Using spectrally accurate, direct numerical simulations, we show that vortices with axial flows (without an imposed strain) generate small scales, i.e., breakdown, when they are randomly perturbed. We show that the breakdown that occurs without the necessity of a stagnation point in the flow is nonlinear and that energy spectra of the breakdown present a range of a $k^{-5/3}$ scaling ($k$ being a wavenumber). These features are the same for centrifugally stable and unstable azimuthal velocities. However, centrifugally unstable azimuthal velocities promote mixing in vortices with an axial flow. We also find that vortex breakdown could be a physical mechanism against a finite time singularity in Navier–Stokes equations. Contrarily, we do not observe a breakdown using spectrally truncated Euler equations. For these equations we find a scaling of the energy spectra compatible with the existence of a finite time singularity.

Linear stability of solid body rotating flows with axisymmetric density variations is addressed analytically. Considering inviscid disturbances, a nontrivial dispersion relation is obtained and it is shown that the instability is of Rayleigh-Taylor type in cylindrical frame. The viscous correction is derived, in the limit of large Reynolds numbers and large azimuthal wave numbers, allowing the determination of the most unstable mode. Theoretical predictions are checked by comparing them to (spectrally accurate) computed eigenvalues and direct numerical simulations.

Though the influence of surfactant type on foam rheological properties is well established experimentally, the underlying physical mechanisms are far from understood. Here, using fully resolved numerical simulation of an elementary T1 event taking into account both flow and surfactant dynamics, we unveil the origin of surfactant-induced dissipation in sheared foams. To model the diffusive and exchange contributions, we revisit the classical Lucassen model by switching from a mechanical to a thermodynamic perspective, and we find that in spite of its extreme simplicity, it captures well some behaviors of our numerical foam. Our approach should be useful in the class of surfactant-controlled systems, from soap films and emulsions to coating films and spreading droplets.