1 of 8

Vertical motion and Physics-Dynamics Coupling

Terry Davies Dynamics Research

www.metoffice.gov.uk

© Crown Copyright 2024, Met Office

2 of 8

Equations

 

 

 

,

,

Potential temperature

 

,

 

Exner pressure

 

 

physics changes

,

 

for adiabatic motion

 

, where

 

3 of 8

Equations of motion

 

 

 

4 of 8

Vertical motion

 

 

 

 

 

is the diabatic heating and for adiabatic motion

 

 

is the diabatic vertical motion.

5 of 8

 

 

 

 

 

 

 

 

 

where

 

 

 

heating

cooling

Over time

 

a fluid element will move a distance

 

To represent this on the vertical grid add

 

to level

 

and

 

level

 

6 of 8

 

 

 

 

 

 

 

 

 

where

 

 

 

heating

cooling

Lagrangian advection followed by linear interpolation

Similarly, cooling results in downward motion,

Diabatic vertical motion is effectively a mixing process.

7 of 8

 

 

 

 

 

 

 

 

 

where

 

 

 

heating

cooling

What happens when

or

What about

 

 

 

How should we treat tracers and other prognostic variables?

8 of 8

Remarks

  • Reconsider how we think about diabatic vertical motion.

​

  • Radiative and latent heating/cooling results in a mixing rather than vertical motion.

​

  • How do we treat the adiabatic vertical motion?

​

  • May have a significant impact on the Brewer-Dobson circulation and the general circulation, particularly in the Tropics.