Applied mathematics symposium: Instability and flow transition

Update (01.01.2023): The recordings of the talks are embedded below. You can also watch the entire playlist here.

Together with Satyajit Pramanik I am co-organising an applied mathematics symposium loosely based on the theme of instability and flow transition. There will be nine invited talks from faculty, postdocs and students working in the broad area. There will also be a plenary talk by Professor Hendrik Kuhlmann (TU Vienna). The flyer and program for the event is below or can be downloaded here. The abstracts of the talks can be found further below.

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Plenary talk

Professor Hendrik Kuhlmann (TU Vienna)

"Attractors for density-matched particles in steady incompressible three-dimensional flow"

Small finite-size spherical particles which have the same density as an incompressible fluid almost move like the fluid. Therefore, they are often used as tracers. However, if such a particle is transported very close to a tangentially moving boundary (wall or free surface), it may not be able to follow the flow owing to its finite size. In recirculating laminar flow this particle-boundary interaction can lead to attractors for the moving particle. Experimental and numerical results for the phenomenon are presented, ranging from thermocapillary liquid bridges to cavity flows, and a simple model is discussed to explain the phenomenon. The effect may find application in two-phase micro-flows when it comes to manipulate the motion of suspended particles. The figure shows experimental Poincare sections of trajectories of different neutrally-buoyant spherical particles in a three-dimensional cavity flow. The particle size is coded by color. One can recognize chaotic motion (grey), quasi-periodic motion (e.g. cyan) and periodic motion (e.g. yellow or blue). Reproduced from Wu et al., JFM 906, A4 (2021).

Invited talks

Dr. Siddhartha Mukherjee (ICTS Bengaluru)

"Transition to universality and Lagrangian anomalies in active turbulence"

Download this abstract here.

Dr. Gautam Kumar (IFCAI Tech, IFHE Hyderabad)

"Linear and Nonlinear thermosolutal instabilities in an inclined porous layer"

Download this abstract here.

Professor Morten Brons (TU Denmark)

"Topological bifurcations in the transition from two single vortices to a pair and a single vortex in the periodic wake behind an oscillating cylinder"

The formation of vortices in the wake behind a bluff body is a robust and ubiquitous phenomenon in nature and technology. The typical situation is the periodic von Kármán vortex street behind a circular cylinder which is known as a 2S mode: Two single vortices of opposite circulation are shed during each cycle. If cylinder is also allowed to move, either by external forcing or vortex-induced vibrations, more complicated wake patterns may occur. A simple example is the P + S wake, where a pair and a single vortex are created in each cycle. Here we explore the transition from a 2S to a P + S wake of a periodically forced cylinder as the amplitude of the forcing is varied. We find that the transition is composed of many local topological bifurcations of the vorticity field combined with a symmetry-breaking dynamical bifurcation. We propose an extended classification scheme to describe the various topological stages in the transition.

Dr. Sanghasri Mukhopadhyay (VIT Vellore)

"Thin-film on structured packing"

Thin-film devices are of great industrial interest these days. Chemical devices such as evaporators, packed bed heat exchangers, distillation columns for the separation of components use the modern structured packings that provide fundamental advantages like lowering the pressure drop, excellent liquid spreading etc. Our motivation is to investigate the hydrodynamics of falling film over structured packing. In this work, we focused on how the porous property and anisotropic behaviour of permeability of such structured packing modify the instability mechanism in linear and nonlinear regimes.

Mr. Harvansh Dandelia (IIT Gandhinagar)

"Control of growth of perturbation in airfoil boundary layers"

Download this abstract here.

Professor R. Usha (IIT Madras)

"Modeling of dynamics and stability of a thin film down an incline: a new perspective"


Dr. Sukhendu Ghosh (IIT Jodhpur)

"Linear stability analysis of some complex flows""

In a large variety of physical systems, the fluid-flow properties are a function of space and time, and their variation can have a dramatic effect on the flow instability. The knowledge of instability behaviour of such complicated flows is essential for mathematical modeling, design and application of compact tools to ensure desired mechanical, optical properties and barriers of the products. Moreover, many intriguing and important fluid dynamic phenomena in nature and engineering tools are associated with complex spatio-temporal patterns (e.g., water waves, clouds, sprays, blood flow and complicated flows in various industries etc.). The study of linear instability is a mathematical way to understand the overall dynamics of flow systems using perturbation theory. This talk includes the discussion on modal linear stability analysis, analytical and numerical techniques for solving a class of complicated flow problems, like stratified multilayer flows and rotating flows etc. I will discuss thoroughly how to derive the generalized Orr-Sommerfeld equation and Reynolds-Orr energy equation as well as the solution procedure using spectral collocation method. Further, I will explain the variation of instability characteristics in viscosity- stratified and rotating flows by the influence of different flow parameters.

Mr. Surya Narayan Maharana (IIT Ropar)

"Stability of a layered flow where a reaction induces viscosity stratification"

Download this abstract here.

Dr. Duncan Hewitt (University College London)

"The impact of layering on vigorous convection in porous media"

Vigorous (high Rayleigh number) convection in fluid-saturated porous media is important in numerous geophysical settings, perhaps most pertinently with respect to the long-term stability of geologically sequestered carbon dioxide. Natural rock formations are typically highly heterogeneous; here we explore the impact of thin horizontal strata or layers - which is a characteristic form of heterogeneity in sedimentary formations - with the aid of numerical simulations and theory. After discussing the remarkable columnar structures that are a ubiquitous feature of strong porous convection, we explore the spreading and evolution of both an isolated buoyant plume and a distributed buoyant source in the presence of thin low-permeability baffles or layers. These layers are characterised by their impedance to flow, which controls the degree to which they disrupt the convective structures and fluxes. When the impedance is high, the layers have a very strong influence on the flow and this disruption can be dramatic. Physical implications will be briefly discussed.