Lorenz energy cycle

1
Lorenz energy cyclesummary
2
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 mid- latitude eddies to all eddies
  and the entire atmosphere!
• We write
• Now need to find equations for ZKE etc. (i.e.,
  for d(ZKE)/dt etc.)

3
Review

• We take the momentum equation zonally average
  to get an equation for
• 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!

4
ZAPE?EAPE
G
ZAPE
EAPE
G?
EAPE?EKE
ZKE?ZAPE
ZKE
EKE
ZEKE ?EKE
D
D?
5
ZAPE?EAPE
ZAPE
EAPE
Conversion involves product
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.
6
EAPE
Conversion involves product Correlation of
warm air rising AND cold air sinking at SAME
latitudes. Prevalent in synoptic storms. Can be
contributions from all types of
eddies! Observationally a STRONG conversion EAPE
?? EKE.
EAPE?EKE
EKE
7
Conversion involves the product
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
EKE
ZEKE ?EKE
8
Conversion involves product This involves warm
air rising AND cold air sinking in the
zonally-averaged 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???
ZAPE
ZKE?ZAPE
ZKE
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Read the summary of the energy cycle on page 343!