TY - JOUR

T1 - Three-dimensional instabilities and inertial waves in a rapidly rotating split-cylinder flow

AU - Lopez, Juan

AU - Gutierrez-Castillo, Paloma

N1 - Publisher Copyright:
© 2016 Cambridge University Press.

PY - 2016/8/10

Y1 - 2016/8/10

N2 - The nonlinear dynamics of the flow in a differentially rotating split cylinder is investigated numerically. The differential rotation, with the top half of the cylinder rotating faster than the bottom half, establishes a basic state consisting of a bulk flow that is essentially in solid-body rotation at the mean rotation rate of the cylinder and boundary layers where the bulk flow adjusts to the differential rotation of the cylinder halves, which drives a strong meridional flow. There are Ekman-like layers on the top and bottom end walls, and a Stewartson-like side wall layer with a strong downward axial flow component. The complicated bottom corner region, where the downward flow in the side wall layer decelerates and negotiates the corner, is the epicentre of a variety of instabilities associated with the local shear and curvature of the flow, both of which are very non-uniform. Families of both high and low azimuthal wavenumber rotating waves bifurcate from the basic state in Eckhaus bands, but the most prominent states found near onset are quasiperiodic states corresponding to mixed modes of the high and low azimuthal wavenumber rotating waves. The frequencies associated with most of these unsteady three-dimensional states are such that spiral inertial wave beams are emitted from the bottom corner region into the bulk, along cones at angles that are well predicted by the inertial wave dispersion relation, driving the bulk flow away from solid-body rotation.

AB - The nonlinear dynamics of the flow in a differentially rotating split cylinder is investigated numerically. The differential rotation, with the top half of the cylinder rotating faster than the bottom half, establishes a basic state consisting of a bulk flow that is essentially in solid-body rotation at the mean rotation rate of the cylinder and boundary layers where the bulk flow adjusts to the differential rotation of the cylinder halves, which drives a strong meridional flow. There are Ekman-like layers on the top and bottom end walls, and a Stewartson-like side wall layer with a strong downward axial flow component. The complicated bottom corner region, where the downward flow in the side wall layer decelerates and negotiates the corner, is the epicentre of a variety of instabilities associated with the local shear and curvature of the flow, both of which are very non-uniform. Families of both high and low azimuthal wavenumber rotating waves bifurcate from the basic state in Eckhaus bands, but the most prominent states found near onset are quasiperiodic states corresponding to mixed modes of the high and low azimuthal wavenumber rotating waves. The frequencies associated with most of these unsteady three-dimensional states are such that spiral inertial wave beams are emitted from the bottom corner region into the bulk, along cones at angles that are well predicted by the inertial wave dispersion relation, driving the bulk flow away from solid-body rotation.

KW - boundary layer stability

KW - nonlinear instability

KW - rotating flows

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U2 - 10.1017/jfm.2016.419

DO - 10.1017/jfm.2016.419

M3 - Article

AN - SCOPUS:84978370336

VL - 800

SP - 666

EP - 687

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -