Oceanic Dynamics Seminars

1. Oceanic Dynamics Seminars Charles Dong, Greg King School of Marine Sciences, NUIST 2014, June-July

3. Grading policy : 40% for participation and classroom behaviors and 60% for the final oral presentation (5 minutes) and written reports (3-5 pages).

4. www.atmos.ucla.edu/~cdong/OD_2014_NJ

5. Seminar 1Fundamental Conceptsin Oceanic Dynamics

6. Outline • Three Approximations • Navier-Stokes Equations and others

7. Three Approximations • Hydrostatic Approximation • Geostrophic Approximation • Bousinesque Approximation

8. Momentum Equations

9. Hydrostatic Approximation • The hydrostatic approximation is a simplification of the equation governing the vertical component of velocity. • It simply says that the pressure at any point in the ocean (atmosphere) is due to the weight of the water (air) above it. • When vertical accelerations are small compared to the gravitational acceleration, the hydrostatic approximation is valid.

10. Hydrostatic Approximation H

11. Geostrophic Approximation • The geostrophic approximation is a simplification of the equations governing the horizontal components of velocity. It is valid when the largest terms in the equations of motion are those involving the Coriolis force and the pressure gradient. • Geostrophic flow represents a steady-state balance (i.e. there is no variation in time) between the pressure gradient and Coriolis forces.

12. Geostrophic Approximation

13. Hydrostatic + Geostrophic Approximations

14. Bousineque Approximation • It states that density differences are sufficiently small to be neglected, except where they appear in terms multiplied by g, the gravity acceleration rate.

15. Bousinesque Approximation • The approximation's advantage arises because when considering a flow of, say, warm and cold water of density and one needs only consider a single density , • the difference is negligible.

16. Hydrostatic + Geostrophic + Bousineque Approximations o o

17. Example I

18. Example II