viscous Flow;
 Angular Velocity;
 Atmospheric Circulation;
 Boundary Value Problems;
 Differential Interferometry;
 Flow Distribution;
 Flow Stability;
 NavierStokes Equation;
 Prandtl Number;
 Fluid Mechanics and Heat Transfer