2. Surface LH, SH, and momentum drag are determined by turbulent transport near the surface

3. How to estimate LH, SH and momentum drag? Eddy covariance measurements Bulk aerodynamic formula

5. Instability of an axisymmetric jet

6. Leonardo da Vinci

7. Big whirls have little whirls that feed on their velocity, and little whirls have lesser whirls and so on to viscosity. ---Lewis Richardson, 1922

10. Equations of motion Eulerian view versus Lagrangian view Lagrangian derivative –Chain rule

11. Derivation of the equations of motion The laws of physics are more conveniently applied to a fixed collection of matter. For fluids, this body may move and change its shape and volume. One can go from the integral form to a differential form by differentiating an integral of variable limits, using the Leibniz’s rule and the Gauss’s theorem (see notes). Here, we go with a Eulerian derivation (following Marshall and Plumb)

12. Dry atmosphere or ocean without salt Unknowns: velocity U=(u,v,w), p, and T –(density is known from p, T through the equation of state) –We will use Cartesian coordinate Equations: –Newton’s 2 nd law applied in three directions –Conservation of mass –First law of thermodynamics

14. Forces Gravity Pressure gradient

16. Friction –Ultimately come from molecular diffusion –When the equation is viewed as describing broad scale motions, “friction” can come from smaller turbulent eddies. –Symbolically

17. Equation of motion In component form –Neglecting vertical acceleration and friction gives us the hydrostatic balance

18. Conservation of mass Or

19. Define We have Reynolds decomposition

20. Surface LH, SH, and momentum drag are determined by turbulent transport near the surface

27. Earth’s eccentricity is currently 0.0167 but can vary between 0.005 and 0.058 on timescales of 400Kyr and 100Kyr.

28. Obliquity cycle (41Kyr)

29. Precession cycle (26Kyr)

30. Q: Why the pole is not warmer than the tropics in the summer?

31. Earth closer to the sun in winter solstice

33. Being warmer (colder) than radiative-convective equilibrium implies the column is losing (gaining) heat radiatively. Steady state requires meridional heat transport.

34. With a warm column (tropics) and a cold column (the pole), both in (approximately) hydrostatic balance, is it possible for the horizontal velocity to be zero?

35. With a warm column (tropics) and a cold column (the pole), both in (approximately) hydrostatic balance, how does the adjustment proceed?

36. We live on Earth which is rotating… How does rotation modify the picture?

37. Thermodynamic equation After some manipulations