FEATURES OF TURBULENT TRANSPORT OF MOMENTUM AND HEAT IN STABLY STRATIFIED BOUNDARY LAYERS AND THEIR REPRODUCTION IN ATMOSPHERIC MESOSCALE MODELS

Transcription

1 C I T E S 009_ Krasnoyarsk 009 FEATURES OF TURBULENT TRANSPORT OF MOMENTUM AND HEAT IN STABLY STRATIFIED BOUNDARY LAYERS AND THEIR REPRODUCTION IN ATMOSPHERIC MESOSCALE MODELS A. F. Kurbatsky Insttute of Theoretcal and Appled Mechancs of Russan Academy of Scences, Sberan Branch and Novosbrsk State Unversty, Russa L. I. Kurbatskaya Insttute of Computatonal Mathematcs and Mathematcal Geophyscs of Russan Academy of Scences, Sberan Branch, Russa

2 Introducton Boundary layers becomes stably stratfed whenever surface s colder than the ar. Under ths condton, turbulence s generated by shear and destroyed by negatve buoyancy and vscosty. Because of ths competton between shear and buoyancy effects, the strength of turbulence n the stable boundary layer s much weaker n comparson to the neutral and convectve boundary layers. As result, the stable boundary layer s also much shallower and characterzed by smaller eddy motons.

3 Study Motvaton: Stable boundary layer turbulence has not receved much attenton despte ts scentfcally ntrgung nature and practcal sgnfcance (e.g., pollutant transport). Ths mght be attrbuted to lack of adequate feld or laboratory measurements and complexty of ts dynamcs: e.g., occurrence of Kelvn- Helmholtz nstablty (K-H), gravty waves, low-level et (LLJ), etc.

4 Some features of the vertcal turbulent transfer of momentum and scalar n stably stratfed flows

5 Rchardson number The relatve mportance of the dfferently drected effects of shear and stratfcaton s characterzed usually by the gradent Rchardson number K R g N /S ms KhN ε N g( / z) / s the Brunt Vasala & && frequency 0 S U / z - s the vertcal shear, of the U(z) The gradent Rchardson number s a measure of the relatve ntensty of densty gradent n the stably stratfed flows. Beng based on ths crteron, n early studes t was assumed thatt turbulence completely l attenuates, t f Rchardson number exceeds a certan crtcal value, 0,5 < R < 1 (Rchardson, 190). R gc

6 K m S Flux Rchardson number, K h N ε m Rf K S (1 R ) f R R / Pr ; Pr f g T T K K m h The undamped turbulence s possble only at R R, and R 1 f fc fc

7 Inverse Prandtl number, Prt K H / KM, s stablty (Rg) )dependentd 1

8 1 Pr K / K Inverse Prandtl number, t H M s stablty (Rg) dependent Wnd tunnel experment: Ohya, Y. Boundary-Layer Meteorology Vol.98, 57-8

9 Flux Rchardson number: dataset from Mont et al. (00) R Pr K / K f R g / PrT t m h

10 Vertcal turbulent transfer, К-H nstabltes and nternal waves: the laboratory experment of Ohya (001) Vsualzaton by smoke shows the nstantaneous pcture of flow (from left to rght) n the strongly steady boundary layer. Turbulent flow s formed wth buoyancy and are ncluded wave-lke motons. Local shear causes nstablty analogous to the wave breakdown of Kelvn - Helmholtz. Generated turbulence ntermxes momentum and heat, whch decreases the shear and leads to an ncrease n Rchardson number.

11 RANS-approach for turbulent stratfed flows DU 1 P g U ; k k Dt x x. D Dt x h, τ uu the turbulent stresses tensor huθ the turbulent heat f lux vector

12 D Dt Dt Turbulence equatons Reynolds stresses, uu u P D D P h h П x k k U x uu u k k k U x pu 3 k k П u p x k u u u x x k p x 3 3 x k pu k g Heat fluxes, h u θ Dh U Θ D h П, Dt x x h П p x, D h x u u

13 New dependence for the pressure correlaton p n the stably stratfed turbulence, p Relaxaton lnear model for the slow term: Standard the SOC models usually assume, that p E, u p Such closure may not necessarly apply to the stably stratfed flows! Because we use the orgnal theoretcal work of Wenstock (1989), ponted out that the tme scale p must nclude a buoyancy dampng factor p 1 a N Wenstock s dampng factor

14 Full Explct Algebrac Models for Reynolds Stresses and Scalar Fluxes Db D 0 4 ES B П Dt 3 Dh U D 0 h П, Dt x x h Algebrac equatons for b uu /E /3 and h u : b 1ES 3B Ah b E 4g3 3 x

15 Improved Full Explct Algebrac Models for Reynolds Stresses and Scalar Fluxes : D case U V uw, vw K, z z M K K M H E S E S M H E wkh z c 1 c 1 GM s6gh5( g) D 3 GH S N G S M 1 s 1sG s s G s s N g U V S z z z 0 1 H 3 H 4 5 M S D 1 s H 1sG * 6 H 6G H g / E D3 c1 D 1 d 1 G M d G H d 3 G M G H d 4 G H ( d 5 G H d 6 G M G H ) G H

16 Three-parametrc turbulence model Turbulent knetc energy E (1/) uu DE 1 U D τ β h ε, Dt x Dε Dt D ε TKE dsspaton, ε U ε cε1 uuk βgδ3uθ c ε, E xk E Temperature varance, Dθ Θ D h θ ε θ, Dt x

17 Modelng and Smulaton of SBL

18 Low-Level Jet n the SBL When the wnd shear s domnant durng nght, the nocturnal Low-Level Level Jet ( sketch on the rght sde) forms followng the attenuaton of convectve turbulent stresses from ther afternoon maxmum, allowng nghttme wnds above a stable boundary layer to accelerate wth formaton of et maxmum or nose.

19 The SBL over flat terran Q capng nverson Velocty U K-H h 00 m Low-Level L Jet KH K-H sunset

20 Stable Boundary-Layer Experment The ntal temperature profle conssts of an adabatc layer wth potental temperature 65 K from surface up to 100m, above whch h the ar s stable wth a constant t lapse of K/m (t s based upon the Kosovc and Carry (000) stable nocturnal boundary layer LES-smulatons). A prescrbed coolng rate of 0.5 K /hr s enforced at the surface. Wnd profles are ntally set equal to the geostrophc wnd value (8 m/s n the x-drecton) throughout the layer. At the ground turbulent fluxes are computng usng the MOST accordng to the non-teratve formulaton.

21 Temperature and Velocty Profles n SBL wth Low-Level L Jet U G =8 ms -1 z(km) ntal profle Arctc experment (BASE data) smulaton z,km smulaton LES model (Beare et al. 005) [K] ) Wnd velocty (ms 1 )

22 Generaton of Low-Level Jet n the nocturnal ABL U G =8 ms z(km) 0.4 ntal profle 14 z(km) K U(ms -1)

23 Inverse Turbulent Prandtl Number, Pr t -1 Pr -1 =K / t h K m Data: Mont et al. (00) Strang and Fernando, 001 Smulaton wthout Wenstock's s factor wth Wenstock's factor R g =N /S Asymptotc: R 0, Pr K / K g t m h Computng results of Pr t -1 n the SBL over a flat terran: p E/ (wthout the Wenstock s factor) 1 a p N (wth the Wenstock s factor) N g / z s the Brunt-Väsälä frequency

24 CONCLUSION The mproved nonlocal turbulence model for descrbng the SBL over the aerodynamcally rough surface wth thermal nhomogenetes was presented. By usng of smple D computatonal test the some features of turbulent transport of momentum and heat n the SBL was reproduced. d Smulatons based on the mproved expressons for turbulent fluxes of momentum and heat showed, that turbulent Prandtl number s stablty dependent from Rchardson number and momentum can be transferred more effectvely than heat under stably stratfed condtons.

25 THANK YOU!