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Steady circulation induced by inertial modes in a librating cylinder
Phys. Rev. Fluids 5, 014804 – Published 24 January, 2020
DOI: https://doi.org/10.1103/PhysRevFluids.5.014804
Abstract
The paper is devoted to an experimental study of steady flows excited by an oscillating motion of fluid in a cylinder, the rotation rate of which periodically changes (librations). The rotational oscillations lead to the appearance of a system of averaged toroidal vortices in a viscous Stokes boundary layer close to the cylinder side wall. The number of vortices depends on the frequency of librations, σ. If σ exceeds twice the rotation rate, the steady flow structure has the form of two vortices located close to the cavity ends, i.e., corner flow. If at some libration frequencies, inertial modes—natural modes of rotating fluid oscillations in the closed cavity—are excited. In this case additional averaged vortices arise. The number of vortices is determined by the axial wave number of the inertial mode. With a decrease in the dimensionless frequency of fluid oscillation, the vortices increase in size, which leads to a transformation of the vortex structure. In this case, the flow near the ends is a superposition of the flows excited by inertial mode and corner flow. At the same time, the vortices which are the most distant from the periphery do not feel the corner flow. It is shown that the viscous dissipation of the oscillating motion in the fluid bulk leads to a linear decrease in the velocity of steady circulation with the dimensionless frequency.
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