TY - GEN

T1 - Subcritical instability of Taylor–Couette flow with stationary inner cylinder

AU - Lopez, J. M.

N1 - Funding Information:
This work was supported by NSF grant CBET-1336410.

PY - 2016

Y1 - 2016

N2 - The presence of endwalls in Taylor–Couette flows has far reaching effects, leading to dynamics that are qualitatively different to the idealized flow involving infinitely long cylinders. This is well known when the inner cylinder is rotating and the outer cylinder is stationary. The effects of endwalls in the centrifugally stable situation with stationary inner cylinder have not been previously considered in detail. The meridional flows induced by the endwalls lead to the formation of a thin sidewall boundary layer on the inner cylinder wall if the endwalls are rotating, or on the outer cylinder wall if they are stationary. At sufficiently high Reynolds numbers, the sidewall boundary layer has concentrated shear, the pressure gradient in the azimuthal direction (which is the streamwise direction for the boundary layer flow) is zero (the flow is axisymmetric) and the boundary layer thickness is constant. At a critical Reynolds number, the sidewall boundary layer loses stability at a subcritical Hopf bifurcation, breaking the axisymmetry of the flow, and for Reynolds numbers slightly above critical, a packet of Hopf modes with azimuthal wavenumbers clustered about the critical wavenumber grow. The early time evolution of the critical Hopf mode is a rotating wave analogous to a Tollmien–Schlichting wave. As the Hopf modes grow, nonlinear interactions lead to modulations, localization of the disturbances and the evolution of concentrated streamwise vortical streaks which become very long and intense via vortex stretching.

AB - The presence of endwalls in Taylor–Couette flows has far reaching effects, leading to dynamics that are qualitatively different to the idealized flow involving infinitely long cylinders. This is well known when the inner cylinder is rotating and the outer cylinder is stationary. The effects of endwalls in the centrifugally stable situation with stationary inner cylinder have not been previously considered in detail. The meridional flows induced by the endwalls lead to the formation of a thin sidewall boundary layer on the inner cylinder wall if the endwalls are rotating, or on the outer cylinder wall if they are stationary. At sufficiently high Reynolds numbers, the sidewall boundary layer has concentrated shear, the pressure gradient in the azimuthal direction (which is the streamwise direction for the boundary layer flow) is zero (the flow is axisymmetric) and the boundary layer thickness is constant. At a critical Reynolds number, the sidewall boundary layer loses stability at a subcritical Hopf bifurcation, breaking the axisymmetry of the flow, and for Reynolds numbers slightly above critical, a packet of Hopf modes with azimuthal wavenumbers clustered about the critical wavenumber grow. The early time evolution of the critical Hopf mode is a rotating wave analogous to a Tollmien–Schlichting wave. As the Hopf modes grow, nonlinear interactions lead to modulations, localization of the disturbances and the evolution of concentrated streamwise vortical streaks which become very long and intense via vortex stretching.

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M3 - Conference contribution

AN - SCOPUS:85084012405

T3 - Proceedings of the 20th Australasian Fluid Mechanics Conference, AFMC 2016

BT - Proceedings of the 20th Australasian Fluid Mechanics Conference, AFMC 2006

PB - Australasian Fluid Mechanics Society

T2 - 20th Australasian Fluid Mechanics Conference, AFMC 2006

Y2 - 5 December 2016 through 8 December 2016

ER -