What is Mesoscale?

Question 1

Ordinary Rossby Number

Answer 1

Ro=U/Lf

U = velocity of the fluid
L = horizontal length scale
f = Coriolis parameter

• So, Ro «< 1 for geostrophic (rotationally balanced) flow
• Ro is essentially a ratio of the local acceleration (U/L) and the Coriolis parameter (f)

Question 2

What would make Ro larger?

Answer 2

• Decreasing the size of a system (decreasing the size of L)
• Decreasing the latitude (decreasing the value of f)
• Increasing the wind speed (increasing U)

Question 3

So a system is less likely to conform to geostrophic balance (i.e. larger Ro) if:

Answer 3

• The system is small
• A system is located at low latitudes (closer to the equator)
• A system contains strong winds

Question 4

Wave Rossy Number (Rw)

Answer 4

Rw = c/Lf

c = gravity wave speed
L = horizontal length scale
f = Coriolis parameter

Question 5

The Wave Rossy Number is used to derive another number known as the external “Rossby Radius of Deformation” (Lr)

Answer 5

Lr = c/f

c = gravity wave speed as a function of static stability (i.e. buoyancy) 
f = Coriolis parameter 

-this version assumes we ignore the potential temperature contrast between warm and cold air.

Question 6

Rossby Radius of Deformation (Lr)

Answer 6

A length scale of fundamental importance in atmospheric dynamics.
-it is the horizontal scale at which rotation effects become as important as buoyancy effects

Question 7

When the scale of a weather system is smaller

than Lr, buoyancy dominates over rotation.

Answer 7

This defines the mesoscale, or smaller.
-buoyancy dominates over rotation (i.e. gravity waves
dominate over geostrophic flow)
-> mass (height or pressure) field adjusts to the wind
field

Question 8

When the scale of a weather system is larger than

Lr, rotation dominates buoyancy.

Answer 8

Rotation dominates over buoyancy (i.e. geostrophic flow dominates over gravity waves)
-the momentum (wind) field responds to the mass
(height or pressure) field.

Question 9

The Maximum Size of the Mesoscale is Essentially Whatever the Rossby Radius of Deformation is
at that Location. Examples:

Answer 9

• Mid-latitude Convection Lr ~ 300 km
• Equatorial convection Lr ~ infinity
• Near-equatorial convection Lr ~ 1500 km
• Tropical Cyclone Lr ~ 5 km

Question 10

Example of the Rossby Radius of Deformation in Action:

Answer 10

Tropical Plumes