General Theme:
….Consider the evolution of convection in
the absence of significant larger-scale
forcing influences…or even boundary
layer features….
The spectrum of convective storms and
convective systems can largely be
explained based on just two environmental
parameters:
…..Buoyancy
….Vertical Wind Shear
Ordinary Cell:
Multicell:
Supercell:
Archetypes: Building blocks of the
observed spectrum
Ordinary Cells: short lived (30-60 min),
propagate with the mean wind
Multicells: long-lived group of ordinary cells
Supercells: quasi-steady, rotating, propagate
right or left of the vertical wind shear vector
Physical processes controlling cell types:
•Buoyancy processes: basic
updraft/downdraft, (ordinary cells)
•Gust front processes: triggering of
new cells, upscale growth, (multicells)
•Dynamic processes: rotating updraft,
dynamic vertical pressure gradient
forcing, (supercells)
http://www.meted.ucar.edu/convectn/csmatrix/
What Goes
Up……
Must Come Down
Ordinary Cell Evolution:
What Goes
Up……
Basic Equations:
æ pö
p ºç ÷
è p0 ø
Rd
Cp
(Exner Function)
du
¶p
= -C p q v
+ fv + Fx
dt
¶x
dv
¶p
= -C p qv
- fu + Fy
dt
¶y
dw
¶p
=- C p q v
+ B (Buoyancy)
dt ¶z
(
)
éq ¢
ù
B º g ê + .61 qv - q v - qc - qr ú
ëq
û
+ ice….
Buoyancy Force:
Archimedes Principal: Buoyancy is simply the difference
between the weight of a body and
the fluid it displaces.
æ r2 - r1 ö
F
A=
= gç
÷
M
è r1 ø
Parcel Theory:
.…ignores
pressure effects
1/2
Wmax = (2 CAPE)
…real bubble in
3D simulation
Buoyancy is Scale-Dependent!!!
Diagnostic Pressure: Ñ ×(Momentum)
(
)
(
)
¶B
Ñ × C p rq v Ñp = -Ñ × rv × Ñv +
¶z
Dynamic Pressure:
(
)
(
Ñ × C p rq v Ñp dn = -Ñ × rv × Ñv
æ ¶B ö
Buoyancy Pressure: Ñ ×(C p r q vÑp B ) =
è ¶z ø
**For wavelike disturbances:
Ñ p » -p
2
)
Vertical Momentum Eq. (rewritten)
ù
¶p dn é
¶p b
dw
= -C p q v
+ ê -C p q v
+ Bú
dt
¶z
¶z
ë
û
(dynamic) +
(buoyancy)
Basic 2D Equations:
du
¶p
= -C p q v
+ fv + Fx
dt
¶x
⁄
dw
¶p
=- C p q v
+B
dt ¶z
Or, more simply, consider the 2D
horizontal vorticity equation:
dh
¶B
=dt
¶x
æ ¶u ¶w ö
where h =
è ¶z ¶x ø
Buoyant Processes:
Buoyancy is Scale-Dependent!!!
Basic Equations:
æ pö
p ºç ÷
è p0 ø
Rd
Cp
(Exner Function)
du
¶p
= -C p q v
+ fv + Fx
dt
¶x
dv
¶p
= -C p qv
- fu + Fy
dt
¶y
dw
¶p
=- C p q v
+ B (Buoyancy)
dt ¶z
(
)
éq ¢
ù
B º g ê + .61 qv - q v - qc - qr ú
ëq
û
+ ice….
Cold Pools: Density Currents
Droegemeier and Wilhelmson, JAS, 1987
…2D
…30 – 40 km
…100 – 200 m
You’ve all heard of “Kelvin” Helmholtz instability…????
Shallow (Trapped) Wave-Like Disturbances
Density Current
Internal Bore of
Wavelength l
• Gravity-wave related phenomena can be excited by antecedent convection
• Statically stable nocturnal PBL provides an environment where such
disturbances can maintain coherence
From Simpson (1997), An Introduction to Atmospheric Density Currents
Density Current:
dh
¶B
=dt
¶x
Theoretical speed
of propagation:
c = 2ò
2
H
o
( -B) dz
c = 2g
r¢
r
H
RKW Theory
Rotunno et al.
(JAS, 1988)
“Optimal”
condition for
cold pool lifting
C/∆u > 1
C/∆u = 1
C/∆u < 1