Linear dynamics of weakly viscous accretion disks: A disk analog of Tollmien-Schlichting waves

This paper discusses new perspectives and approaches to the problem of disk dynamics where, in this study, we focus on the effects of viscous instabilities influenced by boundary effects. The Boussinesq approximation of the viscous large shearing box equations is analyzed in which the azimuthal length scale of the disturbance is much larger than the radial and vertical scales. We examine the stability of a non-axisymmetric potential vorticity mode, i.e. a PV-anomaly. in a configuration in which buoyant convection and the strato-rotational instability do not to operate. We consider a series of boundary conditions which show the PV-anomaly to be unstable both on a finite and semi-infinite radial domains. We find these conditions leading to an instability which is the disk analog of Tollmien-Schlichting waves. When the viscosity is weak, evidence of the instability is most pronounced by the emergence of a vortex sheet at the critical layer located away from the boundary where the instability is generated. For some boundary conditions a necessary criterion for the onset of instability for vertical wavelengths that are a sizable fraction of the layer's thickness and when the viscosity is small is that the appropriate Froude number of the flow be greater than one. This instability persists if more realistic boundary conditions are applied, although the criterion on the Froude number is more complicated. The unstable waves studied here share qualitative features to the instability seen in rotating Blasius boundary layers. The implications of these results are discussed. An overall new strategy for exploring and interpreting disk instability mechanisms is also suggested.Comment: Accepted for publication in Astronomy and Astrophysics. 18 pages. This version 3 with corrected style fil

Hydrodynamic stability of rotationally supported flows: Linear and nonlinear 2D shearing box results

We present here both analytical and numerical results of hydrodynamic stability investigations of rotationally supported circumstellar flows using the shearing box formalism. Asymptotic scaling arguments justifying the shearing box approximation are systematically derived, showing that there exist two limits which we call small shearing box (SSB) and large shearing box (LSB). The physical meaning of these two limits and their relationship to model equations implemented by previous investigators are discussed briefly. Two dimensional (2D) dynamics of the SSB are explored and shown to contain transiently growing (TG) linear modes, whose nature is first discussed within the context of linear theory. The fully nonlinear regime in 2D is investigated numerically for very high Reynolds (Re) numbers. Solutions exhibiting sustained dynamics are found and manifest episodic but recurrent TG behavior and these are associated with the formation and long-term survival of coherent vortices. The life-time of this spatio-temporal complexity depends on the Re number and the strength and nature of the initial disturbance. We show results for a case in which the dynamical activity persists for the entire duration of the simulation (hundreds of box orbits). Some combinations of the Re number and the initial perturbation spectrum (and strength) show the transiently growing phenomenon to ultimately fade away or, in some instances, to be absent altogether. Because the SSB approximation used here is equivalent to a 2D incompressible flow, the dynamics can not depend on the Coriolis force. Therefore, three dimensional (3D) simulations are needed in order to decide if this force indeed suppresses nonlinear hydrodynamical instability in rotationally supported disks in the shearing box.Comment: Submitted to A+A on April 1, 2004, Accepted August 3, 200

Functional associations at global brain level during perception of an auditory illusion by applying maximal information coefficient

Maximal information coefficient (MIC) is a recently introduced information-theoretic measure of functional association with a promising potential of application to high dimensional complex data sets. Here, we applied MIC to reveal the nature of the functional associations between different brain regions during the perception of binaural beat (BB); BB is an auditory illusion occurring when two sinusoidal tones of slightly different frequency are presented separately to each ear and an illusory beat at the different frequency is perceived. We recorded sixty-four channels EEG from two groups of participants, musicians and non-musicians, during the presentation of BB, and systematically varied the frequency difference from 1 Hz to 48 Hz. Participants were also presented non-binuaral beat (NBB) stimuli, in which same frequencies were presented to both ears. Across groups, as compared to NBB, (i) BB conditions produced the most robust changes in the MIC values at the whole brain level when the frequency differences were in the classical alpha range (8-12 Hz), and (ii) the number of electrode pairs showing nonlinear associations decreased gradually with increasing frequency difference. Between groups, significant effects were found for BBs in the broad gamma frequency range (34-48 Hz), but such effects were not observed between groups during NBB. Altogether, these results revealed the nature of functional associations at the whole brain level during the binaural beat perception and demonstrated the usefulness of MIC in characterizing interregional neural dependencies