Characteristics of disturbances in the laminarturbulent transition of spherical Couette flow. 1. Spiral TaylorGörtler vortices and traveling waves for narrow gaps
Abstract
The fundamental frequencies of velocity fluctuations caused by disturbances (vortices and waves) in the laminarturbulent transition of spherical Couette flow between two concentric spheres with only the inner sphere rotating are investigated by simultaneous and flowvisualization measurements for two small ratios, 0.06 and 0.024, of the clearance to innersphere radius for which spiral TaylorGörtler (TG) vortices and traveling waves on TG vortices play an important role. As the Reynolds number Re is increased for both clearance ratios, first toroidal TG vortices occur at the equator, but the flow is steady. Second, spiral TG vortices (fundamental frequency f_{Si}) occur next to the toroidal ones, so that the flow becomes singly periodic. Third, in addition to these spiral TG vortices, new spiral TG vortices occur between them at the different colatitude θ, so that the pair number of spiral TG vortices around the spherical annulus differs by θ. Therefore, plural fundamental frequencies f_{Si} (i=1,2,…) of spiral TG vortices are detected, corresponding to the different pair numbers. However, the flow is not quasiperiodic, because ratios of the different frequencies f_{Si} are in rational. Fourth, traveling waves (fundamental frequency f_{W}) occur on TG vortices, so that the flow becomes quasiperiodic (f_{Si} and f_{W}). Fifth, the plural frequencies f_{Si} change to a broadband frequency f_{B}, which indicates the onset of chaos. Sixth, f_{W} disappears, so that the flow becomes chaotic spiral TG vortexflow with only f_{B}. The rotation frequency (wave speed) of traveling waves is larger than that of spiral TG vortices, and the value of f_{B} exists about between the two rotation frequencies.
 Publication:

Physics of Fluids
 Pub Date:
 November 2002
 DOI:
 10.1063/1.1502661
 Bibcode:
 2002PhFl...14.3963N
 Keywords:

 Boundary Layer Transition;
 Concentric Spheres;
 Couette Flow;
 Flow Stability;
 Flow Visualization;
 Laminar Flow;
 Liquid Surfaces;
 Surface Waves;
 Transition Flow;
 Traveling Waves;
 Turbulence;
 Turbulent Boundary Layer;
 Variations;
 Vortices;
 47.15.Fe;
 47.27.Cn;
 47.32.Cc;
 47.35.+i;
 05.40.a;
 Fluid Mechanics and Thermodynamics;
 Stability of laminar flows;
 Transition to turbulence;
 Fluctuation phenomena random processes noise and Brownian motion