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| Understanding the behavior of shear layers and their instabilities is
crucial because they are present in many rotating geophysical systems
and they are responsible for important natural effects in the
atmosphere and oceans. The flow in a completely filled rapidly
rotating cylinder is studied numerically solving the three-dimensional
Navier-Stokes equations using a spectral method. The cylinder is split
in two with the top half rotating slightly faster than the bottom
half. As the mean rotation is increased, the differential rotation
drives thin boundary layers on the sidewall as well as on the top and
bottom endwalls. In the absence of instabilities, the bulk is in
solid-body rotation and the sidewall layer is of Stewartson-type. When
the mean rotation increases, combined with an increase in the
differential rotation, the sidewall boundary layer and the corner flow
on the slower half-cylinder undergo a number of three-dimensional
instabilities. These include slow low-azimuthal-wavenumber modes whose
frequencies excite inertial waves in the interior as well as fast
high-azimuthal-wavenumber modes whose impact is contained in the
sidewall boundary layer region. Nonlinear competition due to Eckhaus
instabilities and mode interactions abound. |
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