- Georgia Institute of Technology, Atlanta (2009 - Present)
- PhD in Physics (Expected Graduation Spring 2017)
- Minor in Mechanical Engineering
- Indian Institute of Technology (IIT) Kharagpur, India (2004 - 2009)
- Integrated Masters in Physics
- Member for
- 3 years 11 months
- Fluid Dynamics - quasi-two-dimensional flows, transition to turbulence, exact coherent structures, thermal convection, computational fluid dynamics
- Nonlinear Dynamics - bifurcations, symmetries, pattern formation
- Topology - persistent homology
A turbulent fluid flow is a classic example of a deterministic, nonlinear system of very high dimensionality (requiring data from several spatial locations for a quantitative description). While nonlinearity generates chaotic dynamics, high-dimensionality makes quantitative analysis in experiments and numerical simulations extremely challenging. Consequently, despite the availability of well defined equations (Navier-Stokes) that determine its evolution, turbulence has been notoriously difficult to understand, characterize, and forecast. My work in Prof. Michael Schatz' Pattern Formation and Control Lab is aimed at developing and testing novel methods to address and overcome these challenges.
Exact Coherent Structures in Two-Dimensional (2D) Turbulence
Recent theoretical advances suggest that turbulence at moderate Reynolds numbers can be understood - its statistical properties as well as its dynamical behaviour - using special solutions of Navier-Stokes equation with nonchaotic temporal behaviour, called Exact Coherent Structures (ECS). We study turbulence generated in experiments by electromagnetically driving a shallow layer of electrolytic fluid. To describe the evolution of the Quasi-Two-Dimensional (Q2D) flow in the experiment we developed a strictly 2D model by depth-averaging the three-dimensional Navier-Stokes equation. We validated the 2D model by comparing the bifurcation sequence as the driving is increased, enroute to turbulence, in numerical simulations with those in the experiment. In the weakly turbulent regime we identified that instants of dramatic slowdown in the dynamics of the turbulent flow are associated with close passes to unstable equilibrium ECS. Furthermore, we found that the turbulent flow departs from the ECS following its unstable manifold, both in experiment and numerical simulations. We are currently exploring the possibility of developing an ECS based forecasting of fluid turbulence.
Using Persistent Homology to Characterise Two-Dimensional Patterns
Recently, ideas from topology have proven useful in characertising patterns and their dynamics in spatiotemporally chaotic systems in an efficient manner. These methods complement the dynamical systems based approach, in that they can be applied to systems for which the governing equations are yet to be formulated. We use Persistent Homology, a branch of algebraic topology, as a tool for symmetry and dimensionality reduction. Equations governing the evolution of spatially extended systems may remain equivariant under certain symmetries. Consequently, patterns that appear distinct, in fact, may be related to each other via a symmetry. Using persistent homology we studied chaotic dynamics in numerical simulations of 2D Kolmogorov flow and Rayleigh Benard Convection (RBC) and have demonstrated reduction of both continuous and discrete symmetries. We have recently started using persistent homology to analyse shadowgraph images from experiments of RBC to identify localised defects such as targets, centers, disclinations, etc in convection roll patterns.
Graduate Research Assistant
- Experimental Observation of Exact Coherent Structures in a Weakly Turbulent Quasi-Two-Dimensional Flow. (APS-DFD Meeting 2015, Boston)
- Search for Exact Coherent Structures in a Quasi-Two-Dimensional Kolmogorov-Like Flow. (APS-DFD Meeting 2014, San Francisco)
- Experimental and Numerical Study of Transition to Turbulence in a Kolmogorov-Like Flow. (APS-DFD Meeting 2013, Pittsburgh)
- Experimental Study of Transition to Turbulence in a Kolmogorov-Like Flow. (APS-DFD Meeting 2012, San Diego)
- Forecasting Flows from Target Pattern Instability in Rayleigh Benard Convection. (APS-DFD Meeting 2011, Baltimore)
- "Forecasting Fluid Flows Using the Geometry of Turbulence." Balachandra Suri, Jeffrey Tithof, Roman O. Grigoriev, and Michael F. Schatz. (In preparation)
- "An Experimental and Numerical Investigation of Bifurcations in a Kolmogorov-like flow." Jeffrey Tithof, Balachandra Suri, Ravi Kumar Pallantla, Roman O. Grigoriev, and Michael F. Schatz. (Under Review) (preprint)
- "Analysis of Kolmogorov Flow and Rayleigh-Bénard Convection using Persistent Homology." Miroslav Kramar, Rachel Levanger, Jeffrey Tithof, Balachandra Suri, Mu Xu, Mark Paul, Michael F. Schatz, and Konstantin Mischaikow. Physica D, Volume 334, 1 November 2016, Pages 82–98 (preprint)
- "Velocity profile in a two-layer Kolmogorov-like flow." Balachandra Suri, Jeffrey Tithof, Radford Mitchell, Jr., Roman O. Grigoriev, and Michael F. Schatz. Phys. Fluids 26.5 (2014): 053601 (preprint)
Honors and Awards Block:
- Kishore Vaigyanik Protsahan Yojana (2005 - 2009) - Awarded by the Department of Science and Technology, Govt. of India.
- Saha Undergraduate Associateship (2005 - 2007) - Awarded by the Saha Institute of Nuclear Physics, Kolkata.
- National Initiative for Undergraduate Science (2005) - Awarded by the Homi Bhabha Center for Science Education and Research (TIFR), Mumbai.