The first-ever detection of gravitational waves a few months back has reconfirmed our picture of the universe. Specifically, it corroborated the existence of black holes, one of the most mysterious and yet interesting constituents of the universe. While much that we know about black holes has now been proved to be correct, there is still a lot that we do not fully understand about them. Some more information about black holes can potentially be revealed by our group’s recent work on fluid dynamics. Our group has been successful in finding a solution to a long-standing (century old) problem in fluid dynamics, the results of which can be applied to know a little more about the properties of black holes. Based on a part of this work, one of my students, Sujit Kumar Nath, completed his PhD thesis.
In laboratory experiments, scientists have very often observed that a turbulent motion is induced in a viscous fluid when it is exposed to some ‘disturbance’ and perturbation. This turbulent motion is generated in the fluid as the result of perturbation that increases with time, even after the disturbance is over. Unless controlled, this perturbation grows till infinite time, and leads to this turbulence. Scientists have been unable to satisfactorily explain why this happens in certain flows. Existing mathematical models on fluid dynamics have so far not been able to account for this turbulent motion.
Such kind of motion is very evident in a specific kind of fluid flow called Couette flow. It was while studying this Couette flow that we got a clue to the possible explanation to the problem. Plane Couette flow, the simpler version of Couette flow, involves a system in which a fluid is trapped between two solid boundaries moving in opposite direction, or having a relative difference in velocities. The layers of fluid along the opposite boundaries develop a differential velocity relative to each other. This differential velocity reduces as we move towards the middle of the fluid layer and at some point it turns zero. In absence of disturbance, fluid seems stable, but a particle between two layers, having different velocities, would still be dragged, producing some thermal fluctuation therein. It causes the fluid particles to have random motion that we called ‘noise’. This ‘noise’ had so far been overlooked in calculations.
When we included this ‘noise’ in our calculations, along with conventional disturbance, the results thrown by mathematical models were in conformity with the experimental observations.
This explanation of ever-increasing perturbation in fluids exposed to some disturbance is a significant breakthrough in itself. An important problem in fluid dynamics has been solved. But this solution has important implications for similar problem in astrophysics as well.
We know that black holes keep attracting matter from nearby stars and other objects. We also know that these stars, being attracted by black holes, have their own revolution. Hence, the matter separating from the stars attains a tangential velocity as well, along with its radial velocity due to a black hole’s massive pull. Because of this, all the mass flying towards a black hole start moving in a spiral fashion, giving rise to what is known as ‘accretion disc’ around the black hole.
Just like in Couette flow, observationally inferred turbulent motion cannot be explained by mathematical/theoretical modeling in accretion discs as well.
The difference in tangential and radial velocities gives rise to a situation very similar to that in the Couette flow. The flow profile interpreted from observed data in the accretion disc is comparable to what we see in the fluids in the laboratory experiments.
We therefore believe that some ‘noise’ must be getting generated in the accretion discs as well which we must be neglecting till now from our equations. All our information about black holes comes from observations of the accretion disc, since there is no way to ‘see’ the black holes directly. If the accretion disc is not modelled properly, we might get erroneous information about black holes.
We believe that some important modifications in our model of the accretion disc seem necessary. And this modification is likely to reveal new information about the properties of black holes.
Banibrata Mukhopadhyay & team, IISc, Bangalore