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Below are files that can be manipulated or used as initial conditions, <tt>state.cdf.in</tt>.  A [[Main.info]] should be provided with each state file containing parameter settings.   
Below are files that can be manipulated or used as initial conditions, <tt>state.cdf.in</tt>.  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.
* '''Files may be loaded with with different parameter settings'''.  If there is a change in resolution, data will be interpolated or truncated automatically.
* The state file contains spectral coefficients of the velocity perturbation.  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]].
* '''For visualisation, data needs converting to real space'''.  See comments in the file <tt>matlab/Readme.txt</tt> supplied with the code.
* For visualisation, data needs converting to real space.  See comments in the file <tt>matlab/Readme.txt</tt> 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==
==Sample Initial Conditions==
* Turbulence at Re=2400. L=2.5D (alpha=1.25) [[File:Re2400a1.25.tgz]]
* 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=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=4500 in the '2+epsilon' model.  L=10D [[File:Re4500.2eps.a0.314.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]]


==Relative Equilibria==
* Turbulence at Re=5300. L=5D, Re_tau approx 180. LES  [[File:Re5300.Retau180.5D.LES.tgz]]
* S1, S2...
* Turb in shear-thinning fluid, Re_wall approx 10000, L=5D, Carreau-Yasuda model [[File:Re0160.Rew10000.5D.CY.tgz]]
* M1, M2...
 
* N1, N2...
==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]] Pringle and Kerswell (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).

Latest revision as of 06:05, 27 March 2023

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

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.

Relative Periodic Orbits

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