Download Lorenz energy cycle summary

Lorenz energy cycle…summary
Review…
•
•
Energy is conserved in the absence of sources/sinks (equations must
satisfy this!)
Within the “total energy”, energy can be converted from one type to
another (interesting!)
– e.g., PE  KE
•
•
•
•
Energy analysis of baroclinic waves (2-level QG model) leads to the idea
of ZAPE  EAPE  EKE to maintain growth/amplification of the
eddies
We have now expanded this idea beyond “just” synoptic-scale midlatitude eddies to all eddies and the entire atmosphere!
We write: u  u  u ',K  K  K 'orKE  ZKE  EKEetc.
Now need to find equations for ZKE etc. (i.e., for d(ZKE)/dt etc.)
Review…
•
•
•
•
•
•
•
•
We take the momentum equation & zonally average to get an equation
for  u / t
This equation is then multiplied by “ubar” to get an equation for ZKE!
Alternatively - multiply mean vorticity equation by “psi”  same result.
By this approach, we get a set of 4 equations for the evolution of ZKE,
EKE, ZAPE & EAPE.
These are shown in the Lorenz energy cycle.
We notice common terms in the equations - each “conversion” term
appears in two equations with opposite signs - representing an energy
conversion!
All we need to do now is to figure what motions & phenomena are
associated with each energy conversion.
The “full story” is at the end of section 10.4 in JRH - you should read it!
G
{ZAPEEAPE}
ZAPE
EAPE
{EAPEEKE}
{ZKEZAPE}
ZKE
D
G
{ZEKE EKE}
EKE
D
{ZAPEEAPE}
ZAPE
Conversion involves product:
EAPE
v 'T '  T y
North-south eddy heat fluxes building up west-east
temperature gradients.
Can be any eddies BUT certainly occurs in synoptic
eddies.
Observationally a STRONG conversion ZAPE 
EAPE.
Conversion involves product:
EAPE
w 'T '
Correlation of warm air rising AND
cold air sinking at SAME latitudes.
{EAPEEKE}
Prevalent in synoptic storms.
Can be contributions from all types of
eddies!
Observationally a STRONG
conversion EAPE  EKE.
EKE
Conversion involves the product:
u ' v '  u y
Eddies cause the north-south flux of westerly
momentum, and this can converge into a region and
accelerate the background winds there.
This would diminish EKE and build up ZKE.
ZKE
{ZEKE EKE}
EKE
Conversion involves product:
ZAPE
{ZKEZAPE}
ZKE
wT
This involves warm air rising AND
cold air sinking in the zonallyaveraged sense at DIFFERENT
latitudes.
Warm air  + cooler air  in Hadley
cell  ZAPE  EAPE … strong
circulation, weak N-S temp. gradient
Cooler air  + warmer air  in Ferrel
cell  EAPE  ZAPE … weaker
circulation, strong N-S temp. gradient
Net effect???
Read the summary of the energy cycle
on page 343!