Inertial waves and mean velocity profiles in a rotating pipe and a circular annulus with axial flow

Yantao Yang, Rodolfo Ostilla Monico, Jiezhi Wu, Paolo Orlandi

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Abstract

In this paper we solve the inviscid inertial wave solutions in a circular pipe or annulus rotating constantly about its axis with moderate angular speed. The solutions are constructed by the so-called helical wave functions. We reveal that the mean velocity profiles must satisfy certain conditions to accommodate the inertial waves at the bulk region away from boundary. These conditions require the axial and azimuthal components of the mean velocity to take the shapes of the zeroth and first order Bessel functions of the first kind, respectively. The theory is then verified by data obtained from direct numerical simulations for both rotating pipe and circular annulus, and excellent agreement is found between theory and numerical results. Large scale vortex clusters are found in the bulk region where the mean velocity profiles match the theoretical predictions. The success of the theory in rotating pipe, circular annulus, and streamwise rotating channel suggests that such inertial waves are quite common in wall bounded flow with background rotation.
Original languageEnglish
Article number013015
Number of pages6
JournalPhysical review E: Statistical, nonlinear, and soft matter physics
Volume91
Issue number1
DOIs
Publication statusPublished - 2015

Keywords

  • IR-95717
  • METIS-309249

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