August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and...
-
Upload
kerrie-gregory -
Category
Documents
-
view
217 -
download
2
description
Transcript of August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and...
![Page 1: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/1.jpg)
August 28, 2013
John P. McHughUniversity of New Hampshire
Internal waves, mean flows, and turbulence at the tropopause
![Page 2: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/2.jpg)
Is there more turbulence at the tropopause altitude?
Observations say ‘maybe’ Tropopause has a sudden change
in N, suggesting a wave effect Recent results point to three or
more possible explanations
![Page 3: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/3.jpg)
Schematic of Earth’s vertical temperature profile
![Page 4: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/4.jpg)
![Page 5: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/5.jpg)
McHugh, Dors, Jumper, Roadcap, Murphy, and Hahn, JGR, 2008
Experiments over HawaiiBalloon 2, first day
![Page 6: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/6.jpg)
McHugh, Dors, Jumper, Roadcap, Murphy, and Hahn, JGR, 2008
Experiments over HawaiiBalloon 2, second day
![Page 7: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/7.jpg)
McHugh, Jumper, Chen, PASP, 2008
Experiments over HawaiiBalloon 1, first day
![Page 8: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/8.jpg)
• Boussinesq• Two-layers with constant N• Periodic side boundaries• Uniform wave amplitude• Velocity is continuous at the
interface
First reason: nonlinear wave behavior near the tropopause
Uniform (Stokes) waves
![Page 9: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/9.jpg)
![Page 10: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/10.jpg)
• First few harmonics are scattered by the interface.• Remaining harmonics are evanescent in both layers.• Wave behavior at the interface is ‘Stokesian’.• Wave-generated mean flow is not local to the interface.• JAS, 66, 2009.
Results
![Page 11: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/11.jpg)
Direct numerical solution of wave packets
Reason 2: Wave induced mean flow at the tropopause
![Page 12: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/12.jpg)
Simulations
• Inviscid Anelastic equations• Spectral filter with p = 15• Two layers of constant N• Periodic boundaries on the sides• Damping (Rayleigh) layer at the top• Spectral method in space• TCFD, v 22, 2008
![Page 13: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/13.jpg)
![Page 14: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/14.jpg)
![Page 15: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/15.jpg)
![Page 16: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/16.jpg)
Primary Results of DNS
• Wave packet creates a localised mean flow (jet) at the interface.
• If wave amplitude is high enough, this mean flow exceeds horizontal wave speed and waves overturn below interface.
![Page 17: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/17.jpg)
Why does this jet form? Consider a simpler model.
Reason 3: Mean flow velocity gradients at the tropopause
• NLS amplitude equations• Two layers with constant N• Periodic side boundaries• Wave amplitude varies vertically• Paper being revised for JFM• Grimshaw and McHugh, to appear in QJRMS.
![Page 18: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/18.jpg)
Overall, have three nonlinear Schrodinger-likeequations, coupled through the linear interfacialconditions and the (nonlinear) mean flow.
and on z=0.
0221 22
12222
12' RInkRInkiRciRcR gg
0221 22
12222
12' IRnkRInkiIciIcI gg
0221 22
22' TTnkiTciTcT gg
JITKIR ,
![Page 19: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/19.jpg)
The wave-induced mean flow is
0,2
2
2
0,
22
22
*2
21
22
2
21
2*2 11
zTNc
u
RINc
u
RINc
u
zeueuuu
p
pi
pm
znii
zniim
![Page 20: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/20.jpg)
![Page 21: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/21.jpg)
![Page 22: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/22.jpg)
4.01 kn
![Page 23: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/23.jpg)
4.01 kn
![Page 24: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/24.jpg)
4.01 kn
![Page 25: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/25.jpg)
4.01 kn
![Page 26: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/26.jpg)
4.01 kn
![Page 27: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/27.jpg)
21 kn
![Page 28: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/28.jpg)
21 kn
![Page 29: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/29.jpg)
21 kn
![Page 30: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/30.jpg)
21 kn
![Page 31: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/31.jpg)
21 kn
![Page 32: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/32.jpg)
Results from amplitude equations
• Either frequency modulation or the oscillating mean flow may form a 'jet' underneath the mean interface.
• Mean flow is discontinous at the mean position of the interface (this feature was missing in DNS).
• Frequency modulation appears to be the stronger feature but is not significant in large amplitude waves.
![Page 33: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/33.jpg)
Unsteady flow past an obstacle
McHugh and Sharman, QJRMS, 2012.
![Page 34: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/34.jpg)
Numerical simulations
• Witch of Agnesi mountain shape• Linear bottom boundary condition• No rotation• Mountain is introduced gradually• 2nd order finite difference• Arakawa C grid• Leap frog method for time stepping• Typical case is U=10 m/s, H=1000,• A=1000m, N2/N1=2
![Page 35: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/35.jpg)
Unsteady mountain waves
U= 10 m/s, H=1000m, NH/U=1
![Page 36: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/36.jpg)
Mean flow• Need a mean definition that is analogous to the periodic
case• But no scale separation between waves and wave-induced
mean flow• Average over the computational domain depends strongly
on domain length.• Finally:
dxuuA
u 021
![Page 37: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/37.jpg)
U= 10 m/s, H=1000m, NH/U=1
dxuuA
u 021
![Page 38: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/38.jpg)
dxuuA
u 021
![Page 39: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/39.jpg)
Contours of horizontal velocity: closeup of tropopause region.
![Page 40: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/40.jpg)
U= 5 m/s, H=500m, NH/U=1
dxuuA
u 021
![Page 41: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/41.jpg)
dxuuA
u 021
![Page 42: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/42.jpg)
Conclusions for mountain wave case
• An upstream wave-induced mean flow usually forms above the mean position of the tropopause
• A counter flow forms beneath the mean tropopause, not present in the periodic simulations
• Mean flow remains in the steady mountain wave flow, and is different than the flow determined with the steady equations directly
• The combination of upstream and downstream flow at the tropopause suggests a higher likelihood of breaking there, or perhaps even a circulation
![Page 43: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/43.jpg)
Some concluding remarks
• The tropopause region is complex when the tropopause is sharp
• Probably need a two-layer simulation (DNS) that allows slip to get the correct mean flow at the tropopause
• If N is constant, then wave amplitude may be unity and the dispersive term doesn't exist. What happens to the jet?
• Still cannot completely explain the observations over Hawaii
![Page 44: August 28, 2013 John P. McHugh University of New Hampshire Internal waves, mean flows, and turbulence at the tropopause.](https://reader036.fdocuments.us/reader036/viewer/2022062905/5a4d1adb7f8b9ab059974b30/html5/thumbnails/44.jpg)
END