Introduction to Hydrodynamic Stability
From: ₹1,299.00
Last Date of Registration : 12th June 2025
Register before 4th June 2025 to avail an Early Bird discount
Student : 1299 + GST
Faculty: 1499 + GST
Industry: 1799 + GST
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- Course Description
- Profile of the Instructor
- Pre Requisites
- Session Details
- Workshop Details
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Profile of the Instructor
Prof. Anirban Guha is currently serving as a Senior Lecturer (Associate Professor) in the School of Science and Engineering at the University of Dundee. His research is primarily driven by curiosity, focusing on the formulation of reduced-order physical and mathematical models for various problems encountered in fluid dynamics. His work is particularly centered around geophysical and environmental flows, with applications in critical areas such as ocean mixing (and its implications for climate change) and aquatic pollution mitigation. He was awarded Alexander von Humboldt Research Fellowship, by Govt. of the Federal Republic of Germany, 2019.
Pre Requisites
Basic understanding of Fluid Dynamics, Linear Algebra, Ordinary Differential Equations (ODEs), Partial Differentiation, Complex Numbers and Fourier Transform.
Session Details
Day 1:
Introduction to dynamical systems – linearizing nonlinear system of ODEs, Phase Plane Analysis, fixed points and their stability, Bifurcation Analysis with the damped oscillator example, Lyapunov and Asymptotic stability.
Day 2:
Motivating linear stability analysis of generic Fluid Dynamical Systems, normal mode analysis, problems with density variation having exact solutions, e.g. Rayleigh- Taylor Instability and Rayleigh–Bénard Convection, shear flow problem with exact solution – Kelvin-Helmholtz instability.
Day 3:
Stability of smooth Velocity profiles, Rayleigh’s inflexion point Theorem, Squire’s Theorem, deriving the governing equation for density stratified shear flows with Viscosity – the density stratified Orr-Sommerfeld equation (also known as the Viscous Taylor- Goldstein equation).
Day 4:
Exploring numerical solutions (using MATLAB) of the density stratified Orr- Sommerfeld equation with various examples – boundary layer instabilities in channel (or pipe) flows, Kelvin-Helmholtz instability in mixing layers, discussion of applications in industry (e.g. combustion in IC engines, multiphase flows, industrial displacement flows) and geophysics (ocean mixing, barotropic instability of atmospheric jets). Limitations of normal mode theory and pointers to recent developments in linear stability analysis, including data-driven stability analysis.
Workshop Details
Date of the Workshop : 14th, 15th, 21st and 22nd June, 2025
Timings: 07:00 p.m. to 09:00 p.m. (IST) – On all the days
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