Session R14: Rotating Flows II

Boundary layers and global stability of laboratory quasi-Keplerian flow

Studies in the HTX device at PPPL, a modified Taylor-Couette experiment, have demonstrated a robust stability of astrophysically relevant, quasi-Keplerian flows. Independent rings on the axial boundary can be used to fine tune the rotation profile, allowing ideal Couette rotation to be achieved over nearly the entire radial gap. Fluctuation levels in these flows are observed to be at nearly the noise floor of the laser Doppler velocimetry (LDV) diagnostic, in agreement with prior studies under similar conditions. Deviations from optimal operating parameters illustrate the importance of centrifugally unstable boundary layers in Taylor-Couette devices of the classical configuration where the axial boundaries rotate with the outer cylinder. The global stability of nearly ideal-Couette flows, with implications for astrophysical systems, will be discussed in light of the global stability of these flows with respect to externally applied perturbations of large magnitude.   

Hydrodynamic turbulence in quasi-Keplerian rotating flows?

The origin of turbulence in astrophysical accretion discs has been under scrutiny for decades and remains still unclear. The velocity profiles of discs (Keplerien profiles) are centrifugally stable and therefore a different instability mechanism is required for turbulence to arise. While in hot discs turbulence can be triggered through magnetorotational instability, cooler discs lack sufficient ionization and it is unclear how turbulence sets in. In analogy to other linearly stable flows like pipe and Couette flow, subcritical transition to turbulence may be the mechanism. Recently, experimental studies of Taylor-Couette flow in quasi-Keplerian regime have given conflicting results and numerical simulations of above experimental flows showed that the top and bottom end-wall leads to strong deviations from the Keplerian velocity profile and drives turbulence. In order to clarify this, we perform direct numerical simulations of incompressible Taylor-Couette flow without end walls in the quasi Keplerian regime for Re up to 200000. Strong transient growth is observed and gives rise to strongly disorted motion, suggesting that for large enough Re this mechanism may lead to turbulence even for Keplerian flows.   

Geometrical statistics of the vorticity vector in rotating turbulence

We report results on the geometrical statistics of the vorticity vector obtained from particle tracking experiments in electromagnetically forced rotating turbulence. A range of rotation rates is considered, from non-rotating to rapidly rotating turbulence. Based on the full set of velocity derivatives, measured in a Lagrangian way by 3D Particle Tracking Velocimetry, we have been able to quantify statistically the effect of system rotation on several flow properties. We have studied the orientation of the vorticity vector with respect to the three eigenvectors of the local strain rate tensor and with respect to the vortex stretching vector. Additionally, we have quantified the role of system rotation on the self-amplification terms of the enstrophy and strain rate equations and the direct contribution of the background rotation on these evolution equations. The main effect of background rotation is the strong reduction of extreme events and related (strong) reduction of the skewness of PDFs of several quantities such as, for example, the intermediate eigenvalue of the strain rate tensor and the enstrophy self-amplification term. These results reflect the two-dimensionalisation of the flow at the highest rotation rates.   

Torque scaling and number of states in turbulent Taylor-Couette flow

Torque measurements in a Taylor-Couette flow over a range of velocities up to a Reynolds number of 16 000 are presented. Here only the inner cylinder is rotating, the radius ratio is 0.9 and the aspect ratio is 30. Simultaneously to the torque, the evolution of the flow pattern is observed. Different states are observed depending on the range of Reynolds. The relationship between the states, the speed and the torque is studied in the form of scaling laws. The effect of the number of vortices and the meaning of the exponents will be discussed. In addition to Newtonian fluids, polymer solutions are also used. Specifically, the properties of low concentrations of high molecular weight poly-ethylene-oxide in water will be reported. The effect of the additives to the flow patterns and the torque scaling will be discussed.   

Turbulence decay towards the linearly-stable regime of Taylor Couette

DNS of turbulence decay in Taylor-Couette flow in the linearly stable regime is presented. A fixed radius ratio $\eta=0.714$ is used, and initial Reynolds numbers of up to $Re\sim10^5$ are reached. Simulations are run in an axially-periodic domain, and thus completely lack the end-plates effects which are present in experiments and cause Ekman effects leading to a supercritical transition to turbulence. Here, we start with a fully turbulent state in the unstable regime and enter the linearly stable regime by suddenly starting a (stabilizing) outer cylinder rotation. This stabilization causes the system to behave as a damped oscillator and correspondingly the turbulence decays. The evolution of the torque and wind kinetic energy is analysed and the period and damping of the oscillations are quantified as a function of Reynolds number.   

Angular momentum transport and flow super-rotation in Rayleigh stable Taylor-Couette

We present experimental velocimetry and torque measurements for Taylor-Couette flow in the Rayleigh stable regime. Measurements are taken on two geometrically similar experiments, both of which had axial boundaries attatched to the outer cylinder, which is known to cause Ekman pumping. The Twente experiment has a radius ratio of 0.716, an aspect ratio of 11.68, and measures azimuthal velocities by Laser Doppler Anenometry. The Maryland experiment has a radius ratio of 0.725, an aspect ratio of 11.47, and measures the torque required to rotate the inner cylinder. The torque on the inner cylinder is observed to be greater than that of the analytical Couette profile and has a complex dependence on the Reynolds number and $\Omega_i / \Omega_o$. The azimuthal velocity profiles also deviate from the laminar Couette profile. Signficantly, super-rotation in the angular velocity has been observed for $1 > \Omega_i / \Omega_o > 0$. In the quasi-Keplerian regime, the angular momentum profiles consist of an approximately constant inner region connected to an outer region approximately in solid-body rotation at $\Omega_o$, which suggests that angular momentum is being actively transported from the inner region to the axial boundaries.   

Receptivity Mechanisms in a Rotating Torus: Experiments and Simulations

We consider the flow within a rotating fluid-filled torus subject to a sudden change in angular velocity. Previous DNS computations showed the occurence of boundary-layer separation (Hewitt et al., JFM 688), which was conjectured to be linked with structures observed in the top-down visualisations of Madden \& Mullin (JFM 265). These showed a ``flow front'' in the equatorial plane propagating from the outer wall, the position of which was seen to match well with the separated flow structures seen in the DNS. However, in the experiments a second streak was observed at later times on the opposite wall, not seen in the DNS. To better understand this structure, we present the first measurements of the cross-sectional flow, using PIV on an experiment designed to overcome the optical issues in cross-sectional measurements. These demonstrate both the post-separated flow structures seen in earlier DNS, as well as the appearance of a vortex-pair on the opposite equator. These we believe to be likely candidates for the second fronts noted in the Madden experiments. We hypothesise that this vortex pair is generated by small geometric imperfections, an idea seemingly borne out by striking agreement with new DNS conducted in a modified geometry that better represents experimental reality.   

Whirling skirts

Steady dihedral patterns, consisting of sharply peaked traveling waves, may be observed on a spinning skirt. These qualitative features are captured with a minimal model of flowing material on an inextensible, flexible, generalized-conical sheet rotating about a fixed axis. Analytical results indicate that Coriolis forces are essential for establishing the wave patterns, which arise only for a narrow range of Rossby number.