Anne Cadiou

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.

The laminar–turbulent transition of a plane channel entrance flow is revisited using global linear optimization analyses and direct numerical simulations. The investigated case corresponds to uniform upstream velocity conditions and a moderate value of Reynolds number so that the two-dimensional developing flow is linearly stable under the parallel flow assumption. However, the boundary layers in the entry zone are capable of supporting the development of streaks, which may experience secondary instability and evolve to turbulence. In this study, global optimal linear perturbations are computed and studied in the nonlinear regime for different values of streak amplitude and optimization time. These optimal perturbations take the form of wavepackets having either varicose or sinuous symmetry. It is shown that, for short optimization times, varicose wavepackets grow through a combination of Orr and lift-up effects, whereas for longer target times, both sinuous and varicose wavepackets exhibit an instability mechanism driven by the presence of inflection points in the streaky flow. In addition, while the optimal varicose modes obtained for short optimization times are localized near the inlet, where the base flow is strongly three-dimensional, when the target time is increased, the sinuous and varicose optimal modes are displaced farther downstream, in the nearly parallel streaky flow. Finally, the optimal wavepackets are found to lead to turbulence for sufficiently high initial amplitudes. It is noticed that the resulting turbulent flows have the same wall-shear stress, whether the wavepackets have been obtained for short or for long time optimization.

Massively parallel simulations generate increasing volumes of big data, whose exploitation requires increasingly large storage resources, efficient networking technologies and post-processing facilities. In the coming era of exascale supercomputing, there is an emerging need for new data analysis and visualization strategies. A promising solution consists of coupling analysis with simulation, so that both are performed simultaneously. This paper describes a client–server in situ analysis for massively parallel time-evolving computations. Its application to very large turbulent transition simulations using a spectral approximation is presented. It is shown to have a low impact on the computational time with a reasonable increase of resource usage, while enriching data exploration. Computational steering is performed with real-time adjustment of the simulation parameters, thereby getting closer to a numerical experiment process. This would not have been achieved with a classical work flow using off-line visualization.