Bifurcation-theoretic origin of RPO11

Determine the bifurcation-theoretic origin of the relative periodic orbit RPO11 in vertical convection, specifying the invariant solution or bifurcation mechanism that generates RPO11.

Background

RPO11 has no spatial symmetry and undergoes multiple saddle-node bifurcations; it exhibits roll-breaking and defect dynamics along the orbit.

Continuation to Ra=6680 did not reveal the parent bifurcation or source branch, leaving its origin unknown.

References

We stopped the continuation at $(Ra, T) = (6680, 212)$ for the lower branch and at $(Ra, T) = (6680, 230.6)$ for the upper branch; its origin remains unknown.

— Natural convection in a vertical channel. Part 3. Bifurcations of many (additional) unstable equilibria and periodic orbits (2504.05524 - Zheng et al., 7 Apr 2025) in Section 4.8.2 (RPO11: saddle-node bifurcations)