FE03: Faisst, H. & Eckhardt, B. ``Travelling waves in pipe flow.'' Phys. Rev. Lett. 91, 224502, 2003.
WK04: Wedin, H. & Kerswell, R.R. ``Exact coherent structures in pipe flow: travelling wave solutions.'' J. Fluid Mech. 508, 333-371, 2004.
PK07: Pringle, C.C.T. & Kerswell, R.R. ``Asymmetric, helical and mirror-symmetric travelling waves in pipe flow.'' Phys. Rev. Lett. 99, 074502, 2007
PDK09: Pringle, C.C.T., Duguet, Y. & Kerswell, R.R.``Highly symmetric travelling waves in pipe flow'' Phil. Trans. R. Soc. A 367, 457-472, 2009. (doi: 10.1095/rsta.2008.0236)
|
Source |
Symmetries |
Remin |
α* |
|
|
FE03 & WK04 |
S2 | S & R2 | 1358 | 1.55 |
| S3 | S & R3 | 1251 | 2.44 | |
| S4 | S & R4 | 1647 | 3.23 | |
| S5 | S & R5 | 2485 | 4.11 | |
|
WK04 |
S6 | S & R6 | 2869 | 4.73 |
| U1 | S & Ω1 | 3046 | 2.17 | |
|
PK07 |
Asymmetric (S1) | S | ~820 | ~1.8 |
| Mirror-symmetric (M1) | S & Ω1 | 773 | 1.44 | |
| Helical | Ωβ | 773 | 1.44 | |
|
PDK09 |
M2 | S, R2 & Ω2 | 1125 | 2.0 |
| M3 (upper) | S, R3 & Ω3 | 1552 | 2.2 | |
| M4 (upper) | S, R4 & Ω4 | 1824 | 2.6 | |
| M5 | S, R5 & Ω5 | 2143 | 3.1 | |
| M6 | S, R6 & Ω6 | 2531 | 3.5 | |
| N1 | S, R1 & Ω1 | 1554 | 0.9 | |
| N2 | S, R2 & Ω2 | 1141 | 1.2 | |
| N3 (upper) | S, R3 & Ω3 | 1037 | 2.0 | |
| N4 (upper) | S, R4 & Ω4 | 1290 | 2.5 | |
| N5 | S, R5 & Ω5 | 1622 | 2.9 | |
| Z2 | Z & R2 | 3250 | 0.8 | |
| D2 | Z & R2 | <2875 | ? |
FE03: