3d numerical simulations of shear-driven atmospheric turbulence
DESCRIPTION
3D Numerical Simulations of Shear-Driven Atmospheric Turbulence. Joe Werne, Dave Fritts, Reg Hill Colorado Research Associates Division (CoRA) NorthWest Research Associates, Inc. (NWRA) Paul Bernhardt Naval Research Laboratory. Turbulence in Stably Stratified Environments. - PowerPoint PPT PresentationTRANSCRIPT
D.C., January 2007 Joe Werne NWRA/CoRA1
3D Numerical Simulations of Shear-Driven Atmospheric Turbulence
Joe Werne, Dave Fritts, Reg Hill
Colorado Research Associates Division (CoRA)
NorthWest Research Associates, Inc. (NWRA)
Paul Bernhardt
Naval Research Laboratory
D.C., January 2007 Joe Werne NWRA/CoRA2
Two processes dominate turbulence generation in stable stratification:
• Wind-shear instability
• Gravity-wave breaking
The resulting turbulence is
• Temporally episodic
• Spatially intermittent (inhomogeneous and anisotropic)
• Nearly all subgrid-scale
At lower altitudes, measurements reveal and help quantify the dominant
processes. These measurements include:
• Cloud imagery
• Balloon (rawinsonde) data
• Aircraft data
• Radar measurements
Turbulence in Stably Stratified Environments
D.C., January 2007 Joe Werne NWRA/CoRA3
Clear Air Turbulence: Wind Shear
Estes Park, Colorado, 1979 (photo by Bob Perney)
O(0.1-1km)
D.C., January 2007 Joe Werne CoRA, NWRA, Inc.
Gravity-Wave Breaking
Wind Shear
U=Uotanh(z/h)
Stably Stratified Dynamics Simulations
T = αz
D.C., January 2007 Joe Werne CoRA, NWRA, Inc.
Ri = N2
h2/Uo2
Re=Uoh/ν Pe=Uoh/κ
U=Uotanh(z/h)wind shear
Stably Stratified Dynamics Simulations
T = αz
D.C., January 2007 Joe Werne CoRA, NWRA, Inc.
wind shearU=Uotanh(z/h)
wind shear asymptotic linear stability
Ri
kx2
Ri = N2
h2/Uo2
Re=Uoh/ν Pe=Uoh/κ
Stably Stratified Dynamics Simulations
Note: ν = μ / ρ and ρ = ρ0 exp(z/H)
ν increases by 105 from z=20km to 100km.
Shear turbulence is easier to resolve in the mesosphere than in the stratosphere.
Note: ν = μ / ρ and ρ = ρ0 exp(z/H)
ν increases by 105 from z=20km to 100km.
Shear turbulence is easier to resolve in the mesosphere than in the stratosphere.
D.C., January 2007 Joe Werne NWRA/CoRA7
FFT
• Stream-function/vorticity formulation (T, W, ω3)
• Fully spectral (3D FFT’s = 75% computation)
• Radix 2,3,4,5 FFT’s
• Spectral modes and NCPUs must be commensurate
• Communication: MPI or shmem, global transpose
• Parallel I/O every ~ 60 δt
Ky
Kx
Kz
PE 7PE 6PE 5PE 4PE 3PE 2PE 1PE 0
X
Z
Y
PE 7PE 6PE 5PE 4PE 3PE 2PE 1PE 0
DNS-Code Details
D.C., January 2007 Joe Werne NWRA/CoRA8
Re=2500 (ReL=30,000) Ri=0.05
3000 x 1500 x 1500 spectral modesvorticity magnitude, side view
D.C., January 2007 Joe Werne NWRA/CoRA9
Re=2500 (ReL=30,000) Ri=0.05
3000 x 1500 x 1500 spectral modesvorticity magnitude, side view
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are needed to see this picture.
D.C., January 2007 Joe Werne NWRA/CoRA10
Re=2500 (ReL=30,000) Ri=0.05
3000 x 1500 x 1500 spectral modesvorticity magnitude, top view of midplane
D.C., January 2007 Joe Werne NWRA/CoRA11
Re=2500 (ReL=30,000) Ri=0.05
3000 x 1500 x 1500 spectral modesvorticity magnitude, top view of midplane
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D.C., January 2007 Joe Werne NWRA/CoRA12
Re=2500 (ReL=12,000) Ri=0.20
2000 x 1000 x 1000 spectral modesvorticity magnitude, side view
D.C., January 2007 Joe Werne NWRA/CoRA13
Re=2500 (ReL=12,000) Ri=0.20
2000 x 1000 x 1000 spectral modesvorticity magnitude, side view
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
D.C., January 2007 Joe Werne NWRA/CoRA14
Re=2500 (ReL=12,000) Ri=0.20
2000 x 1000 x 1000 spectral modesvorticity magnitude, top view of midplane
D.C., January 2007 Joe Werne NWRA/CoRA15
Re=2500 (ReL=12,000) Ri=0.20
2000 x 1000 x 1000 spectral modesvorticity magnitude, top view of midplane
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
D.C., January 2007 Joe Werne NWRA/CoRA16
consistent with atmospheric measurements
CT2 T Ri
DNS
CT2 T Ri
Rawinsonde
Computed T, CT2, Ri profiles agree with rawinsonde observations.
Validation of DNS Solutions
Low-Ri solutions consistent with cloud images.
High-Ri solutions consistent with aircraft cliff-ramp measurements.
Spectral slopes between -5/3 and -7/5, consistent with recent aircraft data
2nd-order structure function fits agree with aircraft and tower data
Kolmogorov predicts 1.33
Rescaled numerical solutions (with Re=104-105) are relevant to atmospheric shear layers (even when Re=107-108).
Mesospheric simulations are much easier to resolve.
Rescaled numerical solutions (with Re=104-105) are relevant to atmospheric shear layers (even when Re=107-108).
Mesospheric simulations are much easier to resolve.
D.C., January 2007 Joe Werne NWRA/CoRA17
Good News:
• Reduced density means lower Re, which is easier to resolve
New Twist:
• Local wind profile can take the form of turning shear:
u(z) = U0 tanh(z/h) v(z) = V0 sech(z/h)
Mesospheric Simulations
β = 0 β = 0.5 β = 1
Ux (m/s)
Uy (m/s)
Rel
ativ
e A
ltit
ud
e (k
m)
D.C., January 2007 Joe Werne NWRA/CoRA18
Stratospheric Shear-Layer Census Data
L ΔU ΔT
z Re Ri
D.C., January 2007 Joe Werne NWRA/CoRA19
Turning-shear run matrix
0.0 0.5 1.0
0.05
0.10
0.15
0.20
Ri
Re=300
D.C., January 2007 Joe Werne NWRA/CoRA20
0.0 0.5 1.0
0.05
0.10
0.15
0.20
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Ri
Re=300 Ri=0.05 β=0vorticity magnitude360×360×361 modes
Re=300 Ri=0.05 β=1
side view
top view
D.C., January 2007 Joe Werne NWRA/CoRA21
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0.0 0.5 1.0
0.05
0.10
0.15
0.20
Ri
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Re=300 Ri=0.15 β=0vorticity magnitude360×360×361 modes
Re=300 Ri=0.15 β=1
side view
top view
D.C., January 2007 Joe Werne NWRA/CoRA22
Conclusions
1. Dramatically different turbulence dynamics and flow morphology result for weakly and strongly stratified wind shear.
2. Turning shear significantly affects instability dynamics and evolution.
3. Ramifications for transport and mixing?
Ongoing & Future Work
1. Construct atmospheric Ri, Re, and β census PDFs using available observational data.
2. Generalize linear stability analysis for turning shear.
3. Quantify instability (morphology, evolution, etc.) as functions of Ri, Re, and β in order to determine implications for mixing and transport.
4. Include passive tracer particles and quantify mixing efficiency.