Three-Dimensional Instabilities in a Discretely Heated Annular Flow: Onset of Spatio-Temporal Complexity Via Defect Dynamics

The transition to three-dimensional and unsteady flow in an annulus with a discrete heat source on the inner cylinder is studied numerically. For large applied heat flux through the heater (large Grashof number Gr), there is a strong wall plume originating at the heater that reaches the top and forms a large scale axisymmetric wavy structure along the top. For Gr ≈ 6 × 10⁹, this wavy structure becomes unstable to three-dimensional instabilities with high azimuthal wavenumbers m ∼ 30, influenced by mode competition within an Eckhaus band of wavenumbers. Coexisting with some of these steady three-dimensional states, solution branches with localized defects break parity and result in spatio-temporal dynamics. We have identified two such time dependent states. One is a limit cycle that while breaking spatial parity, retains spatio-temporal parity. The other branch corresponds to quasi-periodic states that have globally broken parity.