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Instabilities and inertial waves generated in a librating cylinder

Published online by Cambridge University Press:  07 November 2011

J. M. Lopez  and
F. Marques
J. M. Lopez*
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA Department of Mathematics, Kyungpook National University, Daegu 702-701, Republic of Korea
F. Marques
Affiliation:
Departament de Física Aplicada, Universitat Politècnica de Catalunya, Barcelona 08034, Spain
*
†Email address for correspondence: [email protected]
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Abstract

A librating cylinder consists of a rotating cylinder whose rate of rotation is modulated. When the mean rotation rate is large compared with the viscous damping rate, the flow may support inertial waves, depending on the frequency of the modulation. The modulation also produces time-dependent boundary layers on the cylinder endwalls and sidewall, and the sidewall boundary layer flow in particular is susceptible to instabilities which can introduce additional forcing on the interior flow with time scales different from the modulation period. These instabilities may also drive and/or modify the inertial waves. In this paper, we explore such flows numerically using a spectral-collocation code solving the Navier–Stokes equations in order to capture the dynamics involved in the interactions between the inertial waves and the viscous boundary layer flows.

JFM classification

Boundary Layers: Boundary layer stability Instability: Nonlinear instability Turbulent Flows: Rotating turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 687 , 25 November 2011 , pp. 171 - 193
Copyright
Copyright © Cambridge University Press 2011

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Lopez and Marques supplementary movie

Movie 1. Azimuthal vorticity on the sidewall over one period at $Re=10^4$, $\gamma=1$,$\omega=0.8\pi$ and $\alpha=0.82$. (Movie corresponds to figure 8c in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 3.9 MB

Lopez and Marques supplementary movie

Movie 1. Azimuthal vorticity on the sidewall over one period at $Re=10^4$, $\gamma=1$,$\omega=0.8\pi$ and $\alpha=0.82$. (Movie corresponds to figure 8c in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 6.5 MB

Lopez and Marques supplementary movie

Movie 2. Azimuthal vorticity on the sidewall over one period at $Re=10^4$, $\gamma=1$,$\omega=0.8\pi$ and $\alpha=0.90$. (Movie corresponds to figure 8d in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 4.2 MB

Lopez and Marques supplementary movie

Movie 2. Azimuthal vorticity on the sidewall over one period at $Re=10^4$, $\gamma=1$,$\omega=0.8\pi$ and $\alpha=0.90$. (Movie corresponds to figure 8d in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 7.8 MB

Lopez and Marques supplementary movie

Movie 3. Azimuthal vorticity in a meridional plane $\theta=0$ over one period at $Re=10^4$, $\gamma=1$, $\omega=0.9\pi$ and $\alpha=0.8$. (Movie corresponds to figure 9c in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 3.8 MB

Lopez and Marques supplementary movie

Movie 3. Azimuthal vorticity in a meridional plane $\theta=0$ over one period at $Re=10^4$, $\gamma=1$, $\omega=0.9\pi$ and $\alpha=0.8$. (Movie corresponds to figure 9c in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 5.8 MB

Lopez and Marques supplementary movie

Movie 4. Azimuthal vorticity in a horizontal plane $z=0.25$ over one period at $Re=10^4$, $\gamma=1$, $\omega=0.9\pi$ and $\alpha=0.8$. (Movie corresponds to figure 9d in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 4.1 MB

Lopez and Marques supplementary movie

Movie 4. Azimuthal vorticity in a horizontal plane $z=0.25$ over one period at $Re=10^4$, $\gamma=1$, $\omega=0.9\pi$ and $\alpha=0.8$. (Movie corresponds to figure 9d in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 7.6 MB

Lopez and Marques supplementary movie

Movie 5. Azimuthal vorticity on the sidewall over one period at $Re=10^4$, $\gamma=1$, $\omega=0.6\pi$ and $\alpha=0.7$. (Movie corresponds to figure 10d in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 4.1 MB

Lopez and Marques supplementary movie

Movie 5. Azimuthal vorticity on the sidewall over one period at $Re=10^4$, $\gamma=1$, $\omega=0.6\pi$ and $\alpha=0.7$. (Movie corresponds to figure 10d in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 7.1 MB

Lopez and Marques supplementary movie

Movie 6. Azimuthal vorticity in a meridional plane $\thata=0$ at $Re=10^4$, $\gamma=1$, $\omega=0.6\pi$ and $\alpha=0.7$. (Movie corresponds to figure 11d in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 3.8 MB

Lopez and Marques supplementary movie

Movie 6. Azimuthal vorticity in a meridional plane $\thata=0$ at $Re=10^4$, $\gamma=1$, $\omega=0.6\pi$ and $\alpha=0.7$. (Movie corresponds to figure 11d in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 5.5 MB

Lopez and Marques supplementary movie

Movie 7. Azimuthal vorticity in a horizontal plane $z=0.25$ over one period at $Re=10^4$, $\gamma=1$, $\omega=0.6\pi$ and $\alpha=0.3$ (Movie corresponds to figure 12b in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 3.6 MB

Lopez and Marques supplementary movie

Movie 7. Azimuthal vorticity in a horizontal plane $z=0.25$ over one period at $Re=10^4$, $\gamma=1$, $\omega=0.6\pi$ and $\alpha=0.3$ (Movie corresponds to figure 12b in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 4.7 MB

Lopez and Marques supplementary movie

Movie 8. Azimuthal vorticity in a horizontal plane $z=0.25$ over one period at $Re=10^4$, $\gamma=1$, $\omega=0.6\pi$ and $\alpha=0.7$. (Movie corresponds to figure 12d in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 4.2 MB

Lopez and Marques supplementary movie

Movie 8. Azimuthal vorticity in a horizontal plane $z=0.25$ over one period at $Re=10^4$, $\gamma=1$, $\omega=0.6\pi$ and $\alpha=0.7$. (Movie corresponds to figure 12d in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 7.5 MB

Lopez and Marques supplementary movie

Movie 9. Azimuthal vorticity in a meridional plane $\thata=0$ at $Re=10^4$, $\gamma=1$, $\omega=0.4\pi$ and $\alpha=0.7$. (Movie corresponds to figure 16d in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 3.7 MB

Lopez and Marques supplementary movie

Movie 9. Azimuthal vorticity in a meridional plane $\thata=0$ at $Re=10^4$, $\gamma=1$, $\omega=0.4\pi$ and $\alpha=0.7$. (Movie corresponds to figure 16d in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 5.3 MB

Lopez and Marques supplementary movie

Movie 10. Azimuthal vorticity in a horizontal plane $z=0.25$ over one period at $Re=10^4$, $\gamma=1$, $\omega=0.4\pi$ and $\alpha=0.7$. (Movie corresponds to figure 17d in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 3.8 MB

Lopez and Marques supplementary movie

Movie 10. Azimuthal vorticity in a horizontal plane $z=0.25$ over one period at $Re=10^4$, $\gamma=1$, $\omega=0.4\pi$ and $\alpha=0.7$. (Movie corresponds to figure 17d in the paper).

Download Lopez and Marques supplementary movie(Video)
Video 6.4 MB