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Origin of instability in Rayleigh stable shear flows including astrophysical accretion disks under various conditions??and its possible link to matter transport and X-ray output therein

Research Group

Banibrata Mukhopadhyay and Soumyendu Raha

Department of Physics, IISc and Computational & Data Sciences, IISc


Astrophysical accretion disks are the natural sites of very high Reynolds number flow, where Reynolds number in the flow around a black hole could be as high as 10^{15}. Note that accretion disks play the indispensable role to identify the existence of black holes. Such rotating shear flows are Rayleigh stable but inferred based on observed data to be turbulent. Hence there is a huge gap in understanding the mismatch between the underlying theory and observation. Similar enigmatic properties are also found in certain laboratory shear flows, e.g. plane Couette flow, plane Poiseuille flow. It is quite reasonable to think that the possible resolution of the said mismatch in astrophysical and laboratory flows is tied up with a single theory. In this project, we venture towards this century old problem mainly centering around two ideas: transient instability and stochastic forcing.

Our basic technical theme is the following. Spatially Fourier transformed or discretized shear flow equations similar to Orr-Sommerfeld/Squire models (which are transformed version of Navier-Stokes equations) used to describe astrophysical accretion disks and Couette and Poiseuille flows constitute differential-algebraic equations when the constraints and/or conservation laws are imposed on the spatially transformed and/or discretized partial differential equations. Due to their structure and due to the effect of various physical conditions, such as high magnetic field and temperature, transient stability of these systems becomes an important property, e.g. governing the physics of the accretion disks in terms of turbulence and transport of matter. Also due to the presence of inherent shear and, hence, some non-zero temperature (however be the magnitude), such flows are naturally driven stochastically (e.g. by white noise). In this proposed project, we shall study to find out if the physical and mathematical structures of these systems also imply local singularities and in turn affect other phenomena such as bremsstrahlung that lead to emission of X-rays etc. from the accretion disks. This might shed enormous light on to uncover the said celebrated old puzzle in fluid physics and astrophysics.
In addition, to using new applied mathematical techniques for modeling transient stability, limited computer simulation is expected to be used for this proposed study.??

We already started working on this problem and a preliminary related result was published jointly by us a few years back in New J. Phys. 13 (2011) 023029, authored by Mukhopadhyay, Mathew, Raha, apart from many other related results published by Mukhopadhyay and Raha independently with their respective group members (e.g. ApJ 830 (2016) 86, authored by Nath and Mukhopadhyay).

 


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