Atmosphere and ocean dynamics

astronomy
computer science
environmental protection
geography
geology
mathematics
physics

Elementary theoretical mechanics, elementary fluid mechanics, phenomenological thermodynamics, elementary differential equations.

Dynamics of the atmosphere and the ocean as dynamics of thin layer of fluid on rotating sphere. Similarities and differences between the atmosphere and the ocean. Primitive equations. Interpretation of geophysical flows in the atmosphere and the ocean. Filtering of equations. Geostrophic and quasi-geostrophic approximations. Waves in the atmosphere and in the ocean. Energetics of atmospheric circulations.

1. Fluids: air, water. Constitutive equations. Structure of the atmosphere and the ocean. Similarities and differences.

2. Equations of motion in rotating coordinate frame (momentum, mass conservation, energy).

3. Atmosphere as a thin layer of fluid on a rotating sphere. Hydrostatic approximation. Potential temperature, potential density.

4. Multiscale atmospheric and oceanic flows. Filtration of equations. Geostrophic approximation.

5. Prognostic equations. Natural coordinates. Balanced flows in the atmosphere and in the ocean.

6. Shallow water equations. Incopmpressibility: Boussinesq and anelastic approximations.

7. Importance of the atmospheric boundary layer. Oceanic surface layer. Ekman layer in the atmosphere and in the ocean. Ocean -atmosphere interactions.

8. Circulation and vorticity. Potential vorticity. Cyclonic and anticyclonic circulation.

9. Quasi-geostrophic approximation. Numerical Weather Prediction. Mid-latitude circulations.

10. Waves in the atmosphere and in the ocean: acoustic, gravity, inertio-gravity, Rossby waves.

11. Hydrodynamic instabilities in the atmosphere and in the ocean. Baroclinic instability. Mesoscale circulations.

12. Global circulation. Energetics of global circulation. Heat transport in the ocean and in the atmosphere.

Geoffrey K. Vallis, Atmospheric and Oceanic Fluid Dynamics

Benoit Cushman-Roisin, Introduction To Geophysical Fluid Dynamics. Physical and Numerical Aspects

J.R. Holton, An Introduction to dynamic meteorology.

M. L. Salby, Fundamentals of Atmospheric Sciences.

Understanding basic principles of geophysical fluid dynamics and dynamic meteorology, in particular geostrophic and quasi-geostrophic approximations.

Understanding scale analysis of the equations of motion. Interpretation of atmospheric and oceanic processes in terms of geophysical fluid dynamics. basic understanding of atmospheric and oceanic waves, linearization equations of motion, stability analysis.

Assessment will be based on documented abilities to solve problems (colloquies and written homework) as well as on theory understanding. Percentage of the final score:

- 50% problems solved in the course of written colloquies (the first colloquium in mid-term, the second colloquium at the end of the term, together with the written theoretical exam);

- 10% home exercises and problems;

-40% - theoretical exam (written).

The additional condition: theoretical exam threshold must be passed