The effect of the Earth’s rotation on the transient amplification of disturbances in pipe flow

In pipe flow, for large Reynolds numbers, Draad and Nieuwstadt [J. Fluid Mech. 361, 297 (1998)] showed that the small Coriolis force due to the Earth’s rotation may affect the mean flow profile of liquids substantially. In this paper, the development of small disturbances superimposed on a laminar mean flow affected by the Coriolis force is investigated analytically. The investigation is focused on the time development and the transient growth of streamwise-independent disturbances since they are the most amplified disturbances without the Coriolis effect included. The results show that the modification of the parabolic mean flow caused by the Coriolis force significantly affects the transient disturbance amplification when the Reynolds number (R) is high. For example, with $R=9000$ and the Ekman number Ek=5.23, due to the Coriolis effect, the peak value of the transient disturbance amplification becomes about two-thirds of the peak value obtained in the case where the mean flow is unaffected by the Coriolis force. When the Reynolds number is decreased, the reduction of the transient growth becomes smaller.