NPTEL : NOC:Introduction to Interfacial Waves (Chemical Engineering)

Co-ordinators : Prof. Ratul Dasgupta


Lecture 1 - Introduction

Lecture 2 - Coupled, linear, spring-mass systems

Lecture 3 - Coupled, linear, spring-mass systems (Continued...)

Lecture 4 - Coupled, linear, spring-mass systems (Continued...)

Lecture 5 - Coupled, linear, spring-mass system: continuum limit

Lecture 6 - Normal modes of a string fixed at both ends

Lecture 7 - Vibrations of clamped membranes

Lecture 8 - Vibrations of clamped membranes (Continued...)

Lecture 9 - Introduction to Jacobian elliptic functions

Lecture 10 - The non-linear pendulum

Lecture 11 - The non-linear pendulum (Continued...)

Lecture 12 - Time period of the non-linear pendulum

Lecture 13 - Introduction to perturbation methods

Lecture 14 - Perturbation methods (Continued...)

Lecture 15 - Non-dimensionalisation

Lecture 16 - Perturbative solution to the projectile equation

Lecture 17 - Perturbative solution to the nonlinear pendulum

Lecture 18 - Lindstedt-Poincare technique

Lecture 19 - Method of multiple scales

Lecture 20 - Method of multiple scales (Continued...)

Lecture 21 - Multiple scale analysis for damped-harmonic oscillator

Lecture 22 - Duffing equation using multiple scales

Lecture 23 - Duffing equation (Continued...)

Lecture 24 - Kapitza pendulum

Lecture 25 - Introduction to Floquet theory

Lecture 26 - Floquet theorem (Continued...)

Lecture 27 - Floquet analysis of the Mathieu equation

Lecture 28 - Introduction to waves on an interface

Lecture 29 - Linearized wave equations in deep water

Lecture 30 - Linearized wave equations in deep water: dispersion relation

Lecture 31 - Linearised deep-water surface gravity waves (Continued...)

Lecture 32 - Standing and travelling waves in deep water

Lecture 33 - Cauchy-Poisson initial value problem for surface-gravity waves in deep water

Lecture 34 - Cauchy-Poisson problem (Continued...)

Lecture 35 - Cauchy-Poisson problem in cylindrical geometry

Lecture 36 - Cauchy-Poisson problem in cylindrical geometry (Continued...)

Lecture 37 - Group-velocity and the Cauchy-Poisson problem

Lecture 38 - Cauchy-Poisson problem for delta function initial condition

Lecture 39 - Cauchy-Poisson problem for delta function initial condition (Continued...)

Lecture 40 - Capillary-gravity waves

Lecture 41 - Waves on a pool of finite depth

Lecture 42 - Axisymmetric Cauchy-Poisson problem visualisation: the pebble in the deep pond problem

Lecture 43 - Rayleigh-Plateau capillary instability

Lecture 44 - Rayleigh-Plateau capillary instability (Continued...)

Lecture 45 - Rayleigh-Plateau capillary instability on thin film coating a rod

Lecture 46 - Rayleigh-Plateau capillary instability of a cylindrical air column in a liquid

Lecture 47 - Mechanism of the Rayleigh-Plateau instability

Lecture 48 - Shape oscillations of a spherical interface

Lecture 49 - Shape oscillations of a spherical interface (Continued...)

Lecture 50 - Shape oscillations of a spherical interface (Continued...)

Lecture 51 - Analysis of l=0 and l=1 modes for a spherical drop

Lecture 52 - Faraday waves on an interface - stability of time dependent base states

Lecture 53 - Mathieu equation for Faraday waves

Lecture 54 - Applications of Faraday waves - atomisation and spray formation

Lecture 55 - Waves and instability on density stratified shear flows - the KH model

Lecture 56 - Limits of KH dispersion relation: Rayleigh-Taylor instability

Lecture 57 - KH dispersion relation : model of wind wave generation

Lecture 58 - Helmholtz instability of a vortex sheet and summary

Lecture 59 - Derivation of the Stokes travelling wave

Lecture 60 - Derivation of the Stokes travelling wave (Continued...)

Lecture 61 - Derivation of the Stokes travelling wave (Continued...)