Angular momentum transport in a stratified Taylor-Couette experiment with applications to accretion disks

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Understanding the mechanisms that can result in an outward angular momentum transport is the central problem of planet formation, particularly in the theory of accretion disks. When a planet forms in a disk, angular momentum has to be carried away from the planet otherwise its rotation speed would be far too large. Only turbulence can achieve such a large angular momentum transport. For disks coupled to a magnetic field the Magneto Rotational Instability (MRI) leads to Magneto Hydrodynamic Turbulence and an associated momentum transport. However, accretion disks can be turbulent even in the absence of a magnetic field, e.g. in regions where the ionization fraction is low. In such regions, the disk cannot be unstable due to MRI and it is an important question to ask whether other instabilities can excite turbulence there. Among other candidates the Strato Rotational Instability (SRI) has attracted attention in recent years. The SRI is a purely hydrodynamic instability and much insight can be obtained from particularly designed laboratory experiments and numerical simulations in an axially-stratified Taylor-Couette (TC) setup. Here the stable axial stratification corresponds with the stratification of the disk while the disk's differential rotation can be approximated by rotating the inner and outer cylinder with different speed. We plan to investigate experimentally and numerically the instability and nonlinear saturation of temperature stratified TC flows in a finite height cylindrical gap and measure/calculate angular-momentum transport in the linear and nonlinear regime. The unstable flow transports angular momentum outwards and will therefore be relevant for astrophysical applications. We will consider different regimes and compare the experimental and numerical findings. In particular, we will measure (i) the transition curve over the full range of numerically feasible Reynolds numbers, (ii) the torque in the stable, unstable, and turbulent regime and we will consider the corresponding spatial patterns, and (iii) the transition to turbulence, the energy spectra in the transition and the turbulent regime, and we want to validate the existence of waves or wave turbulence. The study will give quantitative insight into problems of planet formation and accretion disks.