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Turbulent flow is characterized by unpredictable fluctuations in velocity and pressure, which result in a chaotic fluid movement distinct from the orderly patterns of laminar flow. While laminar flow is governed by smooth, parallel layers with minimal mixing, turbulent flow exhibits highly irregular, three-dimensional patterns. This behavior arises due to instabilities in the fluid's velocity profile, and amplifies as the flow velocity increases. Minor disturbances, known as turbulent...
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Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is...
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Magnetically Induced Rotating Rayleigh-Taylor Instability
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Routes to turbulence in Taylor-Couette flow.

Daniel Feldmann1, Daniel Borrero-Echeverry2, Michael J Burin3

  • 1University of Bremen, Center of Applied Space Technology and Microgravity (ZARM), 28359 Bremen, Germany.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|March 12, 2023
PubMed
Summary
This summary is machine-generated.

Fluid dynamics between rotating cylinders show two paths to turbulence. Inner cylinder rotation causes chaotic dynamics, while outer cylinder rotation leads to abrupt turbulence, both explained by bifurcation theory.

Keywords:
Taylor–Couette flowdynamical systemspattern formationtransition to turbulence

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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.