Weismann (1992) Weisman, M. L., 1992: The role of convectively generated rear- inflow jets in the evolution of long-lived mesoconvective systems. J. Atmos.

Weismann (1992)

Weisman, M. L., 1992: The role of convectively generated rear-inflow jets in the evolution of long-lived mesoconvective systems. J. Atmos. Sci., 49, 1826-1847.

Conceptual model of a squall line from Houze et al. (1989)

Three stages of evolution of an MCS from the previous study we examined (Rotunno et al. 1988)

The three thermodynamic profiles used in the simulations

(CAPE varies from 1182 to 3847 J/kg).

Temperatures (solid lines), Dewpoint (dashed line). Parcel ascent (dotted lines)

Shear was unidirectional with some simulations having shear from

0-2.5 km

Winds increase from 0 m/s at surface to 30 m/s at 2.5 km with constant winds above.

0-5.0 km

Winds increase from 0 m/s at surface to 40 m/s at 2.5 km with constant winds above.

e: dark shaded > 334K, light shaded < 326K; Lines: 0 and 4 g/kg rainwater

System relative wind vectors: 2 grid interval = 25 m/s

Contrast: 60 min: Initially upright convection in both cases with cold pool initially developing from air entrained from downshear side 120 min: upright convection and strong rear inflow developing in strong shear case, convection more slantwise and diffuse with weaker rear inflow in moderate shear case

e: dark shaded > 334K, light shaded < 326K; Lines: 0 and 4 g/kg rainwater

System relative wind vectors: 2 grid interval = 25 m/s

Moderate shear Strong shear

Contrast: 180 min: Strong shear has upright strong convection with trailing stratiform and RIJ does not descend to the surface until it reaches the convective line. Moderate shear has RIJ descending to the surface and rushing into inflow, with weak convection and slantwise ascent. 240 min: Same features as above, only more accentuated. Strong shear convection is long lived, while weak shear convection is gone and system is essentially stratiform.

Note we are seeing the south half of the domain only (symmetric on north side since Coriolis force not included in simulation

Storm relative flow vectors at T = 180 min at the surface and at 2.5 km, along with rainwater in 2 g/kg intervals

Strong shear: convection along gust front and strong “front to rear” flow at surfaceWeak shear: convection over cold pool and strong “rear to front” flow at surface

2

0

2 cdzBuH

L Recall Optimum condition for long lived squall line from Rotunno et al. (1988)

Vorticity generation by shear (u) = Vorticity generation by negative buoyancy within cold pool (c2).

In moderate shear C/ u > 0 so cold poolVorticity dominated and system quickly evolved to stratiform

In strong shear, optimum condition existed for a while, but c/ u became > 0 so why did upright convection persist??

The RIJ in the two systems was distinctly different with the RIJ weaker and descending to the surface in the moderate shear case and elevated and much stronger in the strong shear case.

Buoyancy field (B thick lines, dashed negative) and pressure perturbation field (p thin lines, shaded negative)

Weak shear Strong shear

x

B

dt

d

+ buoyancy

- buoyancy

Low p

High p

Weak shear case and strong shear case show similar patterns, but the buoyancy is greater in the strong shear case and the pressure perturbations are stronger, which lead to greater vorticity forcing. This is particularly evident as time proceeds (next panel).

Weak shear Strong shear

Buoyancy field (B thick lines, dashed negative) and pressure perturbation field (p thin lines, shaded negative)

x

B

dt

d

+ buoyancy

- buoyancy

Low p

High p

Weak shear case and strong shear case show similar patterns, but the buoyancy is greater in the strong shear case and the pressure perturbations are stronger, which lead to greater vorticity forcing.

Buoyancy gradient (B/ x) field (vorticity forcing)

x

B

dt

d

Weak shear Strong shear

Note buoyancy gradient is along the boundaries of the plume of rising warm air – this is where horizontal vorticity is created.

Horizontal vorticity sources combine to create rear inflow jet

Weak shear Strong shear

x

B

dt

d

Buoyancy gradients nearly equalleads to elevated RIJ

Buoyancy gradients unequalleads to sloping RIJ

Buoyancy gradient (B/ x) field (vorticity forcing)

The distribution and intensity of the buoyancy gradients in two cases lead to a stronger and elevated RIJ in the strong shear case, and a weaker and sloping RIJ in the

weak shear case. Fluid mechanics analogy on cartoons.

Question: If both simulations used the same sounding for initialization (same CAPE), why does the stronger shear case exhibit more buoyancy??

2cu

Question: If both simulations used the same sounding for initialization (same CAPE), why does the stronger shear case exhibit more buoyancy??

2cu Answer: Because in the strong shear simulation, the updrafts are upright and the trajectories of air parcels to the upper troposphere are shorter than for the slantwise ascent of the moderate shear case. Mixing is a time dependent process and the parcels mix more with environmental air on the longer trajectories, reducing buoyancy.

Max possible is 9.5 K for adiabatic ascent

dzBBdxwdzudzudzdxt

d

RL

R

L

d

d

R

R

L

d d

L

000 0

Simplifications: Assume air to right of cold pool is not bouyant (BR = 0)

Assume vorticity = far from

edge of cold pool at R and L.

Seek conditions for a steady balance: Therefore set tendency to zero

x

w

z

u

z

u

dzBdxwuuuu d

L

R

L

dRdRLdL

0

20,

2,

20,

2,

22220

Assume the cold air is stagnant relative to the cold pool edge (UL,0= 0) and the cold pool depth (H) is less than the height of the level d.

dzBdxwuuu H

L

R

L

dRdRdL

0

20,

2,

2,

2220

Recall RKW theory

dzBdxwuuuu d

L

R

L

dRdRLdL

0

20,

2,

20,

2,

22220

Assume the cold air is stagnant relative to the cold pool edge (UL,0= 0) and the cold pool depth (H) is less than the height of the level d.

This assumption is equivalent to assuming that there is no rear inflow jet!

For RIJ case, we must retain the first term in brackets on the right. Let d = H, the height of the cold pool.

2

0

20,

2,

20, 2 j

H

LLdLR cdzBuuu

In examining the optimal state with a RIJ, we must consider the additional vorticity source

RKW optimal scenario: vorticity associated with buoyancy gradients near leading edge of cold pool balances vorticity associated with ambient shear

Below RIJ, RIJ vorticity opposes vorticity associated with cold pool buoyancy, so cold pool has to be deeper and stronger to achieve optimal condition – longer time to transition to TSR development. Once above jet, the flow is rapidly diverted rearward by RIJ vorticity.

Jet descending to surface reinforces the vorticity associated with the cold pool bouyancy, accentuating the upshear tilting process already begun by the cold pool, promoting weaker and shallower lifting along the leading edge of the system.

RKW theory for optimal balance Theory with consideration of RIJ

The strong shear and corresponding elevated rear inflow leads to a near balance of the vorticity generation by the ambient shear, the vorticity generation due to the negative buoyancy of the cold pool and the vorticity associated with the vertical shear of the Rear Inflow Jet. The net result, a strong upright updraft – deep convection is maintained for a longer time.

Effect of CAPE and vertical shear on the strength of the RIJ. The shaded region are elevated RIJs. Shear is confined to the lowest 2.5 km.

General interpretation: More CAPE and more shear = stronger and more elevated jet

Effect of CAPE and vertical shear on the strength of the RIJ. The shaded region are elevated RIJs. Shear is confined to the lowest 5.0 km.

Again, general interpretation: More CAPE and more shear = stronger and more elevated jet

Conceptual model of a long lived squall line based on the previous discussions