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 “clear” 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.

𝑅𝑖𝑖𝑛 = 0.5 simulation using a mountain height Hof 1 km. The solid black lines are isotherms, thepurple contour lines are the magnitude of (𝑢’, 𝑣’)vector, the background field is the w velocity. Thevertical cross-section is taken at Y = - 10 km.

WAVE BREAKING

If wave breaking occurs:

𝑹𝒊𝒐𝒖𝒕 < 𝟎

𝑹𝒊𝒐𝒖𝒕 =𝑵𝟐

𝝏𝒖𝝏𝒛

𝟐

+𝝏𝒗𝝏𝒛

𝟐

u = U0+u’v = V0+v’N = N 0+ N’

In real conditions 𝑅𝑖 is a very noisy variable, with alarge vertical scale dependence, and even a flow witha 𝑹𝒊 > 𝟏 can be turbulent

AIM: Developing methods able to diagnose wave breakingwithout relying on the use of the (total) Richardson number.

If wave breaking occurs 𝑹𝒊𝒐𝒖𝒕 < 𝟎 in idealized flows!(and in simulations where the waves are well resolved)

SIMULATIONS SETUP – WRF MODEL

200 km

20 km

The larger the mountain height 𝐇the larger is the amplitude of the

excited waves

𝑵𝟎𝑯

𝑼𝟎

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

∆x = ∆y = 2km

SIMULATIONS SETUP – WRF MODEL

𝑹𝒊𝒊𝒏 = 𝟏𝟔𝟖𝟒𝟐𝟏

WEAK SHEAR FLOWS

STRONG SHEAR FLOWS

𝑹𝒊𝒊𝒏 =𝑵𝟎𝟐

𝝏𝒖𝟎𝝏𝒛

𝟐

+𝝏𝒗𝟎𝝏𝒛

𝟐

𝟎. 𝟓

By changing the directional shear we are changing the distributionof environmental critical levels where: 𝐔 z ∙ 𝐤𝐇 = 0

SIMULATION RESULTS - REGIME DIAGRAM

Regime diagram classifying the flow bycategories based on the 𝑅𝑖𝑚𝑖𝑛 values.

convective instability

dynamic instability(potentially an index ofturbulence)

flow having kineticenergy available forturbulent mixing

non-turbulent flowwhere no wavebreaking events occur

𝑹𝒊𝒊𝒏 = 𝟏𝟔

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SIMULATION RESULTS – FLOW TOPOLOGY

3D plots showing every point in the computationaldomain where 𝑹𝒊𝒐𝒖𝒕 < 𝟎. 𝟐𝟓. The plot refers to the18th hour of simulations and assume a 𝑁𝐻/𝑈 =1 (i.e. mountain height H = 1 km).

Dynamical instability 𝑹𝒊 < 𝟎. 𝟐𝟓

Convective instability 𝑹𝒊 < 𝟎

Turbulence generation (CAT)

REGIONS OF POTENTIAL

OCCURRENCE OF CAT

𝑹𝒊𝒊𝒏 = 𝟏𝟔 𝑹𝒊𝒊𝒏 = 𝟖 𝑹𝒊𝒊𝒏 = 𝟒

𝑹𝒊𝒊𝒏 = 𝟐 𝑹𝒊𝒊𝒏 = 𝟏 𝑹𝒊𝒊𝒏 = 𝟎. 𝟓

𝑹𝒊𝒐𝒖𝒕 < 𝟎. 𝟐𝟓 field

180 degrees

180 degrees

SIMULATION RESULTS - WIND FIELD

𝑹𝒊𝒊𝒏 = 𝟏

also 𝒖𝟎, 𝒗𝟎 ⊥ (𝒖′, 𝒗′)

𝒖𝟎, 𝒗𝟎(𝒖′, 𝒗′) Background field: magnitude of (𝒖′, 𝒗′)Contour line: 𝑹𝒊𝒐𝒖𝒕 < 𝟎. 𝟐𝟓

when 𝒖𝟎, 𝒗𝟎 ⊥ (𝒌, 𝒍)

for the wind profile employed in

these simulations: 𝒖, 𝒗 ∥ (𝒌, 𝒍)

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

𝒎 =𝑵(𝒌𝟐 + 𝒍𝟐)𝟏/𝟐

(𝒖𝒐𝒌 + 𝒗𝟎𝒍)

but 𝑢0 and 𝑣0 vary with height because of the

directional shear

Helical wind profile employed in the simulations:

𝑢0 = 𝑈0𝑐𝑜𝑠(β𝑧)𝑣0 = 𝑈0𝑠𝑖𝑛(β𝑧)

→ ∞

when 𝒖𝟎, 𝒗𝟎 ⊥ (𝒌, 𝒍)also 𝒖𝟎, 𝒗𝟎 ⊥ (𝒖′, 𝒗′)

when 𝒌𝒖𝟎 + 𝒍𝒗𝟎 = 𝟎

At a critical level the second terms are the onlyones that diverge and, therefore, the dominantones. Under these conditions, the ( 𝒖, 𝒗)vector is parallel to the wave-number vector(𝒌, 𝒍).

𝜷 =𝑵𝟎

𝑼 𝑹𝒊𝒊𝒏

CAT FORECAST IMPLICATIONS

𝒖𝟎, 𝒗𝟎 ⊥ 𝒌, 𝒍 𝒗𝒔 𝒖𝟎, 𝒗𝟎 ⊥ (𝒖′, 𝒗′)

Fourier space spectrumof the mountain waveswould have to be computed

Physical space modeloutputs

Condition that may be used to diagnose wave breaking is: 𝒖𝟎, 𝒗𝟎 ⊥ 𝒖′, 𝒗′

instead of 𝒖𝟎, 𝒗𝟎 ⊥ (𝒌, 𝒍)

Further tests are necessary to confirm the applicability and the generalityof this result:

• different wind profiles,• less idealized flows,• realistic orography,• develop an algorithm using the 𝑢0, 𝑣0 ⊥ 𝑢′, 𝑣′ criterion.

SUMMARY AND FUTURE WORK

Results :• Regime diagram: in directional shear flows, wave breaking always occurs when 𝑵𝟎𝑯/𝑼𝟎 = 1.

However, for gradually stronger directional shears (lower 𝑅𝑖𝑖𝑛) wave breaking can occur overlower mountains.

• 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.

• 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 𝑵𝟎𝑯/𝑼𝟎 and intensity of thebackground directional shear (quantified through 𝑹𝒊𝒊𝒏).

• Running numerical simulations with more realistic conditions: realistic orography, PBL, non-hydrostatic effects etc.

• Testing the applicability of the simulation results to more realistic flows.