| Abstract: | The stability of the steady self-similar flow in the boundary layer on a rotating disk of infinite radius with corotation of the surrounding fluid is analyzed by the normal mode method. The spectral problem for infinitesimal three-dimensional disturbances is solved by a collocation method with expansion of the amplitude functions in Chebyshev polynomials. It is established that for all values of the parameter   0, equal to the ratio of the angular velocities of the fluid and the disk, the lower critical Reynolds number is determined byA-type, waves, whose development is governed by the  parallel instability mechanism typical of an Ekman layer. TheB-type instability, associated with the presence of an inflection point on the velocity profile, disappears when  4. The neutral surfaces are calculated for Karman flow (=0) and Bödewadt flow (  ). It is found that in Karman flowA-type waves may grow at values of the Reynolds number several times smaller than the critical Reynolds number for spiral vortices. The results of the analysis are compared with the available experimental data.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 69–77, September–October, 1992. |
