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

Course Content

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

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 75 min 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