Can a gust front tilt horizontal vortex lines to produce a - PowerPoint Presentation

Slide1

Can a gust front tilt horizontal vortex lines to produce a tornado?

Paul

Markowski

Pennsylvania State University

Bob Davies-Jones

Emeritus, NSSLSlide2

Consider two parcels following the same trajectory. Also assume that the parcels lie on the same vortex line.

A

B

In an

inviscid

, barotropic flow, vortex lines move as material lines (vortex lines are ‘‘frozen’’ into the fluid and behave like elastic strings that the flow moves, stretches, and reorients)

At some later time, the parcels have moved and the segment of the vortex line moves as a material line according to the trajectories of the parcels.

Hermann von Helmholtz

(1821–1894)

Helmholtz’ (1858) theoremSlide3

In an

inviscid

, barotropic flow, vortex lines move as material lines (vortex lines are ‘‘frozen’’ into the fluid and behave like elastic strings that the flow moves, stretches, and reorients)

Consider two parcels following the same trajectory. Also assume that the parcels lie on the same vortex line.

At some later time, the parcels have moved and the segment of the vortex line moves as a material line according to the trajectories of the parcels.

Helmholtz’ (1858) theoremSlide4

But what if the tilting is extremely abrupt, e.g., a strong gust front tilts vortex lines?

Simpson, J.,1982:

Cumulus rotation: Model and observations of a waterspout-bearing cloud system.

Intense Atmospheric Vortices.

L. Bengtsson and J. Lighthill, Editors. Springer-

Verlag, 161–173.Slide5

Simulation of density current in environment having strong zonal and

meridional

shear

“Mother of all density currents”—5-km-deep block of cold air with a minimum

q’ of –12 KExtreme low-level shear/horizontal vorticity:

(x0,

h0

, z0) = (–0.02, 0.02, 0.00) s

–1

q’Slide6

Simulation of density current in environment having strong zonal and

meridional

shear

Just ahead of the almost vertical wall of the density current, warm air rises rapidly (

w

>20 m s

–1 as low as 1 km above ground)

streamlinesSlide7

Simulation of density current in environment having strong zonal and

meridional

shear

vertical velocity

Just ahead of the almost vertical wall of the density current, warm air rises rapidly (

w

>

20

m

s

–1

as low as 1 km above ground)Slide8

Simulation of density current in environment having strong zonal and

meridional

shear

Environmental vortex lines turn abruptly upward at the leading edge of the density current, but the peak

z

(0.02 s–1) is located well aloft at 3 km.

Despite the large environmental

x in the lowest 1 km, the maximum z

at 25 m (the lowest scalar level) in the warm air ahead of the density current is only 0.001 s–1

.vortex linesSlide9

Simulation of density current in environment having strong zonal and

meridional

shear

vertical vorticity

Environmental vortex lines turn abruptly upward at the leading edge of the density current, but the peak

z

(0.02 s

–1

) is located well aloft at 3 km.

Despite the large environmental

x

in the lowest 1 km, the maximum

z

at 25 m (the lowest scalar level) in the warm air ahead of the density current is only 0.001 s–1

.Slide10

Simulation of density current in environment having strong zonal and

meridional

shear

The culprit: a stagnation high is present at the surface at the leading edge of the density current

Warm parcels encounter an adverse pressure gradient and decelerate as they get within about 2 km of the gust front.

pressure

HSlide11

Simulation of density current in environment having strong zonal and

meridional

shear

Parcels are compressed in the east-west direction (and stretched vertically to conserve mass).

The magnitude of x

in the lowest 100 m decreases from 0.02 s

–1 to 0.002

s–1 by the time the streamlines turn upward at the density current’s leading edge.

For a steady density current, it can be shown that x ∝

u and z

∝

w.

zonal vorticitySlide12

Conclusions

It cannot be argued that because there is large amount of horizontal vorticity in a surface-based layer in the environment, abrupt tilting of it at an “obstacle” (such as a gust front or topographical barrier) will produce similar strength vertical vorticity very close to the surface.

Linear thinking (i.e., assuming that horizontal vorticity is unmodified from environmental values) is misleading in this case

because the abrupt tilting is unavoidably associated locally with a stagnation flow that greatly compresses the horizontal vortex tubes prior to tilting.Slide13

Summary

The results are consistent with the Dahl et al. (2012) trajectory study, which found that

only outflow parcels entered the near-surface vortices of their simulated

supercells

Dahl et al. (2012)

Trajectories entering the vortex

Trajectories originating in the inflowSlide14

Point of clarification

Note, however, that in papers that have tracked material circuits, the circuits are

much broader

than the core radius of the near-surface

mesocyclone

(and in some studies the circuits are also several hundred meters above the surface)These circuits extend into the inflow at the

start

of the backward trajectory calculations; thus, some of the parcels comprising the material circuits really do come from the inflow

i.e., just because a material circuit has large positive circulation at its starting point surrounding a mesocyclone doesn’t imply that every parcel comprising the material circuit has positive vorticity (or even contributes positively to the circulation)

inflow

inflow

outflow

outflow

Rotunno

&

Klemp

(1985)