Vertical Momentum Eq. (rewritten)

(dynamic) + (buoyancy)

Buoyancy is Scale-Dependent!!!

…real bubble in 3D simulation

Basic 2D Equations:

--

Or, more simply, consider the 2D horizontal vorticity equation:

where

⁄

Buoyant Processes:

Buoyancy is Scale-Dependent!!!

Density Currents…Gravity Currents…Cold Pools

Bernoulli Equation:

Horizontal Vorticity:

(in flux form)

Density Current:

Theoretical speed of propagation:

J. Fluid Mech. (1994)

von Karman:

Benjamin:

“On the dynamics of gravity currents in a channel”

Bernoulli Equation:

Horizontal Vorticity:

(in flux form)

“Optimal” condition for cold pool lifting

C/∆u > 1

C/∆u = 1

C/∆u < 1

RKW Theory

Rotunno et al. (JAS, 1988)

Multicell: