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Home/Biophysics, Fluids & Geoscience/Taylor–Couette Flow (Criterion)

Taylor–Couette Flow (Criterion)

Gap d, cylinders Ω_i, Ω_o, kinematic ν: Taylor number Ta and critical Ta_c for toroidal rolls — cartoon + formula.

Rotation & fluid

8
0
0.04
0.01
0.0001

Taylor–Couette instability sets in when centrifugal destabilization overcomes viscous damping; textbooks quote critical Taylor numbers Ta_c ≈ 1708 for the canonical case. Here Ta is a proportional surrogate of (ΔΩ R d/ν)² — a teaching scale, not a measured experiment.

Measured values

Re (gap)32
Ta (surrogate)4301
Rolls (Ta>Ta_c)yes

About this model

Circular Couette flow between differentially rotating cylinders becomes unstable to toroidal Taylor vortices when a dimensionless Taylor number exceeds a critical value (~1708 in the canonical incompressible case). The simulator reports a surrogate based on gap Reynolds scaling so students can connect angular slip, viscosity, and geometry to pattern formation.

Who it's for: Undergraduates studying rotating flows and hydrodynamic instability criteria.

Key terms

  • Taylor–Couette
  • Taylor number
  • Couette flow
  • Instability

How it works

Concentric cylinders with differential rotation: a gap Reynolds number and a Taylor-number surrogate indicate when toroidal vortices (rolls) replace purely azimuthal Couette flow in this schematic.

Frequently asked questions

Why does the cartoon show rolls even slightly below threshold?
The drawing is illustrative; the numeric readout uses the threshold for the simplified Ta surrogate.