Course Content:

To introduce analytical approaches for solving fluid dynamic problems arising in atmosphere and oceans.

Prerequisite:

Basic fluid mechanics, basic ordinary and partial differential equations

Desirable:

ME681, ME631 (or equivalents)

Instructor:

Ishan Sharma

Lectures per week:

3 hrs

Condensed Syllabus:

Equations of motion in rotating coordinate frames, Cartesian approximations, Density stratified flows and internal gravity waves, Taylor-Proudman theorem, Ekman layer, single and multiple layered shallow-water systems, Geostrophic adjustment and Thermal-wind balance, Potential vorticity, Poincare, Kelvin and Rossby waves, Kelvin-Helmholtz instability, Baroclinic instability, Wave-mean theory, 2D turbulence, chaotic advection in Stratosphere, Laplace tidal equations, Internaltides in deep oceans, tsunami waves.

Lecturewise Breakup (based on 75min per lecture)

I. Introduction: (7 Lectures)

• Equations of motion in rotating coordinate frames.
• Cartesian approximations: f-plane and beta-plane.
• Effect of density stratification, Boussinesq systems, gravity waves.
• Taylor-Proudman problem.
• Ekman layer.

II. Inviscid Shallow-water theory: (15 Lectures)

• Shallow-water theory - single and multiple layers
• Geostrophic adjustment and Thermal-wind balance.
• Potential vorticity conservation.
• Poincare, Kelvin and Rossby waves.
• Quasi-geostrophy.
• Simplified equations of oceans and atmosphere.

III. Instabilities, wave-mean flow interaction and turbulence: (10 Lectures)

• Kelvin-Helmholtz instability, Baroclinic instability, Eady problem.
• Wave-mean theory, Eliassen-Palm flux.
• 2D turbulence, inverse cascade and zonal jet formation.

IV. Advanced topics in geophysical fluid dynamics: (8 Lectures)

• Stratospheric transport.
• Laplace tidal equations, internal tide generation in deep oceans.
• Tsunamis.

References:

1. Atmospheric and Oceanic Fluid Dynamics, G. K. Vallis
2. Geophysical Fluid Dynamics, J. Pedlosky