Database

Below are files that can be manipulated or used as initial conditions, state.cdf.in. A Main.info should be provided with each state file containing parameter settings.

• Files may be loaded with with different parameter settings. If there is a change in resolution, data will be interpolated or truncated automatically.
• For visualisation, data needs converting to real space. See comments in the file matlab/Readme.txt supplied with the code.
• The state file contains positions of radial points and Fourier spectral coefficients of the velocity perturbation evaluated at the radial points. Each component has dimension (N,H,2), where N is the number of radial points, H is the number of Fourier coefficients, and 2 corresponds to real and imaginary parts. Indices [1,H] in the state file correspond to indices [0:H-1] in the code; see Core_implementation#Ordering_the_Fourier_modes.

To unpack

tar -xvvzf file.tgz

Sample Initial Conditions

• Turbulence at Re=2400. L=2.5D (alpha=1.25) File:Re2400a1.25.tgz
• Turbulence at Re=5300. L=5D, Re_tau approx 180. File:Re5300.Retau180.5D.tgz
• Localised puff at Re=1900, L=50D. File:Re1900a0.0625.tgz

• Turbulence at Re=2400 with m=2 symmetry. L=2.5D (alpha=1.25) File:Re2400m2a1.25.tgz
• Turbulence at Re=4500 in the '2+epsilon' model. L=10D File:Re4500.2eps.a0.314.tgz

• Turbulence at Re=5300. L=5D, Re_tau approx 180. LES File:Re5300.Retau180.5D.LES.tgz
• Turb in shear-thinning fluid, Re_wall approx 10000, L=5D, Carreau-Yasuda model File:Re0160.Rew10000.5D.CY.tgz

Relative Equilibria (travelling waves)

See Pringle, Duguet and Kerswell (2009) for classification according to the Symmetries_of_pipe_flow that each solution carries. The states feature prominently in the articles indicated below.

• S1, Re=2400, L=2.5D (alpha=1.25) File:Re2400.S1.a1.25.tgz Kerswell and Tutty (2007)
• M1, Re=775, alpha=1.437 (lowest known Re for a TW) File:Re775.M1.a1.437.tgz Pringle and Kerswell (2007)
• N2_ML, Re=2400, alpha=1.25 (and leading eigvec.) File:Re2400m2.a1.25 N2ML.tgz
• N4L, Re=2500, alpha=1.7 File:Re2500m4a1.7.N4L.tgz
• N4U, Re=2500, alpha=1.7 File:Re2500m4a1.7.N4U.tgz Willis, Cvitanovic & Avila (2013)

Relative Periodic Orbits

• Localised RPO, Lower Branch, Re=1712, m=2, alpha=0.125 (L=25D) File:Re1712.m2.RPO LB.a0.125.tgz; Avila, Mellibovsky, Roland and Hof (2013); Chantry, Willis and Kerswell (2014).
• Localised RPO, Upper Branch, Re=1700, m=2, alpha=0.125 (L=25D) File:Re1700.m2.RPO UB.a0.125.tgz
• Short-period RPO in minimal pipe, Re=2500, m=4, alpha=1.7 File:Re2500m4a1.7.RPO25.65.tgz; Budanur, Short, Farazmand, Willis and Cvitanovic (2017).