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Turbulence generation by mountain wave breaking in flows with
directional wind shear*
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Maria Vittoria Guarino, Miguel Teixeira, Maarten Ambaum
EGU General Assembly 2016, Vienna, 17 - 22 April
Atmospheric processes over complex terrain
* Submitted to Quarterly Journal of the Royal Meteorological Society
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Clear-air turbulence CAT
Mountain wave breaking
Directional wind shear
HIGH ALTITUDE TURBULENCE
It is a βclearβ turbulencebecause it occurs in theabsence of any visualclues such as clouds.
BREAKING MOUNTAIN WAVES
CAN GENERATE CAT
If the wave amplitude islarge enough the wavesbecome unstable andbreak.
WINDS THAT TURN WITH HEIGHT
Directional shear flowsare quite common inatmosphere.
MOTIVATIONS AND AIMS OF THIS STUDY
SUBJECT: Clear air turbulence generation (within thetroposphere) by mountain wave breaking and its triggering bythe effects of directional wind shear.
ULTIMATE AIM: formulate quantitative criteria for theoccurrence of this phenomenon based on differentconfigurations of orography and wind profiles.
METHOD: employment of a 3D non-hydrostatic (non-Boussinesq) numerical model.
π πππ = 0.5 simulation using a mountain height Hof 1 km. The solid black lines are isotherms, thepurple contour lines are the magnitude of (π’β, π£β)vector, the background field is the w velocity. Thevertical cross-section is taken at Y = - 10 km.
WAVE BREAKING
If wave breaking occurs:
πΉππππ < π
πΉππππ =π΅π
ππππ
π
+ππππ
π
u = U0+uβv = V0+vβN = N 0+ Nβ
In real conditions π π is a very noisy variable, with alarge vertical scale dependence, and even a flow witha πΉπ > π can be turbulent
AIM: Developing methods able to diagnose wave breakingwithout relying on the use of the (total) Richardson number.
If wave breaking occurs πΉππππ < π in idealized flows!(and in simulations where the waves are well resolved)
SIMULATIONS SETUP β WRF MODEL
200 km
20 km
The larger the mountain height πthe larger is the amplitude of the
excited waves
π΅ππ―
πΌπ
LINEAR FLOWS
NON LINEAR FLOWS
= 0.1 , 0.2, 0.5, 0.75, 1
N0 constant, U0 constant
H = 100m, 200m, 500m, 750m, 1 Km
βx = βy = 2km
SIMULATIONS SETUP β WRF MODEL
πΉπππ = ππππππ
WEAK SHEAR FLOWS
STRONG SHEAR FLOWS
πΉπππ =π΅ππ
πππππ
π
+πππππ
π
π. π
By changing the directional shear we are changing the distributionof environmental critical levels where: π z β π€π = 0
SIMULATION RESULTS - REGIME DIAGRAM
Regime diagram classifying the flow bycategories based on the π ππππ values.
convective instability
dynamic instability(potentially an index ofturbulence)
flow having kineticenergy available forturbulent mixing
non-turbulent flowwhere no wavebreaking events occur
πΉπππ = ππ
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SIMULATION RESULTS β FLOW TOPOLOGY
3D plots showing every point in the computationaldomain where πΉππππ < π. ππ. The plot refers to the18th hour of simulations and assume a ππ»/π =1 (i.e. mountain height H = 1 km).
Dynamical instability πΉπ < π. ππ
Convective instability πΉπ < π
Turbulence generation (CAT)
REGIONS OF POTENTIAL
OCCURRENCE OF CAT
πΉπππ = ππ πΉπππ = π πΉπππ = π
πΉπππ = π πΉπππ = π πΉπππ = π. π
πΉππππ < π. ππ field
180 degrees
180 degrees
SIMULATION RESULTS - WIND FIELD
πΉπππ = π
also ππ, ππ β₯ (πβ², πβ²)
ππ, ππ(πβ², πβ²) Background field: magnitude of (πβ², πβ²)Contour line: πΉππππ < π. ππ
when ππ, ππ β₯ (π, π)
for the wind profile employed in
these simulations: π, π β₯ (π, π)
SIMULATION RESULTS - THEORY
Adopting a zeroth-order WKB approximation
Assumption: the background flow is varying slowly along z if compared to the vertical wavelength of the waves
π =π΅(ππ + ππ)π/π
(πππ + πππ)
but π’0 and π£0 vary with height because of the
directional shear
Helical wind profile employed in the simulations:
π’0 = π0πππ (Ξ²π§)π£0 = π0π ππ(Ξ²π§)
β β
when ππ, ππ β₯ (π, π)also ππ, ππ β₯ (πβ², πβ²)
when πππ + πππ = π
At a critical level the second terms are the onlyones that diverge and, therefore, the dominantones. Under these conditions, the ( π, π)vector is parallel to the wave-number vector(π, π).
π· =π΅π
πΌ πΉπππ
CAT FORECAST IMPLICATIONS
ππ, ππ β₯ π, π ππ ππ, ππ β₯ (πβ², πβ²)
Fourier space spectrumof the mountain waveswould have to be computed
Physical space modeloutputs
Condition that may be used to diagnose wave breaking is: ππ, ππ β₯ πβ², πβ²
instead of ππ, ππ β₯ (π, π)
Further tests are necessary to confirm the applicability and the generalityof this result:
β’ different wind profiles,β’ less idealized flows,β’ realistic orography,β’ develop an algorithm using the π’0, π£0 β₯ π’β², π£β² criterion.
SUMMARY AND FUTURE WORK
Results :β’ Regime diagram: in directional shear flows, wave breaking always occurs when π΅ππ―/πΌπ = 1.
However, for gradually stronger directional shears (lower π πππ) wave breaking can occur overlower mountains.
β’ Flow topology: increasing the strength of the directional shear leads to wider regions of(potential) turbulence generation. For stronger shear flows wave breaking occurs at lowerlevels.
β’ In a wave breaking event, the background wind vector and the velocity perturbation vector areapproximately perpendicular.
Future work:
Aim: to diagnose wave breaking occurrence (and the potential for turbulence generation) over a3D isolated mountain.Method: running numerical simulations with different values of π΅ππ―/πΌπ and intensity of thebackground directional shear (quantified through πΉπππ).
β’ Running numerical simulations with more realistic conditions: realistic orography, PBL, non-hydrostatic effects etc.
β’ Testing the applicability of the simulation results to more realistic flows.