Traveling disturbances in rotating-disk flow

Abstract

The stability curves for traveling disturbances in rotating-disk flow are computed using the sixth-order system of incompressible linear stability equations. It is found that the neutral curve has two minima for disturbances with positive frequencies as found earlier by Malik (1986) for stationary disturbances. The upper branch minimum occurs at ω=−2.9, R=283.6 while the lower branch minimum occurs at ω=7.9, R=64.46 where R is the Reynolds number. There exists a critical angle of approximately −35.34° (which is about 15° from the direction of maximum wall shear) below which all the waves are linearly damped. The results also show that at high frequencies the wave number for lower branch neutral disturbances varies with Reynolds number like R ⁻¹ while for stationary waves it behaves like R ^−1/2. The eigenfunction distribution suggests that the structure of the nonstationary high-frequency lower branch neutral disturbances are different from the structure of the viscous stationary disturbances.