Abstract
The analysis of the Taylor–Couette problem in the small gap limit is extended to the of nearly columnar (NC) solutions. The theoretical results are derived in the small-gap approximation which is not always well approximated in experiments. Despite this studies in the Cartesian frame work when compared with theoretical results and observations yield good agreement. For higher values of the axial wavenumber, beta, up to b approximately 3 rather narrow Taylor vortices may be realized for Reynolds number R less than 80.These vortices will become unstable to states with columnar components with increasing R. We show that for low R, (R,beta) approximately (62.2,3.5) a state with a strong columnar component drifting in stream-wise direction exists for azimuthal wavenumbers alpha approximately 0.17 with beta =3.5.We examine the bifurcation sequence of these states.
| Original language | English |
|---|---|
| Pages (from-to) | 2194-2205 |
| Number of pages | 12 |
| Journal | Lobachevskii Journal of Mathematics |
| Volume | 45 |
| Issue number | 5 |
| Early online date | 28 Aug 2024 |
| DOIs | |
| Publication status | Published - 28 Aug 2024 |
Funding
This work was supported by the European Union Horizon 2020 Research Innovation Staff Exchange (RISE) award ATM2BT (Grant no. 824022) from the European Union. The majority of large scale computations were performed using the 120 processor seat of Aston University\u2019s cloud computing facilities. This work was also supported by the Japanese Society for the Promotion of Science (JSPS) KAKENHI Grant no. JP23K03334.
| Funders | Funder number |
|---|---|
| European Commission | |
| Horizon 2020 | 824022 |
| Japan Society for the Promotion of Science | JP23K03334 |
Keywords
- Floquet parameters
- Taylor–Couette flow
- bifurcation theory
- incompressible flow
- stability theory
- strongly nonlinear solution
- turbulence