On nonmodal stability of elliptic pipe flow

Abstract

The temporal nonmodal stability of the Poiseuille flow in a pipe of axially uniform elliptic cross section is numerically studied. In particular, it is shown that the maximum amplification of kinetic energy of disturbances depends significantly on the pipe aspect ratio, and this dependence is non-monotonic. It agrees with the corresponding dependence of the energy critical Reynolds number, which is the lower limit of the Reynolds numbers enabling the growth of disturbance kinetic energy. In other words, changing the aspect ratio similarly affects both nonmodal and monotonic stability of the flow. The optimal disturbances displaying the maximum amplification are streamwise counter-rotating vortices. These disturbances are streamwise uniform at sufficiently large Reynolds numbers and may become streamwise harmonic as the Reynolds number decreases. In addition, their symmetry with respect to the cross section axes varies with the aspect ratio. Thus, the obtained results suggest that changing the aspect ratio may be a perspective tool for the passive control of the subcritical laminar-turbulent transition in pipe flows. In other words, this factor is worth considering when designing various devices (e.g., heat exchangers or ventilation systems) containing pipes to enhance their efficiency.