On the Wind and Turbulence in the Lower Atmosphere Above Complex Terrain

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International Journal of Geosciences, 2011, 2, 13-28 doi:10.4236/ijg.2011.21002 Published Online February 2011 (http://www.SciRP.org/journal/ijg)

On the Wind and Turbulence in the Lower Atmosphere above Complex Terrain

George Jandieri1, Alexander Surmava2, Anzor Gvelesiani2 1Georgian Technical University, Institute of Cybernetics, Tbilisi, Georgia 2M. Nodia Institute of Geophysics, Tbilisi, Georgia E-mail: [email protected], [email protected] Received November 18, 2010; revised December 20, 2010; accepted December 23, 2010

Abstract

Numerical modeling and studies of the wind fields at the junction of three continents: over the complex terrains of the South-east Europe, Asia Minor, Middle East, Caucasus and over the Black, Caspian and Medi- terranean seas have been carried out for the first time. Traveling synoptic scale vortex wave generation and subsequent evolution of orographic vortices are discovered. Wind fields, spatial distribution of the coefficients of subgrid scale horizontal and vertical turbulence and the Richardson number are calculated. It is shown that the local relief, atmospheric hydrothermodynamics and air-proof tropopause facilitate the generation of  -mesoscale vortex and turbulence amplification in the vicinity of the atmospheric boundary layer and tropopause. Also turbulence parameters distribution in the troposphere has the same nature as in the stratosphere and mesosphere: turbulence coefficients, stratification of the vertical profiles of the Richardson number, thickness of the turbulent and laminar layers.

Keywords: Numerical Modeling, Complex Terrain, Characteristics of Atmospheric Turbulence, Wind Field, Mesoscale Vortex, Bulk Richardson Number

1. Introduction ments and simulations show that despite the complexity of the terrain and the apparent differences from a classi- At present many hydrometeorologists are actively study- cal convective boundary layer, the turbulence structure ing mesoscale atmospheric processes above the complex reveals reproducible patterns and scaling characteristics. terrains. The problem is complex and its solution is Generalization of obtained results by [1] requires an in- closely related to other important problems of dynamical vestigation of other valley geometries and different to- meteorology, including a problem of atmospheric turbu- pographic orientations. In particular, further investigation lence of different scales in the mountainous regions. of the functional dependence between up-valley wind Boundary-layer studies of mountainous terrain have speed and local surface fluxes. The authors of paper [2] mainly focused on global characteristics, such as thermal studied vertical winds and turbulence in the troposphere stratification, boundary-layer growth rates, circulation in mountain-wave conditions near Kiruna in Arctic Swe- patterns and valley winds. The relatively few studies den. They show that the horizontal and vertical wave- devoted to the turbulence structure over non-flat terrain lengths of the dominating mountain-waves were ~10 - 20 have mainly been restricted to comparatively gentle hills. km, the amplitudes in vertical wind 1-2 ms  1 , and In [1], the nature of turbulent kinetic energy in a steep turbulence velocities below 5500 m height were about and narrow Alpine valley in Switzerland under fair- 40% of the time during winter months. This is a much weather summertime conditions was investigated for a higher rate than the Advanced Research and Weather detailed case study, in which the evaluation of aircraft Forecasting model (WRF) predictions for conditions of data was combined with the application of high-resolution Richardson number Ri  1 but similar to WRF predic- large-eddy simulations using the numerical model ARPS. tions of Ri  2 . The cause of low Ri is a combination Excellent correlation was established between surface of wind-shear at synoptic upper-level fronts and pertur- heat flux and the up-valley wind speed. The measure- bations in static stability due to the mountain-waves.

Comparison with radiosondes suggests that WRF under- instability associated with quick veering of the wind with estimates wind-shear and the occurrence of thin layers height. with very low static stability, so that vertical mixing by Meteorological researchers have made efforts to im- turbulence associated with mountain waves may be sig- prove the stability description of a moist atmosphere by nificantly more than suggested by the model. A statistical using variations of the Richardson number [7]. The correlation between enhanced turbulence and gravity Richardson number is often used as an important index waves was noted in [3]. for judging shearing instability and symmetry instability: The authors [4] investigating turbulence of a neutral the conventional baroclinic instabilities dominate if atmosphere at different heights obtained the following Ri  0.95 , symmetry instabilities dominate if 0.25  results: 1) Radar observations of the mesosphere, air- Ri  0.95 , and Kelvin-Helmholtz instabilities dominate crafts smoke trails into the stratosphere, radar observa- if Ri  0.5 . A new Richardson number is defined for tions of thin layers in the troposphere and lower strato- describing the stability of a moist atmosphere ( Ri* ). The sphere show that layered and stratified phenomena are results show that convective instability is concentrated in common in the atmosphere. It was shown that “cat’s-eye” the lower troposphere while instability determined by structures are not uncommon in the atmosphere as a pre- Ri*  1 is mainly located in the middle and upper tro- cursor to turbulence breakdown and such structures are posphere above the rainfall areas, may be used to indi- often associated with Kelvin-Helmholtz (K-H) billows. cate and estimate the rainfall occurrence and develop- Authors of [5] have indicated that other mechanism, such ment. Richardson numbers in the three thermodynamic as the Holmboe instability, can also generate such struc- states of the atmosphere can be obtained when potential tures. K-H instabilities are only dominant in weakly stra- temperature,  (of dry atmosphere), equivalent poten- tified flows, whereas the Holmboe instability is more tial temperature, e (saturated moist region), and gen- likely in strongly stratified flows. There can be occasions eralized potential temperature,  * , are applied to calcu- when other mechanisms of breakdown can be responsi- late Brunt-Väisälä frequency, respectively. ble for the turbulence. The formation of cat’s-eye struc- In [8] spectral and structure function analyses of hori- tures is only one possible mechanism. Cat’s-eye struc- zontal velocity fields observed in the upper troposphere tures are visually impressive, so they tend to dominate and lower stratosphere during the Severe Clear Air Tur- the literature, but it is not clear whether they are in fact bulence Collides with Air Traffic (SCATCAT) field the main mode of turbulence breakdown at all. 2) By program, conducted over the Pacific, were carried out to using radars and various specialized techniques they identify the scale interactions of turbulence and small have also obtained information at smaller scales (~1 m - scale gravity waves. In the presence of turbulence, tran- 100 m).Turbulence is considered here to be generally the sitional power spectra from k 2 to k 5/3 were found to result of a non-linear breakdown of larger, more organ- be associated with the gravity waves and turbulence, ized structures which have become unstable, with scales respectively. The second-order structure function analy- comparable to or larger than the buoyancy scale. sis was able to translate these spectral slopes into r and A number of remote-sensing wind-measuring instru- r 2/3 , consistent with Monin-Yaglom conversion law, in ments such as LIDAR and radar wind profilers [6] have physical space, which presented clearer pictures of scale been used for monitoring of low-level wind shear and interactions between turbulence and gravity waves. The turbulence. Data collected in a field experiment of the third-order structure function analysis indicated the exis- radio metering conducted in Hong Kong in February tence of a narrow region of inverse energy cascade from 2006 were used to obtain the Richardson number profile the scales of turbulence up to the gravity waves scales. up to 1.5 km above ground. The Richardson number pro- This inverse energy cascade region was linked to the files are found to capture the turbulence events reasona- occurrence of Kelvin-Helmholtz instability and other bly well. The atmospheric condition was favorable for wave-amplifying mechanisms, which were conjectured the generation of turbulence when Ri Ric 0.25 . It to lead to the breaking of small-scale gravity waves and was also noted that, at the above four times, the Ri the ensuing generation of turbulence. The multifractal number could be less than 0.25 below 400 m or so, espe- analyses revealed further scale breaks between gravity cially the occurrence of negative Ri value. This feature waves and turbulence. In [9] it is shown with a numerical is mainly related to turbulent airflow associated with simulation that a sharp increase in the vertical tempera- thermodynamic instability near the ground. Downstream ture gradient and Brunt-Väisälä frequency near the tro- of the airflow, there are a number of waves/vortices be- popause may produce an increase in the amplitudes of tween 700 and 1600 m high with the dimensions of sev- internal gravity waves propagating upward from the tro- eral hundred meters in height and a couple of kilometers posphere, wave breaking and generation of stronger tur- horizontally. A possible reason of turbulence is the shear bulence. Turbulent diffusion coefficient calculated nu-

Copyright © 2011 SciRes. IJG G. JANDIERI ET AL. 15 merically and measured with MU radar are of 1 - 10 breaking can coexist and complement each other. From ms21  in different seasons in Shigaraki, Japan (35˚N, the above it follows that there are many unresolved 136˚E). These values lead to the estimation of vertical problems related to the hydrodynamic interaction of air ozone flux from the stratosphere to the troposphere of with a complex terrain. (1 10) 1014 ms21 which may substantially add to the The objective of this paper is theoretical investigation usually supposed ozone downward transport with the of the features of hydrodynamic interaction of the at- general atmospheric circulation. Therefore, local en- mosphere with complex terrain at the junction of three hancements of IGW intensity and turbulence at tropo- continents: South-eastern Europe, Asia Minor and Africa, spheric heights over the mountains due to their oro- where there are located several large seas-the eastern part graphic excitation may lead to the changes in tropo- of the Mediterranean sea, the Black, Azov and Caspian spheric and total ozone over different regions. In [10] seas, etc, many high mountain ranges, forests, steppes high resolution (150 m) wind measurements by Meso- and deserts stretched a hundred kilometers. The evolu- sphere-Stratosphere-Troposphere (MST) radar and by tion of the wave of cyclonic and anticyclonic vortices Lower Atmospheric Wind Profiler (LAWP) have been and the obtained mesoscale air flow for the considered used to study variation of turbulence intensity. Layers of complex terrain is modeled for the first time. We use a higher turbulence are observed in the lower stratosphere. regional model of the atmospheric processes elaborated The heights of the turbulent layers in the lower strato- at the M. Nodia Institute of Geophysics [11]. sphere do not correlate with the levels of minimum Richardson number. During the short-period gravity 2. Formulation of the Problem wave activity (~7 h) the high frequency convectively generated gravity waves breakdown generates the ob- 2.1. Basic Equations served turbulence layers. A non-linear interaction between the waves of different scales might be responsible Basic equations of the model describing variations of the for the breakdown and generation of turbulence layers. It meteorological fields are: should be noted that different mechanisms of wave 1) for the troposphere [12,13]:

d1uP z u  lv  g10.61  q   u  , dtx xh2 

d1vP z v  lu  g10.61  q   v   , dtyy h2   g huhvhwh   1d 10.61qh ,   wh 0 ,  RT txy   dz    1 L    uvwSw 2   con , txy h  Cp  t qqqq 1 q  Q   uvw  q  ,   , txy con t x22y mmmm    m  N uvw  m , (1) txy con  t zzz d    wuvwh   , zh   , uvw   , txy dt t x y  2) for the active layer of soil [14,15]: CC EC  TT2 DC , soil  K soil at  zZ, (2) tz  z  z t soil z2 0 soil 3) for the layer of sea water [14]: TT2 1 I sea K sea , at  zZ, (3) tCzsea z2  0 sea sea sea

Copyright © 2011 SciRes. IJG 16 G. JANDIERI ET AL. where t is time; x, y, and z are the axes of the Cartesian gravitational acceleration; R is the universal gas constant coordinate directed to the east, north and vertically up- for dry air; Cp and Csea are the specific heat capacities wards, respectively; zh is the dimensionless of dry air at constant pressure and seawater, respectively; vertical coordinate; 0 xy,50 m is the surface S is the thermal stability parameter; L is the latent heat of layer height; 0 is the height of the relief; H txy,,  condensation; con is the condensation rate; Nt is is the height of the tropopause; hH ; u, v, w, and the intensity of prescription; Nt mmcr  t w are the wind velocity components along the axes x, y, z, when mm cr , and 0 when mm cr [14]; mcr is the and  , respectively;   TT , and   PPz   are critical magnitude of the mass fraction of a cloud water; the analogues of temperature and pressure, respectively; t is the time of setting out of a surplus cloud water; D TK 300 ; T  and P are the devotions of tempera- is the diffusion coefficient of water in soil; E is the filtra- ture and pressure from the standard vertical distributions tion coefficient of water in soil; Isea is the total solar Ttxyz,,, TtxyzT ,,,  zTtxyz,,, , radiation flux in sea water; Ksoil and Ksea are the P txyz,,, Ptxyz ,,, Pz Ptxyz,,, ; T and P thermal diffusivity coefficients of soil and sea water, are the temperature and pressure of the atmosphere, re- respectively;  and  are the horizontal and vertical spectively: Tz and Pz are the standard verti- turbulent diffusion coefficients. cal distributions of the temperature and pressure, respec- The set of Equations (1) and (2), (3) are solved in the tively;  is the standard vertical temperature gradient; coordinate systems txy,,,  and txyz,,, , respec- T and P are the background deviations of the tem- tively.The initial and boundary conditions, the values of perature and pressure from standard vertical distributions; background fields and methods of parameterization of  and  are the mesoscale and background compo- the separate meteorological processes are selected in nents of the analogue of temperature, respectively; accordance with specific objectives of modeling.  ; q and Q are the mass fraction of water vapour and the background mass fraction of water vapour, 2.2. Boundary and Initial Conditions, the Main respectively; qqQ ; m and M are the mass fraction Parameters of the Regional Problem of cloud water and the background mass of cloud water, respectively; mmM  ; Tsoil and Tsea are the tem- The boundary and initial conditions for the set of Equa- peratures of soil and seawater, respectively; C is the vo- tions (1-3) according to [13,16,17] are: lume content of soil water;  z and sea are the standard vertical distributions of the densities of dry air 2.2.1. Vertical Boundary Conditions and seawater, respectively;  1 dp dz; g is the 1) for the system (1):

 0,w 0,1  txy ,,  gRT   htxy,,  h 0,, xy , at   1 , 

uv AV uh 00,, AV vh   m   AV00 h  ,, AV mh   0 at   0 , (4)  q  AV q q00 h ,0w ,   2) for systems (2) and (3): T CKe  C AV T T  LAV q q I ee ez p e00 q e e

 1  CCpor ,atd0 Nt  0  , at z 0 , (5) C  1 DAVqqNtw ,at d 0  e   z  0 T C e  0 at zm  2 , zz 0

1/2 22 where Vuv; 1 is a given function of time modeling area; in other cases the Von Neumann condi- and coordinate and shows the magnitude of the pressure tion  nhn0 is used. Here uv, , and h in the tropopause;  0 is nondimensional thickness of are the background values of the wind velocity compo- the atmospheric surface layer; uv,, , q , m ; in- nents and atmosphere thickness, respectively; n is a nor- dex “0” indicates the value of the function at the level mal to the lateral boundary. z 0 ; qqq00 sat on the sea surface and q0  qqCC0  sat por on the soil surface; Cpor is the po- 2.2.3. Initial Conditions rosity of the soil, index “e” indicates either “sea” or At t  0 we have: “soil” for the sea and soil surfaces; C and  are soil soil 3) for the system (1) the specific heat capacity and soil density, respectively;

A and  0 are constant parameters.  qm0 , uu 0, xy , ,  , vv 0, xy , , ;

2.2.2. Lateral Boundary Conditions and hh0, xy , 9000  xy , m, (6) uutxy ,,, , vvtxy ,,, , hhtxy ,, ,  qm0 if vector v has inward direction inside a 4) for Equations (2) and (3):

CCxyzT00, , , sea T, sea  xyzT, ,  , soil  T 0, soil  xyz, ,  , (7) where u and v are determined by both geostrophic ponents similar to the temperature and pressure at the wind and quasi-static equations at the background com- tropopause level:

txy, , , 6 3sin   x  10 t 568000 sin y 568000 Y 288.15 0.065 z

1 0.012  0.0066sin  xt 10 568000 sin y 568000 (8)

C0 , T0,sea and T0,sea are average monthly values for surface pressure field at the level z  0 and t  0 the June. calculating for a plane surface of the Earth 0  0 . It Coefficient of vertical turbulence decreased in the ver- is the idealized picture of large-scale wave slowly mov- tical direction from the value at the surface layer from 5 ing to the west usually observing in the atmosphere [19]. ms21  up to 0.001 ms21  at a height of 3 - 4 km Temperature differences between the centers of anti- above the Earth’s surface. At more high altitudes equals cyclonic and cyclonic vortices equal to 6˚C. Maximum to 0.001 ms21  . Coefficient of the horizontal turbu- surface wind speed amounts to 18 ms  1 . In 48 hours lence is equal to 5 000 ms21  . Background value of the the vortex wave travels eastward at a distance equalling relative humidity is equal to 40%, the background value to 1400 km, and anticyclonic vortex generates in place of of the water content mass concentration zero. Other me- cyclonic vortex and vice-versa. teorological parameters are the well known values char- acterizing middle latitudes. 2.3. Boundary and Initial Conditions, the Main Numerical integration of Equations (1) and (2), (3) are Parameters of the Mesoscale Problem carried out using [18] and the Crank-Nicolson schemes, respectively. Rectangular finite-difference grid with 96 × 115 km × 105 km territory is selected for investigation of 68 × 17 grid points having 40 km horizontal steps and the wind field spatial distribution and atmospheric tur- the non-dimensional vertical step equals to 1/17 is used. bulence, located on the east coast of the Black Sea in the In soil and sea-water number of levels is equal to 20, vicinity of Batumi. It covers part of the Black Sea, Col- vertical step is 10 cm, and temporal step equals to 4 min. chis plain, Guria and Pontic ranges. The height of the From Equation (7) follows that the background fields of ranges attain to 2 - 3 km (Figure 2). Mesoscale task is temperature, pressure and wind are selected modeling solved by the set of Equations (1-3) and conditions (4-7) horizontal displacement of the cyclonic and anticyclonic in which the solutions of the regional task are obtained vortices having synoptic linear scale 5680 km moving for the mesoscale domain as background meteorological from the west-east direction with the phase velocity 10 fields. Vertical turbulent flows of momentum, heat and ms  1 . Figure 1 shows the fields of the surface back- humidity at   0 and the meteorological parameters ground temperature of the air Ttxy,,,0, correspond- are defined in a surface layer  hz using the ing fields of the velocity at t  0, 48 hours and the well-known formulae [20,21]:

(a) (b) (c) Figure 1. The background distributions of the wind velocity (m · s-1), temperature (solid lines) (˚C) at t = 0 h (a) and t = 48 h (b), pressure (solid lines) fields (mb) at t = 0 h (c). Boundaries of the seas are shown by bold lines; horizontal and vertical grids steps are equal 40 km.

(a) (b) Figure 2. The background wind field distribution of the atmosphere surface layer for t = 72 h (a), and the topography of the mesoscale area around the Batumi port (b). The red circle shows the location of the Batumi port. Thick lines show the coastal lines of the seas; horizontal and vertical grids steps are equal 40 km (a) and 5 km (b), respectively.

2 22 22 uuvv 2 uvg   xy 22    ;  0.05 z  2   , when zh s , (9) x yx y zzz  where hs is the height of the surface layer. If zh s , tion method [22], based on the Monin-Obukhov similar- then the value of  is determined by the parameteriza- ity theory and solution of the following equations:

2  u u* p p* z u*  u ,    ,  pq ,  ,   , L  22 zz z  L  * u z z u  * f  ,, pp pf ,  ,   u ,   0 , if zz ,  uu 0* 0 u L 0 L sur uz uh h   * ,   * s iu , ,   s , (10) i i h   h i  ih L

0.5 22 where u uv is the wind velocity; u* is the vicinity of the eastern Black Sea and Mesopotamia. friction velocity; * and q* are the scales of the po- Strong north-west, north, northeast and east winds are tential temperature and mass fraction of water vapor, obtained over the Caspian Sea, hilly areas of Iran and the respectively;  is the von Karman constant; z0 and Anatolian peninsula. A cyclonic circulation of wind was zu are the parameters of roughness for wind and tem- obtained over the relatively small territory to the east of perature, respectively; L is the length scale;   g T is the Caspian Sea. In general it is evident that the relief of the parameter of convection; u  ,    , fuu ,  the western and central parts of the region strengthens and f  , 0 are universal functions [22]. anticyclonic vorticity of the background movement of air. The background values of the meteorological fields for Figure 4(b) shows that as the background vortex propa- each time step were obtained in the process of modeling gates to the east, the surface flow varies significantly to of the vortex wave propagation along the large-scale the instant of time t  24 hours. Over the western re- territory in the time interval of 96 h t 120 h. gion the anticyclonic vortex splits into medium-scale South-east surface background wind is obtained at t  96 anticyclonic and cyclonic vortices with the centers in the h in the vicinity of Batumi. The modeling is carried out vicinity of the Carpathians and the Crimea, respectively. by numerical integration of the set of Equations (1)-(5) Over the eastern part of the Mediterranean Sea wind was and (9), (10) on the finite-difference grid 23 × 21 × 50 divided into two oppositely directed flows. Two counter- with the grid points along the x, y and  respectively. current flow of air in the vicinity of Mesopotamia con- Horizontal steps were taken as equal to 5 km, vertical verge and form a strong southeast wind, which reaches non-dimensional step-equal to 1/50 in the atmosphere, the South Caucasus. vertical step equal to 10 cm in the soil and sea water During the time interval of t 48  72 hours anti- (with a number of levels equal to 20). Temporal step cyclonic vortex in the vicinity of the Carpathians gradu- equaled to 1 min. ally defuses (Figures 4(с,d)). In the vicinity of the Ana- tolian peninsula, the Caucasus and the Caspian Sea there 3. Simulation Results are anticyclonic and cyclonic wind vortices. A cyclonic air movement over the Mediterranean Sea becomes 3.1. The Results of Regional Model stronger. After t = 96 hours the process of propagation of large-scale wave vortex recurs with some quantitative Calculations showed that in the barotropic approximation differences of the meteorological fields. In general, the (in the absence of heat exchange between the underlying obtained wind fields at the level of the atmospheric sur- surface and atmosphere, T   0 and S  0 ), in case of face layer qualitatively reproduce the fields that were the flat surface of the earth synoptic wave is stable and constructed via the analysis of synoptic maps at the pas- propagates eastward without perceptible variation with sage of large-scale pressure formations [23] over the initial phase velocity of 10 ms  1 . In baroclinic ap- Caucasus. The differences of the wind speeds and tem- proximation and at flat surface of the earth synoptic peratures were calculated for the quantitative estimation wave varies in shape and size in the process of traveling of the relief influence effect, obtained taking into account to the east, at the same time separate mesoscale (500- the influence of orography irregularities and without 1000 km) vortices of the wind velocity (Figure 3) gener- taking it into account at the moment t  24 hours It was ate and disappear. Life period of existing of these vor- found that the influence of relief on the surface layer is tices is about 24-36 hours. Vortices are obtained not only manifested in reduction of large-scale cyclonic and anti- at the surface of the Earth but also in the middle and up- cyclonic vorticities. The wind speed in some parts of per troposphere. This indicates that there is an energy separate territory can vary by the value of the order of transfer from the large-scale vortex to the mesoscale vor- background wind speed, and the temperature-up to 10˚C. tices. The considered process takes place only in case of Thus, we can assume that the roughness of orography in baroclinic atmosphere and is absent in barotropic case. the lower troposphere facilitates a development of As follows from the Figure 4(a), complex relief sig- mesoscale vortical turbulence followed by smoothing of nificantly varies the general picture of large-scale move- the wind speed fields and temperature. ment of the air in the lower troposphere. Along with a dynamic baroclinic effect a kinematic effect of the relief 3.2. Mesoscale Fields of the Wind Speed and lay on the motion of air. The mesoscale wave perturba- Turbulence in the Troposphere tion occurs at t  0 in the vicinity of the Carpathians as a result of the influence of orography. A zone of wind Figure 5 shows spatial distributions of the wind field speed divergence is obtained in the Caucasus and north- obtained at modeling of mesoscale circulation in the vi- ern Iran. The mesoscale cyclonic vortices generate in the cinity of city Batumi. From the figure it follows that the

Figure 3. The surface wind fields in the baroclyne approximation for a flat relief calculated at t = 0 h (a), 24 h (b), 48 h (c), 72 h (d), 96 h (e), and 120 h (f), respectively. Horizontal and vertical grids steps are equal 40 km.

Figure 4. The surface wind at t = 0 h (a), 24 h (b), 48 h (c), and 72 (d) h. Horizontal and vertical grids steps are equal 40 km. calculated field of wind speed in the lower and middle magnitude of the wind speed. The influence of tro- troposphere differs significantly from the background popause dominates at the levels of the upper troposphere, wind both by direction and magnitude. Northern, north- where the wave disturbance lies on the background wind west and west winds were obtained at the surface layer field. Figure 6(a) shows the diagrams of dependence of (z = 50 m). A closed mesoscale vortex is generated at the the vertical turbulence coefficient on the height above level z = 1000 m above the Black Sea. At the height of the earth’s surface calculated at five nodal points of the 2000 meters this vortex travels to the south-west. The modeling region. It is evident that the coefficients of the wind direction varies gradually in the middle and upper vertical turbulence are high in two regions: in the at- troposphere. The wind direction approaches the back- mospheric boundary layer and in the upper troposphere ground direction with removal from the Earth’s surface. (except for the item 5). Coefficients of the vertical tur- The analysis of the calculated wind field shows that the bulence are relatively small in troposphere at the heights influence of relief is significant in the lower atmospheric 2.3 - 7 km from the earth surface. layer having thickness 3-4 km. The values of the horizontal turbulence coefficient are Here the relief can substantially vary the direction and minimal at the heights of 500 - 1 500 m above the earth

Figure 5. The topography and the wind fields at the altitudes z = 50 m, 400 m, 1000 m, 2000 m, and 8000 m, respectively. Ho- rizontal and vertical grids steps are equal 5 km.

(a) (b) Figure 6. The profiles of the vertical ν (m2 · s-1) (a) and horizontal μ (m2 · s-1) (b) turbulence coefficients for the points of the modeling area, respectively. Series 1, 2, 3, 4, and 5 correspond to the values of ν and μ over points 1, 2, 3, 4, and 5, respectively. surface. The values of the horizontal turbulence gradu- Air flow in the mesoscale region is a part of the  - ally increase away from the middle troposphere, by 2.3 - mesovortex (Figure 4(a)) generated due to the interac- 7 km from the earth’s surface. Qualitatively similar ver- tion of the Caucasus relief with the background wind. tical distribution is obtained also for the coefficient of the Vertical distribution of the meteorological parameters horizontal turbulence (Figure 6(b)). The atmospheric varies in the atmospheric boundary layer due to the boundary layer near the tropopause approaches to the thermal and dynamic influence of the Earth’s surface. values obtained in the surface layer. Thus impenetrable BRN numbers in the narrow layers between the heights for air tropopause has almost the same influence on the of 500 m and 2500 m take on the values in the interval horizontal turbulence as the Earth’s surface. It should be 10 - 45. These values of the BRN correspond to the vor- noted that the calculated vertical turbulence coefficients tex generation conditions [24,25] and formation of the β- are in agreement with the measurements data [9]. mesoscale vortex (Figure 5, z = 1000 m and 2 000 m). Figure 7 shows horizontal distribution of the vertical From the analysis of the Figure 10 follows that changing turbulence. Coefficient of the vertical turbulence is of the Richardson BRN number in time at different maximal in the surface layer in which they vary in the heights of the surface layer ( z  50 m) is periodical interval 048 ms21  . with a period of 12 - 26 hours. At certain hours (50-60 h) The values are minimal at the height of z ~2 4 km the BRN number substantially decreases and can become from the Earth’s surface. At this level their values do not less than 0.25 at which small-scale turbulence should exceed 2.5 ms21  . At higher levels  increases again generate. The obtained picture of the temporal depend- and reaches peak values near the tropopause. Similar ence of the BRN is qualitatively consistent with the re- spatial distribution is obtained also for the horizontal sults of [2] (see Figure 9). turbulence (Figure 8). From these figures follow that atmospheric turbulence above the sea surface is less than 4. Discussion above the earth surface. Figure 9 shows vertical profiles of the bulk-Richardson number BRN  g T  The performed calculations showed the peculiarities of TT  z  uz22  vz . The the influence of large-scale relief on formation of the  a   greatest values of this number are obtained in the at- wind fields and vortex turbulence. In particular, it is mospheric layer having thickness 3-6 km above the shown that the influence of relief on the synoptic scale Earth’s surface. In this layer vertical gradient of the wind movement help generate of orographic vortices. The ob- speed is relatively small, the Richardson number is much tained orographic vortices are generated in the lower greater than 45 and the atmosphere is stratified stably. troposphere and their sizes can vary from a few hundred

Figure 7. The horizontal distribution of the vertical turbulence coefficient ν (m2 · s-1) at the altitudes z = 50 m, 2000 m, 4000 m, and 8000 m, respectively. Horizontal and vertical grids steps are equal 5 km. kilometers up to 1000 km and more. Analysis of the which the wind speed exceeds 20 ms  1 are generated Figures 3 and 4 show that evidently the large-scale per- above the flat grounds between the mountain ranges. Due turbations become smoother due to the energy transfer to these airflows the warm air of the Asia Minor can from the large-scale perturbations to the smaller-scale propagate far to the north up to the main Caucasian range ones. (Figure 4(b)). The relief of the Caucasus is a natural The main territories favorable for the generation of barrier to the southern wind. However, the north wind orographic vortices are mountainous areas adjacent to may flow around the Caucasus from the Caspian Sea and seas. High mountain ranges of the Caucasus, Anatolian propagate to the south, reaching the shores of the Medi- peninsula and Asia Minor facilitate formation of me- terranean Sea (Figure 4(a)). Such picture is often ob- dium-scale zones of the wind speed divergence. served in the Caucasus, above the Black and Caspian The bands of relatively narrow and long zones in seas, especially in summer [26-28].

Figure 8. The horizontal distribution of the horizontal turbulence coefficient μ (m2 · s-1) at the altitudes z = 50 m, 2000 m, 4000 m and 8000 m, respectively. Horizontal and vertical grids steps are equal 5 km.

At investigation of mesoscale wind field structure with spatial distribution of the turbulence coefficients (Fig- a horizontal 5-km step of grid it has been found that the ures 7 and 8). It is obtained that in the atmospheric wind field can substantially differ from the large-scale boundary layer over the sea surface the values of hori- field if the background wind speed in the boundary layer zontal and vertical turbulence coefficients are several does not exceed 5m s 1 . In particular, a closed vortex times smaller than the values obtained over rough Earth’s with a diameter of 25 - 30 km (Figure 5) is generated at surface. The more is the height of the area and slope of the height of about 1000 m near the southeastern coast of the earth surface the more is the difference. In the middle the Black Sea. Evidently such vortex can facilitate gen- troposphere (2 - 6 km) the difference between them (over eration of a whirlwind, which is often observed on the the sea and the earth) practically disappears and reappears Black Sea coast of Georgia [26] in summer. again near the tropopause (8, 9 km) but to a lesser extent. Mesoscale roughness of relief exerts influence on the Profiles of horizontal and vertical turbulence coefficients

The obtained vortex cell can not develop more and con- vert into a damp convection system due to the low background relative humidity (40%). Multistratification of the obtained vertical profiles of the turbulent parameters of the medium (with a layer thickness of 0.1-3 km) is also observed in [1] for the complex relief, in the laboratory experiments modeling the process of convective instability in a stratified fluid [29] and at higher levels of the atmosphere (stratosphere and mesosphere) [30-32]. This means that there is much common in the turbulent features of the troposphere, stratosphere and mesosphere: the order of the turbulence coefficients, stratification of the vertical profiles of the Richardson numbers and alternation of the turbulent and laminar layers of the atmosphere.

5. Conclusions

Numerical investigation of the large-scale wind fields at the junction of three continents has been carried out for the first time: over the complex territories of the South- Figure 9. The profiles of Bulk-Richardson number (BRN) east Europe, Asia Minor and Southwest Asia, Caucasus, over 3 points of the area modeling. 1, 2, and 3 correspond to Middle East and the water areas of the Black, Caspian points 1, 2, and 3 (see Figure 5 (a)), respectively. and Mediterranean seas. By the example of a traveling synoptic-scale (~6000 km) vortex wave generation and subsequent evolution of orographic vortices of the order of 1000 km are considered. The mesoscale structures of hydrodynamic fields in the eastern coastal part of the Black Sea are modeled. On the mesoscale area (~100 km) of the generated medium- scale vortex flow in the vicinity of the western Black Sea coast, hydrodynamic structure of the wind is studied by the nested grids method. Wind fields, spatial distribution of the coefficients of subgrid scale horizontal and vertical turbulence and the Richardson number (Bulk Rich- ardson Number, BRN) are calculated. It is shown that the local relief, atmospheric hydrothermodynamics and air-proof tropopause facilitate the generation of β- me- Figure 10. Time variability of BRN at the altitudes z = 2 m soscale vortex and turbulence amplification in the vicin- (series 1), 10 m (series 2) and 50 m (series 3) over point 2 of ity of the atmospheric boundary layer and tropopause. the Figure 5. Minimum values of the turbulence coefficients were obtained at the heights between 2300 m and 4000 m above have the minimums in the atmospheric layer having the earth’s surface. thickness 2-6 km (Figure 6). There is much in common in the nature of turbulence Qualitative similarity temporal dependence of the parameters distribution calculated for the troposphere Richardson numbers (during three days) obtained above and the well-known results of the observations in the (Figure 10) and in [2] (Figure 9) is explained by the stratosphere and mesosphere: the order of the turbulence similarity of the relief and meteorological conditions coefficients, stratification of the vertical profiles of the (Figure 4) and (Figures 1 and 3 in [2]). This allows us to Richardson number and alternation of about 0.1-3 km judge the validity of the obtained results. In the atmos- thickness turbulent and laminar layers. pheric boundary layer the dynamic state of the environ- Calculations showed the features of large- and mesoscale ment becomes favorable (10 BRN  45) for the gen- terrains influence on generation of the wind fields and eration of a vortex cell (Figure 5) at certain moments. vortex turbulence:

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