Teaching

Modelling Stochastic and Turbulent Transport (Graduate)

Graduate elective course (CL 677): Spring 2024, Spring 2026

Most engineering courses on flow and transport focus on the macroscale and the associated deterministic continuum equations. However, in recent times, technological innovations and scientific discoveries are predominantly being made at the microscale where the molecular origins of flow and transport cannot be ignored, e.g. in fields like complex fluids, material science, and biophysics. Moreover, randomness can also arise at the macroscale due to chaotic dynamics in systems involving turbulent flows, such as chemical reactors or the weather. The fluctuations in these systems cannot always be averaged out, rather the stochasticity can give rise to qualitatively distinct dynamics.

This course will enable students to model and understand transport in such stochastic systems by providing a solid foundation in the theory of stochastic processes and stochastic differential equations, and then illustrating the application of these mathematical methods to problems from different domains. Thereby, important unifying ideas will emerge, and the students will develop an appreciation for the creative role of noise in natural and industrial phenomena. Some distinguishing features of this course are:

Reveals connections between the two complementary approaches to random processes—probability distribution functions (macro) and individual fluctuating trajectories (micro)—with concrete examples.
Shows how and when turbulence can be approximated by (multiplicative) noise, and thereby reveals the mathematical basis for the idea of turbulent eddy diffusivity.
Applies the developed theory to many exciting problems, such as the growth of rough random surfaces; and flame propagation, polymer stretching, and pattern formation in turbulent flows.

Link to the typical course syllabus

Link to the lectures on Youtube

Link to the recordings of the lectures on CDEEP (IIT Bombay account required)

Advanced Transport Phenomena (Graduate and Undergraduate)

Graduate core course (CL 601): Fall 2025.

Undergraduate honors course (CL 336): Fall 2020; Fall 2021; Fall 2022.

This course will teach students how to think about problems in transport phenomena. Given a physical problem, students will learn how to formulate a consistent mathematical model based on first principles, and how to simplify and analyse the equations to obtain useful physical insights and make quantitative predictions. The course will introduce a range of concepts and techniques, include order-one scaling and asymptotic methods. The course is structured around model problems which will be worked through in entirety, from formulation to solution and interpretation. These case studies will illustrate various techniques in physically meaningful contexts, while demonstrating the importance of maintaining a close interplay between mathematical methods and physical understanding.

Link to the graduate course syllabus (CL 601)

Link to the undergraduate course syllabus (CL 336)

Playlist of online lectures on Youtube

Process Fluid Mechanics (Undergraduate)

Undergraduate core course (CL 254): Fall 2023; Fall 2024.

This course provides a first introduction to the fascinating field of fluid dynamics. Starting from the basic laws of mechanics, F = ma and mass conservation, we will derive the universal equations that govern the flow of fluids, be they clouds in the Earth’s atmosphere or oil in a pipeline. Along the way, we shall understand the role of internal stresses in a fluid, including pressure and viscous shear, and see the application of several mathematical techniques, including matrix algebra and vector calculus. In this introductory course, we will not be able to solve the equations in all their rich detail, but shall be restricted to approximate analyses which are often sufficient for engineering estimates. Nevertheless, the fundamentals covered in this course will prepare you for further advanced courses in which the many mysteries of fluid flow, including turbulence, are tackled with the aid of advanced mathematical methods and computer simulations.

Link to the typical course syllabus

Photo courtesy Roopam Dey

Communication Skills (Graduate)

Graduate core non-graded course (CL 899): Spring 2020, Spring 2021, Spring 2022.

This course focuses on three aspects of communication that are integral to the professional lives of scientists, engineers and technologists: reading the scientific literature, presenting ideas and results in the form of seminars (using slides), and writing research papers or technical reports. We will also address some topics of particular interest to graduate students, such as writing cover letters for paper submissions, responding to peer-review, communication via email, etc. A major theme of the course will be the importance of planning out the structure of a talk or paper, before beginning to make slides or write sentences. While organizing this structure, one has to make decisions about what the main message or result is, and what is the best point of view from which the audience or readers will be able to most easily understand and appreciate this message. The best way to convince or inspire, is to get the audience to realize the truth for themselves, by positioning them at an ideal vantage point—this is the philosophy of the classic style of prose which we will adopt for both writing and presentations.

Link to the typical course syllabus

Multiphase Flows: Analytical Solutions and Stability Analysis (Graduate)

As a PhD scholar, I delivered 7 lectures in this NPTEL course that was primarily taught by Prof. S. Pushpavanam (IIT Madras). A few lectures were also delivered by my brother-in-arms Dipin S. Pillai (now at IIT Kanpur).