Inertial Waves and Steady Flows in a Liquid Filled Librating Cylinder
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The fluid flow in a non-uniformly rotating (librating) cylinder about a horizontal axis is experimentally studied. In the absence of librations the fluid performs a solid-body rotation together with the cavity. Librations lead to the appearance of steady zonal flow in the whole cylinder and the intensive steady toroidal flows near the cavity corners. If the frequency of librations is twice lower than the mean rotation rate the inertial waves are excited. The oscillating motion associated with the propagation of inertial wave in the fluid bulk leads to the appearance of an additional steady flow in the Stokes boundary layers on the cavity side wall. In this case the heavy particles of the visualizer are assembled on the side wall into ring structures. The patterns are determined by the structure of steady flow, which in turn depends on the number of reflections of inertial wave beams from the cavity side wall. For some frequencies, inertial waves experience spatial resonance, resulting in inertial modes, which are eigenmodes of the cavity geometry. The resonance of the inertial modes modifies the steady flow structure close to the boundary layer that is manifested in the direct rebuilding of patterns. It is shown that the intensity of zonal flow, as well as the intensity of steady flows excited by inertial waves, is proportional to the square of the amplitude of librations.
KeywordsLibrations Inertial waves Steady flows Pattern formation
The research was supported by the Russian Foundation for Basic Research (project Nos. 16-31-60099 mol_a_dk and16-31-00169 mol_a) and grant of the President of the Russian Federation for the support of Leading Scientific Schools of the Russian Federation (grant NSh-9176.2016.1). We are grateful to Professor V.G. Kozlov for a fruitful discussion of the experimental results.
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