3D Numerical Simulations of Shear-Driven Atmospheric Turbulence

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


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


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


Ri = N2

h2/Uo2

Re=Uoh/ν Pe=Uoh/κ

U=Uotanh(z/h)wind shear


T = αz


wind shearU=Uotanh(z/h)

wind shear asymptotic linear stability

Ri

kx2

Ri = N2

h2/Uo2

Re=Uoh/ν Pe=Uoh/κ


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.


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


Re=2500 (ReL=30,000) Ri=0.05

3000 x 1500 x 1500 spectral modesvorticity magnitude, side view


Re=2500 (ReL=30,000) Ri=0.05


QuickTime™ and aPhoto - JPEG decompressor

are needed to see this picture.


Re=2500 (ReL=30,000) Ri=0.05

3000 x 1500 x 1500 spectral modesvorticity magnitude, top view of midplane


Re=2500 (ReL=30,000) Ri=0.05





Re=2500 (ReL=12,000) Ri=0.20



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.


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)


Stratospheric Shear-Layer Census Data

L ΔU ΔT

z Re Ri


Turning-shear run matrix

0.0 0.5 1.0

0.05

0.10

0.15

0.20

Ri

Re=300


0.0 0.5 1.0

0.05

0.10

0.15

0.20









Ri

Re=300 Ri=0.05 β=0vorticity magnitude360×360×361 modes

Re=300 Ri=0.05 β=1

side view

top view






0.0 0.5 1.0

0.05

0.10

0.15

0.20

Ri





Re=300 Ri=0.15 β=0vorticity magnitude360×360×361 modes

Re=300 Ri=0.15 β=1

side view

top view


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.

3D Numerical Simulations of Shear-Driven Atmospheric Turbulence

Documents

Transcript of 3D Numerical Simulations of Shear-Driven Atmospheric Turbulence