Supersonic Shear Instabilities in Astrophysical Boundary Layers

Disk accretion onto weakly magnetized astrophysical objects often proceeds via a boundary layer that forms near the object's surface, in which the rotation speed of the accreted gas changes rapidly. Here we study the initial stages of formation for such a boundary layer around a white dwarf or a young star by examining the hydrodynamical shear instabilities that may initiate mixing and momentum transport between the two fluids of different densities moving supersonically with respect to each other. We find that an initially laminar boundary layer is unstable to two different kinds of instabilities. One is an instability of a supersonic vortex sheet (implying a discontinuous initial profile of the angular speed of the gas) in the presence of gravity, which we find to have a growth rate of order (but less than) the orbital frequency. The other is a sonic instability of a finite width, supersonic shear layer, which is similar to the Papaloizou-Pringle instability. It has a growth rate proportional to the shear inside the transition layer, which is of order the orbital frequency times the ratio of stellar radius to the boundary layer thickness. For a boundary layer that is thin compared to the radius of the star, the shear rate is much larger than the orbital frequency. Thus, we conclude that sonic instabilities play a dominant role in the initial stages of nonmagnetic boundary layer formation and give rise to very fast mixing between disk gas and stellar fluid in the supersonic regime.Comment: 35 pages, 6 figures, submitted to Ap

The Properties of G-modes in Layered Semi-Convection

We study low frequency waves that propagate in a region of layered semi-convection. Layered semi-convection is predicted to be present in stellar and planetary interiors and can significantly modify the rate of thermal and compositional mixing. We derive a series of analytical dispersion relations for plane-parallel layered semi-convection in the Boussinesq approximation using a matrix transfer formalism. We find that like a continuously stratified medium, a semi-convective staircase -- in which small convective regions are separated by sharp density jumps -- supports internal gravity waves (g-modes). When the wavelength is much longer than the distance between semi-convective steps, these behave nearly like g-modes in a continuously stratified medium. However, the g-mode period spacing in a semi-convective region is systematically {\em smaller} than in a continuously stratified medium, and it decreases with decreasing mode frequency. When the g-mode wavelength becomes comparable to the distance between semi-convective steps, the g-mode frequencies deviate significantly from those of a continuously stratified medium (the frequencies are higher). G-modes with vertical wavelengths smaller than the distance between semi-convective steps are evanescent and do not propagate in the staircase. Thus, there is a lower cutoff frequency for a given horizontal wavenumber. We generalize our results to gravito-inertial waves relevant for rapidly rotating stars and planets. Finally, we assess the prospects for detecting layered semi-convection using astero/planetary seismology.Comment: 13 pages, 5 figures, accepted to MNRA

Threshold of microvascular occlusion: injury size defines the thrombosis scenario

Damage to the blood vessel triggers formation of a hemostatic plug, which is meant to prevent bleeding, yet the same phenomenon may result in a total blockade of a blood vessel by a thrombus, causing severe medical conditions. Here, we show that the physical interplay between platelet adhesion and hemodynamics in a microchannel manifests in a critical threshold behavior of a growing thrombus. Depending on the size of injury, two distinct dynamic pathways of thrombosis were found: the formation of a nonocclusive plug, if injury length does not exceed the critical value, and the total occlusion of the vessel by the thrombus otherwise. We develop a mathematical model that demonstrates that switching between these regimes occurs as a result of a saddle-node bifurcation. Our study reveals the mechanism of self-regulation of thrombosis in blood microvessels and explains experimentally observed distinctions between thrombi of different physical etiology. This also can be useful for the design of platelet-aggregation-inspired engineering solutions.Comment: 7 pages, 5 figures + Supplementary informatio