Important Information

Status: The course is complete.

Course Duration: ~20 weeks

Announcements will be made here and mailed to the registered participants if required.

Announcements 

• Lecture videos will be available at the ISSS Course Website: https://coursesisssonline.in/course/view.php?id=133

• Login credentials were sent over email to the registered participants. [User ID: Registered mail ID. Default Password: P@ssw0rd]

• New participants can enrol as guests. Email your details to jatinraosaini@gmail.com to get the password for access.

Resources

• Nonlinear Dynamics and Chaos by S. Strogatz [Book link] 

• Introduction to Hydrodynamic Stability by P. G. Drazin [Book link] 

Additional resources:

• Album of Fluid Motion by Milton Van Dyke [Book link]

Note: These resource links are shared corresponding to openly available files on the Internet and can be subject to publisher copyrights.

Course Content

Section 0: Introductory Concepts and Visualisation

This (miscellaneous) section can be referred to independently and covers various concepts through visual depictions and external resources.

[coming soon]

Section 1: Mathematical Preliminaries

The basic mathematics covered in this section is crucial to understand the concept of stability. The main course content starts here.

Lecture 1.0 - Introduction (Lecture)

Lecture 1.1 - Non-linear dynamics (Lecture)

Lecture 1.2 - 1D Systems (Lecture)

Lecture 1.3 - 2D Systems (Lecture)

Lecture 1.4 - Eigenvalue problem (Lecture)

Section 2: Stability Analysis - Framework

The basic framework to perform stability analysis is presented here.

Lecture 2.1 - Waves (Lecture)

Lecture 2.2 - Linearization (Lecture)

Lecture 2.3 - Normal modes (Lecture)

Lecture 2.4 - Method of Normal modes (Lecture)

Lecture 2.5 - Fluid interfaces-1 (Lecture)

Lecture 2.6 - Fluid interfaces-2 (Lecture)

Section 3: Rayleigh-Taylor Instability

Stability analysis is presented here for fluid interface with misaligned density gradient and gravity (pressure gradients).

Lecture 3.1 - Rayleigh-Taylor Instability-1 (Lecture)

Lecture 3.2 - Rayleigh-Taylor Instability-2 (Lecture)

Lecture 3.3 - Rayleigh-Taylor Instability-3 (Lecture)

Lecture 3.4 - Rayleigh-Taylor Instability-4 (Lecture)

Lecture 3.5 - Rayleigh-Taylor Instability-5 (Lecture)

Section 4:  Kelvin-Helmholtz Instability

Stability analysis is presented here for fluid interface with shear and velocity gradient.

Lecture 4.1 -  Kelvin-Helmholtz Instability-1 (Lecture)

Lecture 4.2 -  Kelvin-Helmholtz Instability-2 (Lecture)

Lecture 4.3 -  Kelvin-Helmholtz Instability-3 (Lecture)

Section 5:  Rayleigh-Plateau Instability

Stability analysis is presented here for a liquid jet involving capillary effects (surface tension).

Lecture 5.1 -  Rayleigh-Plateau Instability-1 (Lecture)

Lecture 5.2 -  Rayleigh-Plateau Instability-2 (Lecture)

Lecture 5.3 -  Rayleigh-Plateau Instability-3 (Lecture)

Lecture 5.4 -  Rayleigh-Plateau Instability-4 (Lecture)

Lecture 5.5 -  Rayleigh-Plateau Instability-5 (Lecture)

Lecture 5.6 -  Rayleigh-Plateau Instability-6 (Lecture)

Section 6:  Rayleigh-Bernard Instability

Stability analysis is presented here for fluid system with misaligned thermal gradient and gravity.

Lecture 6.1 -  Rayleigh-Bernard Instability-1 (Lecture)

Lecture 6.2 -  Rayleigh-Bernard Instability-2 (Lecture)

Lecture 6.3 -  Rayleigh-Bernard Instability-3 (Lecture)

Lecture 6.4 -  Rayleigh-Bernard Instability-4 (Lecture)

Lecture 6.5 -  Rayleigh-Bernard Instability-5 (Lecture)