Wave propagation reversal for wavy vortices in wide-gap counter-rotating cylindrical Couette flow

S. Altmeyer and Richard M. Lueptow
Phys. Rev. E 95, 053103 – Published 10 May 2017
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Abstract

We present a numerical study of wavy supercritical cylindrical Couette flow between counter-rotating cylinders in which the wavy pattern propagates either prograde with the inner cylinder or retrograde opposite the rotation of the inner cylinder. The wave propagation reversals from prograde to retrograde and vice versa occur at distinct values of the inner cylinder Reynolds number when the associated frequency of the wavy instability vanishes. The reversal occurs for both twofold and threefold symmetric wavy vortices. Moreover, the wave propagation reversal only occurs for sufficiently strong counter-rotation. The flow pattern reversal appears to be intrinsic in the system as either periodic boundary conditions or fixed end wall boundary conditions for different system sizes always result in the wave propagation reversal. We present a detailed bifurcation sequence and parameter space diagram with respect to retrograde behavior of wavy flows. The retrograde propagation of the instability occurs when the inner Reynolds number is about two times the outer Reynolds number. The mechanism for the retrograde propagation is associated with the inviscidly unstable region near the inner cylinder and the direction of the global average azimuthal velocity. Flow dynamics, spatio-temporal behavior, global mean angular velocity, and torque of the flow with the wavy pattern are explored.

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  • Received 28 October 2016

DOI:https://doi.org/10.1103/PhysRevE.95.053103

©2017 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

S. Altmeyer*

  • Institute of Science and Technology Austria (IST Austria), 3400 Klosterneuburg, Austria

Richard M. Lueptow

  • Department of Mechanical Engineering and Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, USA

  • *sebastian.altmeyer@ist.ac.at
  • r-lueptow@northwestern.edu

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Issue

Vol. 95, Iss. 5 — May 2017

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