Chaotic diffusion in steady wavy vortex flow—Dependence on wave state and correlation with Eulerian symmetry measures

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• 作者：G.P. King ; Murray Rudman ; G. Rowl ; s
• 关键词：Taylor– ; Couette ; Wavy vortex flow ; Chaotic advection ; Chaotic diffusion ; Symmetry measures ; Escape rates
• 刊名：Fluid Dynamics Research
• 出版年：2008
• 出版时间：January 2008
• 年：2008
• 卷：40
• 期：1
• 页码：45-67
• 全文大小：353 K

文摘

The dimensionless effective axial diffusion coefficient, title=""Click to view the MathML source"">D_z, calculated from particle trajectories in steady wavy vortex flow in a narrow gap Taylor–Couette system, has been determined as a function of Reynolds number title=""Click to view the MathML source"">(R=Re/Re_c), axial wavelength title=""Click to view the MathML source"">(λ_z), and the number of azimuthal waves (m). Two regimes of Reynolds number were found: (i) when title=""Click to view the MathML source"">R<3.5, title=""Click to view the MathML source"">D_z has a complex and sometimes multi-modal dependence on Reynolds number; (ii) when title=""Click to view the MathML source"">R>3.5, title=""Click to view the MathML source"">D_z decreases monotonically.

Eulerian quantities measuring the departure from rotational symmetry, title=""Click to view the MathML source"">_θ, and flexion-free flow, title=""Click to view the MathML source"">_ν, were calculated. The space-averaged quantities and c1106d2b228167515b2421df8ee""> were found to have, unlike title=""Click to view the MathML source"">D_z, a simple unimodal dependence on title=""Click to view the MathML source"">R. In the low title=""Click to view the MathML source"">R regime the correlation between title=""Click to view the MathML source"">D_z and title=""Click to view the MathML source"">_θν was complicated and was attributed to variations in the spatial distribution of the wavy disturbance occurring in this range of title=""Click to view the MathML source"">R. In the large title=""Click to view the MathML source"">R regime, however, the correlation simplified to for all wave states, and this was attributed to the growth of an integrable vortex core and the concentration of the wavy disturbance into narrow regions near the outflow and inflow jets.

A reservoir model of a wavy vortex was used to determine the rate of escape across the outflow and inflow boundaries, the size of the ‘escape basins’ (associated with escape across the outflow and inflow boundaries), and the size of the trapping region in the vortex core. In the low title=""Click to view the MathML source"">R regime after the breakup of all KAM tori, the outflow basin title=""Click to view the MathML source"">(γ_O) is larger than the inflow basin title=""Click to view the MathML source"">(γ_I), and both title=""Click to view the MathML source"">γ_O and title=""Click to view the MathML source"">γ_I are (approximately) independent of title=""Click to view the MathML source"">R. In the large title=""Click to view the MathML source"">R regime, with increasing Reynolds number the trapping region grows, the outflow basin decreases, and the inflow basin shows a slight increase. This implies that the growth of the integrable core occurs at the expense of the outflow escape basin. Finally, it is shown that the variation of the weighted escape rates title=""Click to view the MathML source"">(γ_Or_O,γ_Ir_I) with Reynolds number was in excellent qualitative agreement with the variation of .