Abstract
We may think of this problem as the flow in a gear box. We get this flow by perturbing Couette flow between two concentric rotating cylinders, putting a wave on the inner cylinder. As in the previous examples, the vorticity equation changes type from elliptic to hyperbolic whenever the velocity at some point in the domain exceeds the speed of shear waves into rest. There are two cases: the inner cylinder rotates and the outer cylinder rotates. The isovorticity lines even in weakly subcritical flow lie in directions swept out by characteristics. This direction is uniquely determined in the regions where the two families lie in the same direction. In the strongly supercritical case, high Mach numbers, one finds that hyperbolicity dominates the flow field. The isovorticity lines are oriented along forward facing characteristics and the vorticity of the perturbed motion is then swept out along these characteristics.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This chapter is based on the thesis of Riccius [1989b].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Joseph, D.D. (1990). Hyperbolicity and Change of Type in the Flow Between Rotating Cylinders When the Inner Cylinder Is Corrugated. In: Fluid Dynamics of Viscoelastic Liquids. Applied Mathematical Sciences, vol 84. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4462-2_14
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4462-2_14
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8785-8
Online ISBN: 978-1-4612-4462-2
eBook Packages: Springer Book Archive