Title of the talk: How does the nonlinear theory help to predict the transition to turbulence in fluid overlying porous systems?

Date, Time & Venue: 24 July 2025, 11:00 AM, Seminar Hall, Dept. of Mathematics

Abstract: In this talk, we will discuss the stability analysis of Poiseuille flow in a fluid overlying porous domain. Such systems find extensive applications in oil reservoirs, underground contaminant flow, etc. We will first start with some preliminary results obtained under linear theory. Next, we will proceed to the weakly nonlinear stability analysis, in which the nonlinear interactions are studied by imposing finite amplitude disturbances to the Poiseuille flow. Using the order parameter theory, the Landau equation is extensively used to understand the bifurcation phenomena in fully nonlinear systems in channel/pipe/annulus. However, this theory has not yet been extended to fluid overlying porous systems. On that account, we introduce the order parameter theory for deriving the Landau equation to carry out the weakly nonlinear stability analysis of plane Poiseuille flow in fluid overlying porous domains.

About the Speaker:  Dr. Anjali is currently working as an Institute Post-Doctoral Fellow in the Department of Chemical Engineering, I.I.T. Bombay, under the mentorship of Prof. Jason R. Picardo. She is working on inverse solutions to unsteady reaction-diffusion problems. She obtained a PhD from the Department of Mathematics, I.I.T. Roorkee. Her research focused on the hydrodynamic stability analysis of shear flows in fluid overlying porous systems.