Die Instabilität der Strömung zwischen zwei rotierenden Zylindern gegenüber Taylor-Wirbeln für beliebige Spaltbreiten

Summary

An investigation is made of the instability of stationary flow between two rotating cylinders for any gap distance. Previous work on this problem, viz. the Taylor theory, has been done with the restriction of small gaps. Moreover, in contrast to the recent work ofS. Chandrasekhar [2], who has also analysed this problem, the method used is independent of the basic flow and is therefore valid for all flows between two coaxial cylinders. In fact, it can even be used for the analysis of the flow in a curved channel.

The major item of physical interst is the critical Reynoldsnumber, i. e. the value of the Reynoldsnumber where small disturbances are amplified for the first time. The value of this parameter is determined by the smallest positive eigen value of the boundary value problem. An existence proof is made for this eigenvalue for any wavenumber and for all possible cases of cylindrical flow, with the exception of the case where the cylinders rotate in opposite directions. The results are depicted in a convenient form, where the critical Reynoldsnumber is the dependent variable and the gap distance and the angular velocity ratio of the two cylinders are the independent variables respectively.

A comparison with experiment is made for the case where the ratio of the two radii is 2: 1 and the outer cylinder is at rest. The agreement with the theory is good; the noticeable error being approximately 1%.