《边界层气象学》课件：CH10_边界层气象学总复习

1、边界层气象学总复习边界层气象学总复习壹：基本概念壹：基本概念掌握：掌握：大气边界层、湍流闭合问题、泰勒湍流冻结大气边界层、湍流闭合问题、泰勒湍流冻结假说、奥布霍夫长度、理查逊数、地表粗糙度、湍流假说、奥布霍夫长度、理查逊数、地表粗糙度、湍流动能、摩擦速度、湍流通量、雷诺应力、湍流强度、动能、摩擦速度、湍流通量、雷诺应力、湍流强度、混合长理论、混合长理论、Monin-Obukhov相似理论、埃克曼螺线、相似理论、埃克曼螺线、埃克曼抽吸、中性边界层、对流边界层、稳定边界层、埃克曼抽吸、中性边界层、对流边界层、稳定边界层、低空急流、惯性振荡理论低空急流、惯性振荡理论ABL general chara

2、cteristicslABL flows are predominately turbulent. Vertical transports of momentum, energy and mass are mainly accomplished by turbulence of various scales, from millimeter up to the whole boundary-layer.lBoundary-layer structure varies with time and space, especially, ABL features a distinct diurnal

3、 cycle. Diurnal evolution of ABLThe formulation suggests ways in which the Reynolds stresses might be measured, but gives no indication of how to express them in terms of the mean quantities. The simplest approach is to draw an analogy with molecular viscosity and, considering a plane boundary in th

4、e xy-plane, write for the eddy stress in the x direction on a plane parallel to the boundarywhere K is the coefficient of eddy viscosity (with the same dimensions as kinematic viscosity) and is effectively defined above.Typical atmospheric values of K lie in the range 1100 m2 s-1. These are high val

5、ues when compared with the molecular viscosity of ordinary fluids (typically 10-5 m2 s-1 for gases at STP). They demonstrate the effectiveness of eddy motions compared with molecular motions in transferring momentum.uu wKz Effects of Turbulence, K - theoryuz The limitations of K theory: 1. eddy visc

6、osities depend on the flow; 2. K not a constant in BL; 3. K theory is not accurate for large eddies. Mixing length hypothesis 1Prt 0.8 is the turbulent Prandtl number for air.For the determination of the turbulent diffusion coefficients, the mixing length parameterization is used, which is based on

7、the work of Prandtl (1925).zqKqwzKwzuKwuEHMHMKKt/Pr Mixing length hypothesis 2Mixing lengthIn the layer within a few tens of meters of the surface, the shearing stress is approximately constanta layer known as the constant flux layer. A further plausible hypothesis is that the size and path of the e

8、ddies should be proportional to height above the surface, i.e., l = z where is known as von Karmans constant and has a value of about 0.4. On integrating under these assumptions the wind profile is given bywhere u* = (/)1/2 is known as the friction velocity and the constant of integration, z0, as th

9、e roughness length, since it depends on the surface roughness. This fits well under conditions of neutral stability. For other situations, as might be expected, the wind profile and the associated momentum, heat, and water vapor fluxes depend very considerably on the vertical stability.22uu wlz *0ln

10、uzuzMixing length hypothesis 3, logarithmic profile M-O similarity theory 1lBuckinghams theoremlSimilarity theories provide a powerful framework for analysis of experimental data, as well as simple parameterisations for representing the complex dynamic processes involved.lA similarity theory has thr

11、ee key ingredients. First, problems governed by similar dynamic processes are identified and then characterized with a few dimensionless parameters (e.g. the Reynolds number) which we call similarity parameters. Second, a set of scaling parameters is identified and used to establish non-dimensionali

12、sed dependent and independent variables. Third, we derive a set of similarity laws which are universally valid. MOST 2, Obukhov lengthMOST 3, flux-gradient relations贰：平均量预报方程贰：平均量预报方程jjijiijijcijijixuuxuxpufgxuutu22331jjpvjjpjjjxucELxQcxxut)(1*22 ) (jjqjjxquSxqutq掌握掌握方程组的推导过程、每项的物理意义、方程组的推导过程、每项的物理意

13、义、并能解决一些实际问题并能解决一些实际问题Navier Stokes equations Claude-Louis Navier(France, 17851836) George Stokes(England, 18191903)lmay be used to model the weather, ocean currents, water flow in a pipe and air flow around a wing. lhelp with the design of aircraft and cars, the study of blood flow, the design of p

14、ower stations, the analysis of pollution, and many other things. lCoupled with Maxwells equations they can be used to model and study magnetohydrodynamics.lThe Clay Mathematics Institute has called this one of the seven most important open problems in mathematics and has offered a US$1,000,000 prize

15、 for a solution or a counter-example叁：湍流动能（叁：湍流动能（TKE）方程）方程zpwzewwgzuwutevv)(1)(经过简化后的经过简化后的TKE方程：要方程：要熟悉熟悉此方程此方程的来源、每项物理含义及对的来源、每项物理含义及对TKE的影响：的影响：肆、肆、Neutral Boundary Layer, Ekman spiral 1Vagn Walfrid Ekman, Sweden, 1874195422221v0(1)1v0(2)pufKxzpfuKyz11,vggppufyfx 22(v)(v)(v )0gguiKif uiif uiz1 e

16、xp()cos(1)vexp()sin(2)gguuzzuzz =(f/2K)0.5Above the level z = / where v = 0, the wind is approximately geostrophic. Below this level the wind direction deviates very considerably from the geostrophic direction; at the surface, for instance, the deviation is 45. The quantity / may, therefore, be cons

17、idered a the approximate depth of the boundary layer. With f = 7 10-5 s-1 and K = 10 m2 s-1, / 1 km. Note that in the boundary layer the wind has a component directed generally towards low pressure. Because the approximation of constant K is not a good one, particularly near z = 0, the Ekman profile

18、 is not accurate.We return to the Ekman layer and assume for the sake of simplicity that the atmosphere is of uniform density of depth H, and that in the boundary layer of depth d (d H) the wind profile is accurately described byand that above the boundary layer there is a flow ug in the x direction

19、, independent of height but varying with the y coordinate. Because of friction in the boundary layer, horizontal convergence of divergence occurs, which leads through the necessity for continuity to vertical motion. The continuity equation for a situation where density changes are neglected is Subst

20、ituting for u and v from (1) and (2) above, and integrating through the boundary layer, we have for the vertical velocity wd at z = dsince u /x = 0 and since on a level surface w = 0 at z = 0.Ekman Pumping1 exp()cos(1)vexp()sin(2)gguuzzuzzvwuzxy 0exp()sindgduwzz dzy The vorticity, g, of the geostrop

21、hic wind above the boundary layer is equal to ug / y = 0 so that on integration, becomesFor typical values, wd is a few mm s-1. The existence of a vertical velocity upwards from the boundary layer has consequences for the flow in the rest of the atmosphere, again because of continuity. Suppose, for

22、instance, we consider the situation in a region of cyclonic vorticity. There is inflow in the boundary layer towards the center of the vortex, rising air above the boundary layer and a balancing outflow at higher levels. This outflow affects the vorticity, g; the rate of change of g can be found, na

23、mely0exp()sindgduwzz dzy 112dgw .gwfftzwhere has been neglected compared withIntegratingbetween the top of the boundary layer (z = d) and the top of the atmosphere, (z = H), we haveAnd on substituting fromThe result is that the vorticity is reduced with a time constant of 2H / f the spin-down time,

24、which is typically several days. The main circulation decays very much more rapidly through this means involving a secondary circulation than by other damping mechanisms. This secondary circulation is driven by friction in the boundary layer, a mechanism known as Ekman pumping. gwftz()gdHdfwt 112dgw

25、 .2ggfdHtH since伍、伍、Convective Boundary Layer 1Mean profileCBL evolution, jump modeltwAththttd) ()21 (2)()(0s02c2csi) () (wwA陆、陆、Stable Boundary Layer 1zgN2Buoyancy frequency or the Brunt-Visl frequencyMean profileLow Level JetsMechanisms of LLJ formationlInertial oscillation, Blackadar 1957, frictions lShallow baroclinicity, Doyle and Warner 1993, (1) a significant change in surface characteristics, strong geostrophic forcing LLJ. (2) the development and evolution of extratropical cyclones produces large regions of significant low level baroclinicitylTerrain effects, (