1. Vertical Momentum Eq. (rewritten) (dynamic) + (buoyancy)

2. Buoyancy is Scale-Dependent!!! …real bubble in 3D simulation

3. Basic 2D Equations:- Or, more simply, consider the 2D horizontal vorticity equation: where ⁄

4. Buoyant Processes: Buoyancy is Scale-Dependent!!!

5. Density Currents…Gravity Currents…Cold Pools

6. Bernoulli Equation: Horizontal Vorticity: (in flux form)

7. Density Current: Theoretical speed of propagation:

8. J. Fluid Mech. (1994) von Karman: Benjamin: “On the dynamics of gravity currents in a channel”

13. Bernoulli Equation: Horizontal Vorticity: (in flux form)

15. “Optimal” condition for cold pool lifting C/∆u > 1 C/∆u = 1 C/∆u < 1 RKW Theory Rotunno et al. (JAS, 1988)

16. Multicell: