Richard J.A.M. Stevens

Physics of Fluids

University of Twente

Publication 70 · Wall-shear turbulence

How turbulent spirals select a wavelength

P. Berghout, R.J. Dingemans, X. Zhu, R. Verzicco, R.J.A.M. Stevens, W. van Saarloos, and D. Lohse, Journal of Fluid Mechanics 887, A18 (2020).

The article and figure are open access under CC BY 4.0.

Main finding

Near the simulated laminar–turbulent transition, spiral Taylor–Couette turbulence followed finite-wavelength Ginzburg–Landau-type amplitude scaling. The preferred axial wavelength was 41 ± 2 gap widths at radius ratio 0.91, and the spiral traveled with the domain-mean angular velocity rather than the arithmetic mean cylinder speed.

Spiral-turbulence amplitude versus axial wavenumber at five reduced distances from the bifurcation, with parabolic fits
How to read the figure. The horizontal axis is the dimensionless axial wavenumber and the vertical axis is the averaged spiral amplitude. Colours denote five reduced distances from the fitted onset, ε = (Rei,c − Rei)/Rei,c. Each parabolic fit has a finite maximum: the inferred preferred wavelengths range from 38.91 to 42.52 gap widths, with a mean of 41.38. The widening unstable-wavenumber band as ε increases is consistent with finite-wavelength amplitude phenomenology. The periodic domain restricts the simulated wavelengths, particularly at small wavenumber. Transport and pattern speed are quantified separately in Figures 4 and 5, and the linear amplitude-squared scaling in Figure 7. Open the full-resolution figure. Figure 8, cropped. P. Berghout et al. (2020), CC BY 4.0.

Why this matters

The simulations connect a turbulent–laminar spiral pattern to finite-wavelength bifurcation phenomenology despite cylinder curvature. Wavelength also changes the turbulent fraction and therefore the global angular-momentum transport. In a representative case, the spiral's nondimensional angular speed was −0.355, matching the domain mean of −0.354 rather than the arithmetic mean cylinder speed of −0.326. These are linked observations within the tested system, not a derivation of the instability from the turbulent base flow.

Research context

The study uses counter-rotating Taylor–Couette direct numerical simulations near the spiral bifurcation at radius ratio 0.91. The full-azimuthal domains have periodic axial boundaries, aspect ratios 42–125, 400 ≤ Rei ≤ 1200, and −2000 ≤ Reo ≤ −1000. The fitted DNS threshold is Rei,c = 863 at Reo = −1200. Periodicity quantizes the permitted wavelengths, initial conditions can influence which spiral is selected, and the simulations omit experimental end plates. Only one radius ratio is simulated in depth, so the preferred wavelength and threshold are case-specific rather than universal.

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