Case #3:  Evolution of Line-End (Bookend) Vortices

With the use of numerical simulations Weisman (1993) showed that the source of vertical vorticity
for circulations at the ends of a bowing structure can be traced to the tilting and subsequent 
stretching of the horizontal vorticity inherented in the ambient vertical wind shear.  His simulations 
showed that one set of parcels originates near the surface downwind (ahead) of the convective
system and is characterized by high-values of theta-e.  A second set of parcels originates in the
3-5 km layer to the rear of the convective system and descends in conjunction with the mesoscale
rear inflow jet.  Convectively generated horizontal vorticity which might contribute to the development
of the line-end vortex, may result from air parcels traveling along horizontal bouyancy gradients 
downshear from the convective system.  This concept of the generation of streamwise vorticity has
been used to explain the development of low-level rotation within supercell updrafts (Rotunno and
Klemp 1985).  Recent work completed by Weisman and Davis (1998) showed that the source of
generation of system-scale and sub-system scale vortices (e.g. large mesovortices) is primarily
due to tilting of system-generated horizontal vorticity within the laterally finite front-to-rear 
ascending current.  This process produces a cyclonic (anticyclonic) vortex just behind the northern
and southern ends of the convective system.
 


Fig. 1 
Schematic diagram of vertical vorticity generation through vortex tilting
 in westerly shear.  The descending motion pushes the vortex lines down
 in the center, resulting in cyclonic rotation on the north end and anticyclonic
 on the south end (after Weisman and Davis 1998).


There are two possible ways in which horizontal vortex lines can be deformed to produce line-end
vortex patterns: a) a localized downdraft in western shear, and b) a localized updraft in easterly
shear.  They suggested that initally that the downdrafts in the ambient westerly shear leads to 
the early development of line-end vortices.  The ambient shear plays an important role in this 
process by producing a preferred zone of lifting along the downshear edge of the systems due to
cold pool shear interactions, thus limiting the lateral extended of the lifting zone.  In stronger shear 
environments, a stronger more vertically erect leading line updraft results in vortices forming just
behind the leading edge of the system.  With time the system cold pool dominates over the ambient
shear and the upward tilting of horizontal vorticity associated with easterly shear becomes the 
dominant source of vertical vorticity for line-end vortices.  In the presence of weaker shear 
environments, a shallow front-to-rear ascending current can also lead to vortex production
well behind the leading edge of the system.  Further analysis and work is underway to clarify the
role of system-generated and ambient horizontal vorticity leading towards the production of line-end
and smaller-scale vortices which form along an north of the apex of a large bow echo.  See Trapp 
and Weisman (2003 - MWR) for further information.


  
Fig. 2  Schematic Diagram of Line-end Vortex Structure (from Weisman 1993). 


The schematic above represents basic properties of a vortex couplet.  The velocity field of the
couplet may be interpreted as the vector sum of the velocity field induced by each vortex individually.
The net flow field includes a jet of air between the two vortices and much weaker flow outside the 
vortices.  The enhancement of flow between the two vortices can be interpreted as a focusing effect of the vortex couplet.  The pressure field is characterized by pressure deficits coincident with
the vortices, and a zone of slightly lower pressure extends between the vortices which produces a 
pressure gradient that is consistent with the acceleration of the flow between the vortices. The 
strength of the jet is dependent on the sizes and magnitudes of the vortices as well as the spacing 
between them. The larger the vortex, the stronger the jet. In the northern hemisphere, the influence of 
the corilois effect and the strength of the vertical wind shear will result in the northern vortex becoming
more dominant compared to its southern member. We often observe this influence with the evolution 
of a comma-shaped reflectivity pattern and a strong vortex within the comma-head of a large bow 
echo.


June 29, 1998 Line-end vortex

The 29 June 1998 Derecho revealed the evolution of a classic 'line-end vortex' (C2a) near the 
northern end of the large bow echo.  The line-end vortex formed after 2030 UTC, however we show 
its pronounced phase between 2138 and 2220 UTC.  The core diameter during this period ranged 
from 13 km at 2138 UTC to as large as 32 km at 2220 UTC.  We have documented the evolution of 
four northern 'line-end' from four separated cases.  In each case, the vortex exhibited a broad but 
strong inbound (outbound) velocity couplet.  Of the three cases, the June 29, 1998 northern line-end 
vortex was quite pronouced for nearly 40 minutes, while the May 25, 2004 line-end vortex also 
exhibited a long lifetime of 60 minutes.  Discussion of the May 25, 2004 line-end vortex will be shown
in the following section (May 25, 2004 Bow Echo event over Northeast Missouri and southwest 
Illinois).  We have documented the evolution of two other line-end vortices from two separate cases.
The life-times of these vortices were shorter lasting only 20 and 25 minutes respectively.  In 3 of the
4 cases documented three common themes surfaced: 1) the line-end vortex appeared to play a role 
in accelerating the bowing convective line, 2) the
strongest damaging winds occurred along the 
southern periphery to as much as 40 km south - southeast of the line-end vortex, and 3) damaging 
winds occurred along the bowing structure as much as 1.5 to 2.5 hours after the demise of the 
northern line-end vortex.  In some cases when the mature line-end vortex was present damaging 
winds may occur over a period of 15 to 20 minutes. In the 4th case (May 25, 2004 QLCS event) a 
stable layer of air within the lowest 1.0 to 1.5 km likely inhibited the strong surface winds from 
reaching the surface (see discussion on May 25, 2004 QLCS).  In the 29 June 1998 Derecho event, 
Mesovortex #2 merged within the larger line-end vortex (C2a) after 2144 UTC.  The outbound
velocity component became part of the larger line-end vortex structure.  Figure 3 shows the 
reflectivity and storm-relative velocity patterns at 2155 UTC from WFO Lincoln Illinois.


Fig 3
Plan view reflectivity (left), storm-relative velocity (right) (0.5° slice) at 2155 UTC,
29 June 1998.  The white circle on SRM image represents the approximate core
diameter of Circulation 2a (19 km diameter).  The red dashed line respresents the
location where strongest wind damage occurred with that part of the bowing segment.
(Click on image for a larger image)


Line-end vortex C2a (shown left - SRM velocity) is embedded within the highly reflective comma-
shaped echo.  The reflectivity plan view shows the smallest width of the convective line immediately 
south of the large line-end vortex (immediately west of the dash red line).  Height of the convective 
towers over this part of the line are lower compared to their counterparts within the region of the line-
end vortex and southwest of the apex of the large bow echo (southwest part of the bow echo).  The 
area of smaller convective towers - weaker reflectivity is similar to Weisman's Stage 3 (upshear 
tilting phase
) where the convective system's cold pool overwhelms the ambient shear and a 
significant rear inflow jet is present.  The convective towers immediately south of the line-end vortex 
do not have the opportunity to mature compared to convective towers in the vicinity of the bookend 
and south of the apex of the bow where the system's cold pool is in a more favorable balance with 
the environmental ambient shear.  At a number of locations south and along the path of the large line-
line end vortex (within the weaker reflectivity line segment) damaging winds of 70 to nearly 100 mph 
persisted for over 10 minutes.


Fig 4
 Similar to Figure 3 except for 2207 UTC, 29 June 1998. 


The plan view reflectivity image taken 12 minutes later (2207 UTC - Fig 4) (left) continues to show
the lower reflectivity magnitudes just south of the comma-head and north of the apex of the bow 
(west of the dash red line).  These towers do not tilt per se upshear with height, rather they do not
mature into tall convective towers due to the strength of the system's cold pool.  The greatest degree 
of wind damage continued to occur over this part of the large bow echo with wind gusts over 85 mph.


Fig. 5
  Rotational Velocity (Vr) time-height trace of line-end vortex (C2a) for the period of 2138
- 2220 UTC .  Magnitudes of Vr are in m s-1. 


The rotational velocity time-height trace (Fig. 5) revealed that Line-end vortex C2a was relative deep
and strong throughout this period.  Note the slightly descending structure of the vortex between 
2138 and 2208 UTC.  The period of strongest rotation was detected at the lowest two elevation 
slices (0.5° / 1.5° slices) between 2149 and 2202 UTC.  This part of the vortex appeared to enhance 
the flow around the periphery of the large line-end vortex and likely enhanced surface wind damage.


Fig. 6
  Map of mesovortex tracks C1 - C4 and line-end vortex C2a across north central Illinois.
Squall line positions are denoted every 30 minutes.  (T) and adjacent then solid line next to
mesovortex tracks show the location of tornadic damage tracks. 


Figure 6 shows the individual paths of the mesovortices and squall line positions every 30 minutes. 
The squall line positions show that the convective line accelerated between 2133 and 2202 UTC 
within the period when the rotation associated the Line-end vortex C2a was strongest (2149 - 2202 
UTC).  Significant wind damage occurred from just east of Peoria through the Bloomington, Illinois 
area (across northern Taswell through McLean counties).  The area of enhanced wind damage 
occurred immediately south and along the southern periphery of C2a's track.  This graphic also 
shows that Mesovortices C3 and C4 did not merge with the larger line-end vortex. 

(See May 25, 2004 QLCS event for more information concerning the evolution of the line-end
vortex associated with this case).
 

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