Opportunities

 Current openings:

I will have an opening in July 2025 for a TA PhD student to work on "numerical modelling of transport phenomena" liquid metal batteries (so as to make them more efficient and safer) and another (TAP) student to work on "liquid metal cooling and its control using magneto-hydro-dynamics" in collaboration with other colleagues. Information about PhD program is given here. 

Before you consider a PhD please read this advice. To enroll into PhD program, you need a masters (M.Tech./M.S.) degree or a GATE score if you wish to enroll directly after B.Tech. (IIT graduates with CPI/CGPA 8.0 or above do not need a GATE score). More information about these programs & entrance procedure is given here . IITB students who wish to work with me for their MTech or BTech (honours) project should contact me by email. There are no openings for interns at present - your email may not get any response. 

General guidelines & expectations:

I love exploring the 'mechanisms' behind the phenomena that we observe in engineering or physical scenarios.  The language in which this is described is mathematics.  If you are someone who wishes to work with me, I would expect that you share my inquisitiveness & enthusiasm for fluid mechanics and mathematics and have a firm grasp of the basic fundamentals (at least UG level). Most of my work is computational. I would expect, therefore, that you must be adept with multivariable & vector calculus, ODEs, PDEs, Fourier Transforms and Linear Algebra. Also, I would expect that you have good writing skills in technical English, excellent programming skills (Fortran/ Python/ C/C++) and good knowledge of softwares such as Matlab/Matplotlib/Scilab etc.  If you have acquired knowledge of (open-source) computational fluid dynamics (CFD) softwares such as OpenFOAM, it is an added advantage.  Communication skills will be evaluated with a oral/written test before I can take you in my group.

The PhD degree is different from the (masters/bachelors) education you have acquired so far - here you learn to think & act independently and add at least an 'iota' (a small amount) to the existing knowledge base. The oral exam at the end of PhD is called 'defense' because you defend your thesis in front of the examiners to prove whether you've really added something or not. Therefore, a PhD requires considerable amount of time, energy & effort from the student apart from resilience, perseverance & patience. The time it takes to earn a PhD (4+ years) depends on several factors such as the nature/difficulty of the problem, the methods, resources, time spent, efficiency, intelligence and attitude, prior knowledge & training, etc.  Do NOT enroll into a PhD program unless you are prepared to devote a significant amount of your time & sacrifice some other aspects of your life for the PhD duration (actually, the real challenge is how you efficiently mange your time!). However, the reward at the end, in terms of your general aptitude, attitude and skill-set, is something you will cherish for your entire lifetime. Read this page  (apart from this) to know whether a PhD is something you really want.

If you wish to work with me as a Post-Doc, in addition to the above-mentioned skill-set, I would expect that you have good publications from your PhD thesis, and you have an ability to work independently. A Post-Doc project is often a short-term, focused, goal-based research work quite unlike PhD where there is often more time available to explore.  

Some of the research questions/ ideas that I am working on or planning to work on are listed below. Further details (for e.g. relevant publications) can be obtained from Google scholar or by emailing me your interest areas & CV at "avishekr [at] iitb [dot] ac [dot] in". Feel free to go through my publications in some of these areas, the list of which is here (please email me if you are not able to download them for any reason). Your project can be computational/theoretical/experimental, and may comprise major or minor aspects of these topics (or some other similar topics) depending on mutual interests. Please read this and this before you write and send your email.  

1. Flow in liquid metal batteries

A promising method of energy storage is using Liquid Metal Batteries (LMB). This method, if perfected, could enable cheap & large-scale (stationary) storage of electrical energy from intermittent renewable sources and also reduce the fluctuations that are expected when renewables are integrated with the grid. Watch this TED talk by Prof Sadoway from MIT. There are several forces at play in a LMB - buoyancy, magnetic field, surface tension, etc. I am interested in studying the flow physics inside a LMB using computational fluid dynamics and, later on, using experiments. The findings from the project will provide input to the battery designers. The image below shows the rich variety of phenomena that can be explored.

2. Flow in rotating compressor cavities

This project will investigate the buoyancy-induced flow in rotating compressor cavities, where the Coriolis force is known to create cyclonic and anticyclonic circulations (similar to those in the atmosphere/oceans). An accurate prediction of the transient convective heat transfer from the compressor blades, which in turn is important for ascertaining the radial growth of compressor discs, is crucial for the aircraft industry. This work will be computational, using the open source CFD solvers of OpenFOAM or any other open source CFD software.

3. MHD flow in continuous casting of metals

When a metal such as steel, aluminum undergoes continuous casting, a static magnetic field is applied to suppress unwanted motion within the mold for the purpose of ensuring purity. (The Lorentz force due to a field perpendicular to the flow will try its best to oppose the flow.) However, if the flow is turbulent, the transient flow behaviour is much more complex than what is expected. The project will explore this subject using CFD and/or experiments. Another application of MHD in casting is electromagnetic stirring to ensure a homogeneous cast. For more details on this project, read the Chapter 9/11 (old/new editions) of the book 'Introduction to Magnetohydrodynamics' by Prof P A Davidson (this book contains the basic theory relevant for almost all projects listed here).

4. Structure formation in rotating turbulence

Columnar flow structures have been observed in direct numerical simulations of rotating turbulence. Their mechanism of formation is not properly understood. One popular explanation uses nonlinear resonant-triad interactions between inertial waves and the resulting transfer of energy into horizontal wavevectors. Another explanation is using purely linear wave propagation of low-frequency inertial waves. So far, there is no clear explanation on why & how exactly the columns form. Is the column below a vortex or wavepacket, or both, or... ?  The project will explore these questions using direct numerical simulations (DNS) with the help of techniques such as wave-vortex decomposition, FFT, wavelet analysis, etc.

5. Rotating-stratified turbulence & the dynamics of inertia-gravity waves

We know that the propagation of low-frequency inertial waves can lead to the formation of columnar structures from a layer of turbulence. Analogously, the propagation of low-frequency internal gravity waves leads to the formation of 'pancake' or 'uthapam'-like flow structures in stratified turbulence as shown below. What happens if rotation & stratification are simultaneously present? It turns out this is not so straightforward to answer. In some situations or configurations, there are no waves at all, and in another situation there are inertia-gravity waves depending on how gravity & rotation vectors are aligned. The project will involve investigating these questions using DNS.

6. Magnetohydrodynamic turbulence & structure formation

This project will involve studying the effect of magnetic field on turbulence at low and high magnetic Reynolds number (ratio of magnetic induction to diffusion). For e.g. one question that can be asked is: what do the kinetic and magnetic energy spectrum and the flow look like at varying strengths of the magnetic field? The applications of this work are in geophysical (Earth's core) & astrophysical (cores of Jupiter, sun, stars) scenarios as well as in engineering (for e.g. flow in tokamaks). This project will also be computational using DNS in a periodic box.

7. Geophysical flow & turbulence

This project will involve computations in a spherical shell geometry using a code called MagIC freely available at https://github.com/magic-sph/magic. The code can be used to study rotating convection with or without a magnetic field. The applications may include core/mantle of the Earth, atmosphere-oceans, or even the cores of other planets, Sun and stars. If you wish to work on geophysical/ astrophysical fluid mechanics for spherical bodies, then this project is for you. This is open to students from physics and geophysics background who are good in fluid dynamics, mathematics and computational methods.