1. Evolution and Vertical Structure of the 20 June 2015 Bore Observed during PECAN
Dana Mueller, Bart Geerts
Min Deng, and Zhien Wang
University of Wyoming
Mention did work on other two cases
in review to Mon. Wea. Rev.
PECAN science meeting, Norman OK, Sept 2016

2. Outline Bore and solitary wave review Objective Data Observations
Comparison with theory
Conclusions

3. Hydraulic theory of bores
Rottman and Simpson (1989)
Froude number
Based on inviscid hydraulic theory for 2 layer flow, nonmixing, over streamlined solid body. Shallow water equations for lower fluid.
Normalized density current height

4. Rottman and Simpson (1989) laboratory studies: Bore Strength:
Bore speed:
Assumptions: no mixing, turbulence, non-hydrostatic effects, shear, & LH release
Post-bore inversion height
Pre-bore inversion height
Mention ranges of S. Based on inviscid hydraulic theory for 2 layer flow, nonmixing, over streamlined solid body. Shallow water equations for lower fluid.
Long gravity wave speed

5. Wave trapping Crook (1988):
Negative Scorer parameter layer above the SBL
2) Curvature of low-level wind profile normal to bore
3) Evanescence aloft due to winds opposing bore motion
Critical layer: U – Cb = 0
l2 < 0 typically requires significant curvature in the wind profile as is found above the LLJ. m2<0 implies evanescent, trapped waves. Wave energy may be reflected at a critical layer where bore-relative flow becomes zero.

6. Solitary waves Wave of elevation Dispersion balanced by nonlinearity
Bores can evolve into soliton (amplitude-ordered solitary waves)
Surface pressure oscillations, but no sustained rise
No wind shift at surface

7. GOES-13 4 km Thermal IR at ~0700 UTC. (source: PECAN EOL data archive)
Objective
18 UWKA flight legs south of a large, long-lived MCS
from ~0700 to 1030 UTC on 20 June 2015
to describe true evolution of bore vertical structure, and (u’, w, T’, p’) phase relationships aloft
GOES-13 4 km Thermal IR at ~0700 UTC. (source: PECAN EOL data archive)

8. NEXRAD radars
FP4
12Z sounding
ASOS station

9. Data UWKA -5 channels: N2, H20, elastic, high J, low J
Compact Raman Lidar (CRL): (Liu et al. 2014; Wu et al. 2016)
-5 channels: N2, H20, elastic, high J, low J
-Temperature not included due to limited spatial resolution at relevant ranges
-Lidar scattering ratio (LSR) and water vapor mixing ratio
Wyoming Cloud Lidar (WCL): (Wang et al. 2009)
-355 nm wavelength compact elastic lidar
-derived LSR
Thermodynamic and wind in-situ variables at flight level
CRL averaged to 1.5 m vertical res. 90 m horiz. Res. Temporal resolution = 1 sec.
WCL 1.5 m along beam and 5 to 20 m.

10. pre-bore ambient vertical structure
-Strong SBL (11 K θ increase in 377 m)
-deep residual mixed layer
-25 m/s southwesterly LLJ
Flight Level

11. Waves observed by KLNX (0.5 degree)
Reflectivity
Radial Velocity
0742 UTC
Say: nw in crests/high refle. Sw in trough. Same speed at 15 m/s.
0830 UTC

12. bore motion crest wave trof upstream flow
Beam height may be overestimated because of high stability and using a constant index of refraction. WSR88D algorithm for range to height. Doviak and Zrnic 1993.
crest
wave trof

13. Transects: Area 1 Clean air in SBL Moisture stratification F2R flow
Strong updrafts
-P’ values in crests
Cooling and moistening in crests
Mostly smooth/
undular
Bore motion
Connect to sounding. Mention vertical displacement values. Add animations. Add animated box/arrow for points.

14. KOAX Area 2 3 waves now Deepening of SBL Weakening of leading wave
2nd wave always highest amplitude
Bore motion
1.6 km vertical displacement led to cap cloud on wave 2. Clouds at 5 km = altostratus…high moisture above residual mixed layer.
KOAX

15. Leading wave locations projected onto bore-normal transect
Area 1
Area 2

16. 13 g/kg isohume traces of boundary layer top
Like isentropes up to cloud edge. Assumes steady flow and wv is conserved without clouds.

17. Evolution & vertical structure
Area 1 wavelength = ~12-25 km
Area 2 wavelength = ~25-30 km
Decrease in speed with time
Never amplitude-ordered
Turbulence in legs

18. (km below flight level) max Δp' (hPa) min Δp' (hPa)
time UTC
leg #
area
flight level (km, AGL)
peak updraft
(m s-1)
max cooling
(θ’ < 0) (K)
source level
(km below flight level)
max Δp' (hPa)
min Δp' (hPa)
leading wave phase speed 1 2 3
1-2
2.3
8.3
-7.5
1.7
0.5
-2.6
22.0
3-8
5.2
9.6
-2.4
-5.1
1.1
1.4
0.3 ~0
-1.1
16.6
9-12
4.3
6.2
-2.1
-5.4
1.0
0.2
-0.9
-1.5
18.3
13-18
3.0
3.9
2.1
-3.2
-1.2
1.2
1.3
-0.4
-0.5
14.1
Max cooling is relative to the upstream average. The source level is based on the pre-bore sounding (Fig. 2), assuming dry adiabatic ascent to flight level. Δp’ is the pressure perturbation relative to the upstream average. Bore speeds are based on the lidar method discussed in Section 4.4.

19. (km below flight level) max Δp' (hPa) min Δp' (hPa)
time UTC
leg #
area
flight level (km, AGL)
peak updraft (m s-1)
max cooling
(θ’ < 0) (K)
source level
(km below flight level)
max Δp' (hPa)
min Δp' (hPa)
leading wave phase speed
(m s-1) 1 2 3
1-2
2.3
8.3
-7.5
1.7
0.5
-2.6
22.0
3-8
5.2
9.6
-2.4
-5.1
1.1
1.4
0.3 ~0
-1.1
16.6
9-12
4.3
6.2
-2.1
-5.4
1.0
0.2
-0.9
-1.5
18.3
13-18
3.0
3.9
2.1
-3.2
-1.2
1.2
1.3
-0.4
-0.5
14.1

20. (km below flight level) max Δp' (hPa) min Δp' (hPa)
time UTC
leg #
area
flight level (km, AGL)
peak updraft (m s-1)
max cooling
(θ’ < 0) (K)
source level
(km below flight level)
max Δp' (hPa)
min Δp' (hPa)
leading wave phase speed
(m s-1) 1 2 3
1-2
2.3
8.3
-7.5
1.7
0.5
-2.6
22.0
3-8
5.2
9.6
-2.4
-5.1
1.1
1.4
0.3 ~0
-1.1
16.6
9-12
4.3
6.2
-2.1
-5.4
1.0
0.2
-0.9
-1.5
18.3
13-18
3.0
3.9
2.1
-3.2
-1.2
1.2
1.3
-0.4
-0.5
14.1

21. Wave train passage at FP4

22. Surface measurements: FP4 915 MHz profiler
Soliton?
4 main waves
Trailing waves = shorter wavelength
Wave signal up to nearly 4 km AGL
5 m/s velocity couplets (strongest in leading wave)
Decoupled from sfc at 13 UTC. Soliton because amplitude-ordered and detached from surface.

23. 12 UTC
13 UTC
FP4 webcam facing south

24. 12Z profiler data across 30 min
12Z profiler data across 30 min. strong shear…radar shows shallower shear layer.

25. (image courtesy David Turner, NSSL)
Surface tower
Wind speed decreases in crests (NW direction). Front-to-rear flow
+P’ in crests (~1.5 mb)
Lack of distinct cooling
AERI
Waves erode SBL
Moisture lofted ~2 km with leading wave
Mixing  slight drying at surface
Soliton
(image courtesy David Turner, NSSL)

26. Phase relationships
Wind direction changes in crests across bore fluid/SBL top, but not in troughs
Shear leads to vorticity (“spin”) and –p’  non-hydrostatic aloft
Convergence and divergence allow for propagation of waves
Stress bore NORMAL winds. Conservation of momentum…bore transported momentum near the surface as a material BL fluid instead of simple gravity waves. FL = trapped gravity wave. –P’ at FL not consistent with hydrostatic pressure patterns in VP waves.

27. Wave-trapping analysis
200 m bin interpolation, FFT with low pass filter
NW jetlet
LLJ

28. Wave-trapping analysis
Criteria:
Inversion and stable layer topped with deep neutral layer
LLJ and flow reversal at 3 km
Negative Scorer parameter ( ) at 4.1 km due to wind curvature
Waves to 4.5 km AGL. No critical layer

29. 700 m increase in inversion height
Northerly wind shift

30. Comparison with theory
parameters
lidar method
sounding or radar method
bore strength S (observed)
2.39
2.89
bore speed Cb (theoretical: Eqn 2)
m s-1
intrinsic: 30.5
intrinsic: 31.1
ground-relative: 14.4
ground-relative: 15.0
bore speed Cb (observed)
15.7
15.3
density current speed Cdc (observed)
N/A
21.4
Froude number
1.48
1.72
density current depth from KAIA surface data (m AGL):
Values of S agree with nature of waves
Predicted speed agrees well with observed
Alliance, NE ASOS station data for density current depth:
Equation derived from hydrostatic assumption…density is constant through depth of DC and sfc pressure difference is hydrostatic only. Subtracted full headwind. Cb eq predicts bore speed to within 25% for 2-4 S values. Ours are within that threshold.
(Koch et al. 1991)

31. S Froude number Normalized DC depth
Lidar method may be more representative:
-DC measurements made earlier and far to the NW of FP UTC sounding
-UWKA flew closer to KAIA at ~0800 UTC
-Lidar method S within observed range
Partially blocked flow
Lidar Aver. Sounding
Completely blocked flow
Partially blocked = subcritical to supercritical at crest and hydraulic jump connects upstream and downstream. Fr and do/ho are the 2 time independent solutions of shallow water equations for this flow configuration.
Normalized DC depth
Froude number

32. Conclusions -Deepening of SBL by 700 m
Phenomenon is a undular bore:
-Deepening of SBL by 700 m
-Quadrature phase shift between updrafts and cooling aloft
-Hydrostatic conditions at surface: +p’ in crests (and sustained higher P) and no cooling
-Observed phase speed (~15 m/s) values agree with theory
-Temperature duct and wind curvature for wave maintenance and trapping
-Vertically-stacked waves
-semi-turbulent nature consistent with 2 < S < 3
–p’ values in crests aloft  non-hydrostatic conditions aloft

33. Acknowledgements Nick Guy (UW) - py-art radar display
William Brown (NCAR) – FP4 wind profiler data analysis
David Turner (NSSL) - AERI
Steven Koch (NSSL), Kevin Haghi (OU), and Ben Toms (OU) - discussions

34. Questions?