Routes to turbulence in Taylor-Couette flow

Area of Science:

• Fluid Dynamics
• Turbulence Theory
• Nonlinear Dynamics

Background:

• Taylor-Couette flow, the fluid dynamics between rotating concentric cylinders, is a classic system for studying transitions to turbulence.
• Two distinct routes to turbulence have been observed, depending on whether the inner or outer cylinder is rotated.

Purpose of the Study:

• To review the main features of the two distinct routes to turbulence in rotating concentric cylinder flows.
• To rationalize the origin of temporal chaos using bifurcation theory and understand abrupt transitions using statistical approaches.
• To highlight the role of the rotation number in determining the onset of intermittent laminar-turbulent patterns.

Main Methods:

• Review of existing literature on Taylor-Couette flow dynamics.
• Application of bifurcation theory to explain temporal chaos.
• Utilization of statistical approaches to analyze spatial proliferation of turbulence.

Main Results:

• Inner-cylinder rotation leads to a sequence of instabilities, resulting in temporally chaotic dynamics with loss of spatial symmetry.
• Outer-cylinder rotation causes an abrupt transition to turbulence, with turbulent regions coexisting with laminar ones.
• The rotation number dictates the lower limit for intermittent laminar-turbulent patterns.

Conclusions:

• Bifurcation theory explains temporal chaos in both routes.
• Statistical methods are crucial for understanding the abrupt transition in outer-cylinder dominated flows.
• The rotation number is a key parameter governing the nature of turbulence in this system.