Fluid flows in a librating cylinder

Abstract

The flow in a cylinder driven by time harmonic oscillations of the rotation rate, called longitudinal librations, is investigated. Using a theoretical approach and axisymmetric numerical simulations, we study two distinct phenomena appearing in this librating flow. First, we investigate the occurrence of a centrifugal instability near the oscillating boundary, leading to the so-called Taylor-Görtler vortices. A viscous stability criterion is derived and compared to numerical results obtained for various libration frequencies and Ekman numbers. The strongly nonlinear regime well above the instability threshold is also documented. We show that a new mechanism of spontaneous generation of inertial waves in the bulk could exist when the sidewall boundary layer becomes turbulent. Then, we analyse the librating flow below the instability threshold and characterize the mean zonal flow correction induced by the nonlinear interaction of the boundary layer flow with itself. In the frequency regime where inertial modes are not excited, we show that the mean flow correction in the bulk is a uniform rotation, independent of the Ekman number and cylinder aspect ratio, in perfect agreement with the analytical results of Wang [J. Fluid. Mech., 41, pp. 581 - 592, 1970]. When inertial modes are resonantly excited, the mean flow correction is found to have a more complex structure. Its amplitude still scales as the square of the libration amplitude but now depends on the Ekman number.

References in corpus (3)

• Inertial waves in a rotating spherical shell: attractors and asymptotic spectrum
• Viscous dissipation by tidally forced inertial modes in a rotating spherical shell
• Experimental and numerical study of mean zonal flows generated by librations of a rotating spherical cavity

Cited by in corpus (11)

• Libration-induced mean flow in a spherical shell
• Experimental study of libration-driven zonal flows in non-axisymmetric containers
• Inertial waves and modes excited by the libration of a rotating cube
• Vortex cluster arising from an axisymmetric inertial wave attractor
• Inviscid instabilities in rotating ellipsoids on eccentric Kepler orbits
• Spontaneous generation of inertial waves from boundary turbulence in a librating sphere
• Latitudinal libration driven flows in triaxial ellipsoids
• Anomalous Features in Internal Cylinder Flow Instabilities subject to Uncertain Rotational Effects
• Mean zonal flows induced by weak mechanical forcings in rotating spheroids
• Libration driven multipolar instabilities
• Zonal flow in a resonant precessing cylinder