Vortex in space – Cotutelle promotion on rotating discs

Gabriel Maltese Meletti de Oliveira from Brazil was the first graduate to complete a Cotutelle doctorate at BTU. As part of this programme, he also spent some time researching at the partner university Aix-Marseille in France. Here he explains what his doctorate is about. It is entitled "High-performance computing and laboratory experiments on strato-rotational instabilities".

Dr.-Ing. Gabriel Meletti

Terrestrial and astronomical vortex systems

Stratified vortices can be found on small to large scales in geophysical and astrophysical flows. On the one hand, tornadoes and hurricanes can cause devastation and even lead to large numbers of casualties. On the other hand, these vortices distribute heat and momentum in the atmosphere, which is particularly important for a habitable environment on Earth.

In the astrophysical context, accretion disks can be seen as stratified vortices. These disks, rotating around a central object (e.g. a black hole), pull matter towards the centre.

In such systems, understanding the mechanisms that can lead to a transport of angular momentum outwards is a central problem. For a planet or star to form in a disc, angular momentum must be carried away from its centre to allow matter aggregation by gravity. Otherwise, its rotational velocity would be far too great for this matter aggregation (and consequent star formation) to occur.

Matter in a spin cycle

The phenomenon is comparable to a spinning washing machine: due to the rotation, we could expect matter in an accretion disc to be spun away radially, just as laundry reaches the outer wall of the washing machine after being spun. So the fact that matter in the centre of a disk clumps together to form stars, as observed by many telescopes, needs to be better understood because the gravitational forces are smaller than the outward angular momentum forces that result from rotation.

In such gas systems, turbulence is the most likely mechanism to achieve such a large angular momentum transport, and the question is how to generate the turbulence. Among other candidates, strato-rotational instability (SRI) has attracted attention in recent years. SRI is a purely hydrodynamic instability that can be modelled by two concentric cylinders rotating at different velocities, added to a stable density stratification due to axial salt or temperature gradients. This type of stratification can be observed, for example, in our planet's atmosphere or in the oceans, when the Sun warms the upper part of the oceans, making them lighter (less dense), and the temperature decreases with depth, making them heavier and consequently denser.

Investigation of strato-rotational instability

In this work, a combined experimental and high-performance computing study of new specific behaviours of strato-rotational instability (SRI) was carried out. Density stratification causes a change in the marginal instability transition to turbulent regimes, making the flow unstable in regions where - without stratification - it would be stable. This property makes SRI a relevant phenomenon in planetary and astrophysical applications, especially in accretion disk theory, where stable density stratification arises due to the denser matter at the centre of the disks and the interactions of the outer regions of the disk with cosmic rays in space.

Despite many advances in the understanding of stratospheric flows, the comparison of experimental data with nonlinear numerical simulations remains relevant, as it involves linear aspects and nonlinear interactions of the SRI modes that still need to be better understood. These comparisons also reveal new nonlinear phenomena and patterns not previously observed in SRI that can contribute to our understanding of geophysical flows.

Doctorate deals with current issue in astrophysics

Modulations in velocity and temperature profiles have been shown to be associated with spirals in the axial direction that form due to instability. Recent astronomical observations made in early 2020 with the Very Large Telescope (VLT), a large facility in the Atacama Desert, have also captured spirals in an accretion disk at an early stage of star formation in the centre of the disk. These observations made the study of these spiral signatures and dynamics a timely and relevant topic for astrophysics, as they could play an important role in our further understanding of planet and star formation in accretion disks. These modulations have also been shown to have an impact on momentum transfer in accretion disks, which could have a major impact on how stars form in the centre of an accretion disk, as the controls on matter accretion could change over time. Observations in accretion disks of galaxies with similar cylindrical geometry also show modulated phenomena of energy transfer and other similar signatures that we observe in our SRI evaluations. Therefore, SRI could help to understand various phenomena related to the relevant problem of how stars and solar systems are formed, which ultimately has everything to do with our understanding of how life itself can exist in our solar system and on our planet.