Session GM4: Mini-conference on Angular Momentum Transport in Laboratory and Nature I

The angular momentum cycle in tropical cyclones: transport, dissipation, and wave-mean flow interactions

Like all strong atmospheric vortices, tropical cyclones (hurricanes) are formed and maintained by the principle of angular momentum conservation. In the developing stage, a net transport of angular momentum into the core region, combined with a contraction of the radius of maximum winds, leads to a large intensification of the vortex. In the mature stage, a quasi-steady balance is maintained between inward transport of angular momentum, loss through the surface due to friction, and a redistribution of angular momentum by both vortex-Rossby waves and inertia-buoyancy waves. When cyclones reach a sufficient strength, these waves can become unstable, leading to a rapid redistribution of angular momentum that ultimately limits the duration of the most intense periods.   

Transport by Vortices in Protoplanetary Disks

We present calculations and analyses of 3D vortices embedded in the vertically-stratified, rotating, shearing environment of a nearly Keplerian accretion disk around a protostar. The vortices can efficiently transport angular momentum radially away from the protostar, enabling mass to accrete on the protostar at rates of approximately one solar mass per million years, or higher. They also are efficient at accumulating dust grains, which is important in planetesimal formation. The vortices are most stable when they are located off the mid-plane of the protoplanetary disk. The 3D vortices are very robust - in part due to the fact that like-signed vortices embedded in a like-signed shear readily merge. The vortices do not require an ad hoc set of arbitrary or unlikely initial conditions. They can form from white noise, but the easiest, and probably most plausible, way in which they form is from internal gravity waves. Simulations show that almost any type of perturbation fills the disk with inertial-gravity waves. The waves ``break'' when they get too far from the disk mid-plane, and then form intense vortices, which readily merge together if they are anticyclonic.   

Theory of momentum transport in rotating/stratified HD and MHD turbulence

The importance of magnetic fields, rotation, and stratification in momentum transport cannot be overemphasized. They excite waves in the system, which modify the property of turbulence, with a crucial effect on transport. Indeed, one of the main difficulties in stellar rotational evolution theory has been the lack of a consistent theory of momentum transport incorporating complex physical interactions between turbulence, waves, and shear flow. In particular, while shear flow is often considered to be a source of turbulence, the effect of stable shear flow on regulating turbulence has been totally ignored in traditional modelling. Here, we first show that shear flows can quench turbulence, leading to weak, anisotropic turbulence and momentum transport [1]. Strong anisotropy caused by shear flow leads to non-diffusive momentum transport (like alpha effect in dynamos) in rotating turbulence [2]. Furthermore, in strongly stratified medium, momentum transport becomes anti-diffusive, with negative eddy viscosity, offering a mechanism for the formation of layer-like structure. The effect of magnetic field on transport reduction by the cancellation of Reynolds stress by Maxwell stress is demonstrated [3]. [1] N. Leprovost and E. Kim, A\&A, 456, 617 (2006) [2] N. Leprovost and E. Kim, A\&A, L654, 1166 (2007) [3] E. Kim and N. Leprovost, A\&A, 468, 1025 (2007); 465, 633 (2007)   

Angular Momentum Transport Studies Relevant to Astrophysical Accretion Disks with the Princeton MagnetoRotational Instability Experiment

Observationally-inferred rates of angular momentum transport in accretion disks are too large to be explained by a non-turbulent viscosity. Investigation of vertically-thin disks has focused on two sources of instability to drive a turbulent viscosity: the MagnetoRotational Instability (MRI) and Subcritical Hydrodynamic Instability (SHI). In MRI, a weak ambient magnetic field linearly destabilizes otherwise neutral hydrodynamic displacements. In SHI, transient amplification of linear disturbances by the differential rotation allows access to non-linearly unstable modes. The Princeton MRI experiment investigates both instabilities. It consists of a Couette-Taylor apparatus which uses water or liquid Gallium alloy to reliably generate rotating flows with linear stability properties analagous to astrophysical disks. In contrast to previous claims, we find no evidence of SHI in water at Reynolds numbers of order one million. We argue that SHI cannot provide astrophysically relevant rates of angular momentum transport. Our hydrodynamically stable flows provide an opportunity to make a conclusive detection of the MRI. The first results of our search for the MRI will be presented. Supported by DOE, NSF and NASA.   

Numerical simulations of magneto-rotational turbulence in cylindrical geometry.

We present numerical simulations of magneto-rotational flows in cylindrical Couette geometry. To the best of our knowledge these simulations are the most highly resolved in this geometry to date. We study regimes in which the magneto-rotational instability is strongly supercritical, and its nonlinear evolution leads to the development of turbulence. We show that in these regimes, the flows act as efficient dynamos and the turbulence persists even in the absence of an externally imposed magnetic field. The mechanism responsible for the saturation amplitude of the turbulence involves both an increase in dissipation and a modification of the background rotational profile. The angular momentum transport is mostly by the Maxwell stresses, and is enhanced from its collisional value by a factor of the order the Reynolds number of the fluctuating velocity.   

Experimental results on the magnetorotational instability in helical magnetic fields

The magnetorotational instability (MRI) is believed to play a crucial role in the formation of stars and black holes. By destabilizing otherwise stable Keplerian flows, the MRI enables outward transport of angular momentum in accretion discs which is a necessity for the growth of the central objects. Usually, MRI is investigated under the assumption of an externally applied axial magnetic field. However, the effort to investigate the MRI in a liquid metal experiment can be dramatically reduced if the purely axial magnetic field is replaced by a helical magnetic field. We summarize the results of a various Taylor-Couette experiments [1,2,3] with the liquid metallic alloy GaInSn under the influence of helical magnetic fields that show typical features of MRI at Reynolds numbers of the order 1000 and Hartmann nubers of the order 10. \newline [1] F. Stefani et al. (2006), Phys. Rev. Lett. 97, 184502. \newline [2] G. R\"udiger et al. (2006), Astrophys. J. 649 (2006), L145-L147. \newline [3] F. Stefani et al. (2007), New J. Phys. (2007), in press; astro-ph/0701030.   

Axisymmetric Numerical and Analytical Studies of the Helical Magnetorotational Instability in a Magnetized Taylor-Couette Flow

Recently, Hollerbach and R\"{u}diger have reported that MRI modes may grow at much reduced $R_{\rm m}$ and $S$ in the presence of a helical background field, a current-free combination of axial and toroidal field. We have investigated these helical MRI modes. In vertically infinite or periodic cylinders, resistive HMRI is a weakly destabilized hydrodynamic inertial oscillation propagating axially along the background Poynting flux. Growth rates are small, however, and require large axial currents. The new mode is stable in Keplerian flow profiles regardless of end conditions. Furthermore, inviscid studies show finite cylinders with insulating endcaps reduce the growth rate and stabilize highly resistive flows entirely, which conflicts with the PROMISE observation at low magnetic Reynolds number. However, in viscous simulations, by accurately modeling all viscous and magnetic boundaries, we reproduce the measured wave patterns and their amplitudes. Contrary to previous claims, the waves are shown to be transiently amplified disturbances launched by viscous boundary layers rather than globally unstable magnetorotational modes.