Vorticity,divergence, and vertical velocity in a baroclinic boundary layer with a linear variation of the geostrophic wind

The Ekman-Taylor problem for the planetary boundary layer is solved in the case of a thermal wind which varies linearly with height. The upper boundary condition is a vanishing ageostrophic wind, while the lower boundary condition is continuity of the stress vector across the interface between the planetary boundary layer and the surface layer. The latter condition is used to determine the magnitude and the direction of the wind at the bottom of the Ekman layer.Theoretical hodographs are compared with observed hodographs based on five years of ohservations from Ship N in the Pacific, giving fair agreement.The divergence, the vorticity, and the vertical velocity are calculated through the Ekman layer with emphasis on differences between the classical barotropic and the baroclinic cases; these differences are significant, especially in the vertical velocities as compared to the standard approximation.An extension of the present study to include thermal stratification is desirable.     

旋转流地转适应过程与能量转换规律

利用一维线性浅水模式从一个比较普遍的角度对地转适应过程中能量转换的特点进行分析。中首先考虑了两类不同的初始不平衡流的适应问题。一个是Gill所采用的质量不平衡模型，即初始场是静止的，只有水面扰动；另一个是Rossby中所考虑的动量不平衡模型，其初始不平衡流中只有风场的扰动，对这两个模型的适应过程而言，一个显的 特点就是能量转换率始终不会大于1／2或小于0，即适应过程中有位（动）能的释放和向动（位）能的转换，但释放出的能量最多只有其中的一半可以保留在最后的平衡场中。另外，本对任意初始不平衡流适应过程中的能量学特征也进行了分析，指出对于偏差场（相对于一定基本态）的动能和位能而言，上述能量转换关系依然成立。     

Estimation of persistence and trends in geostrophic wind speed for the assessment of wind energy yields in Northwest Europe

Wind climate in Northwest Europe is subject to long-term persistence (LTP), also called the Hurst phenomenon. Ignorance of LTP causes underestimation of climatic variability. The quantification of multi-year variability is important for the assessment of the uncertainty of future multi-year wind yields. Estimating LTP requires long homogeneous time series. Such series of wind observations are rare, but annual mean geostrophic wind speed (U) can be used instead. This study demonstrates a method to estimate the 10-year aggregated mean U for the near and the far future and its uncertainty in Northwest Europe. Time series of U were derived from daily sea level pressure from the European Climate Assessment Dataset. Minor inhomogeneities cannot be ruled out, but were shown to hardly affect the estimated Hurst exponent $(\hat{H})$ . A maximum likelihood method was adjusted to remove the biases in $\hat{H}$ . The geostrophic wind speed over the North Sea, the British Isles and along the Scandinavian coast are characterised by statistically significant H between 0.58 and 0.74, (H?=?0.5 implies no LTP). The additional affect of the parameter uncertainty is estimated in a Bayesian way and is highly dependent on the record length. The assessment of structural changes in future wind fields requires general circulation models. An ensemble of seventeen simulations (ESSENCE) with one single climate model (ECHAM5/MPI-OM) was used to evaluate structural trends and LTP. The estimated $\hat{H}$ in the ESSENCE simulations are generally close to 0.5 and not significant. Significant trends in U are found over large parts of the investigated domain, but the trends are small compared to the multi-year variability. Large decreasing trends are found in the vicinity of Iceland and increasing trends near the Greenland coast. This is likely related to the sea ice retreat within the ESSENCE simulations and the associated change in surface temperature gradients.     

地转动量近似下边界层中风场的调整

本文利用地转动量近似,并假设气压场为定常的圆形涡旋和初始风场不满足四力平衡(气压梯度力、科里奥利力、湍流粘性力和半地转惯性力)的条件下,求解了正压边界层中风场向气压场调整的初边值问题,得到了一些初步结论。本工作为利用四力平衡下的风速分布来诊断预报边界层风场提供了理论依据。     

The influence of the geostrophic wind advection approximation on a well-mixed layer

Numerical results indicate that advection of momentum in the boundary layer may significantly alter both the structure of the planetary boundary layer and its influence on the overlying free atmosphere. However, due to the nonlinearity of the inertial terms, it is always difficult to obtain the analytical solution of the boundary-layer model that retains the flow acceleration. In order to overcome this difficulty, the geostrophic momentum (hereafter GM) approximation has been introduced into boundary-layer models. By replacing the advected momentum with the geostrophic wind, the effect of the flow acceleration is partially considered and the original nonlinear partial differential equation set is converted to ordinary differential equations, the solutions of which can be obtained easily with standard techniques. However, the model employing GM fails to capture the features of the boundary layer when the spatio-temporal variation of the boundary-layer flow cannot be properly approximated by the geostrophic wind. In the present work, a modified boundary-layer model with the inertial acceleration in a different approximate form is proposed, in which the advecting wind instead of the advected momentum is approximated by the geostrophic wind (hereafter GAM).Comparing the horizontal velocity and boundary-layer pumping obtained from the classical Ekman theory, and the model incorporating (i) GM and (ii) GAM, it is found that the model with GAM describes most facets of the steady well-mixed layer beneath a north-westerly flow with embedded mesoscale perturbations that is considered in the present work. Inspection of the solution of the model with GAM shows that, within the limit of the validation of the model (i.e., the Rossby number R_O is not very large and the drag coefficient C_D is not too small), the horizontal convergence (divergence) is strengthened by the effect of the inertial acceleration in the region of maximum positive (negative) geostrophic vorticity. Consequently, the boundary-layer pumping there is intensified. It is found that the intensification is firstly strengthened and then weakened as R_O or C_D increases.     

The influence of geostrophic shear on the cross-isobar angle of the surface wind

A Simple slab model of the planetary boundary layer is extended to include vertical shear of the geostrophic wind. The layer depth is assumed to be determined by a Richardson number criterion. The cross-isobar angle for the surface wind is given in terms of the drag coefficient, the Froude number of the layer, and the angle between the thermal wind and the surface isobars. The theoretical results resemble the observations rather well.     

A model for heat patch in the boundary layer of the geostrophic flow

A hydrodynamic model is considered for a disturbance of wind field structure of the boundary layer in the geostrophic flow running onto a warmer underlying surface. It is shown that the breeze effect causes the lowering (or heightening) of streamlines in a narrow area of sharp changes in curvature of horizontal profile of temperature disturbance. The technique by A.A. Dorodnitsyn for solution of parabolic equation set is illustrated by an example of a streamline and vertical velocity calculation over a wide “warm” river. A scheme is presented explaining the breeze effect on the boundary layer structure.     

Shearing wind helicity and thermal wind helicity

Helicity is defined as H ： V ω, where V and ω are the velocity and vorticity vectors, respectively. Many works have pointed out that the larger the helicity is, the longer the life cycle of the weather system is. However, the direct relationship of the helicity to the evolution of the weather system is not quite clear. In this paper, the concept of helicity is generalized as shearing wind helicity （SWH）. Dynamically, it is found that the average SWH is directly related to the increase of the average cyclonic rotation of the weather system. Physically, it is also pointed out that the SWH, as a matter of fact, is the sum of the torsion terms and the divergence term in the vorticity equation. Thermal wind helicity （TWH）, as a derivative of SWH, is also discussed here because it links the temperature field and the vertical wind field. These two quantities may be effective for diagnosing a weather system. This paper applies these two quantities in cylindrical coordinates to study the development of Hurricane Andrew to validate their practical use. Through analyzing the hurricane, it is found that TWH can well describe the characteristics of the hurricane such as the strong convection and release of latent heat. SWH is not only a good quantity for diagnosing the weather system, but also an effective one for diagnosing the development of the hurricane.     

Planetary geostrophic equations for the atmosphere with evolution of the barotropic flow

Atmospheric phenomena such as the quasi-stationary Rossby waves, teleconnection patterns, ultralong persistent blockings and the polar/subtropical jet are characterized by planetary spatial scales, i.e. scales of the order of the earth’s radius. This motivates our interest in the relevant physical processes acting on the planetary scales. Using an asymptotic approach, we systematically derive reduced model equations valid for atmospheric motions with planetary spatial scales and a temporal scale of the order of about 1 week. We assume variations of the background potential temperature comparable in magnitude with those adopted in the classical quasi-geostrophic theory. At leading order, the resulting equations include the planetary geostrophic balance. In order to apply these equations to the atmosphere, one has to prescribe a closure for the vertically averaged pressure. We present an evolution equation for this component of the pressure which was derived in a systematic way from the asymptotic analysis. Relative to the prognostic closures adopted in existing reduced-complexity planetary models, this new dynamical closure may provide for more realistic increased large-scale, long-time variability in future implementations.     

The temporal evolution of a geostrophic flow in a rotating stratified basin

A laboratory study in a rotating stratified basin examines the instability and long time evolution of the geostrophic double gyre introduced by the baroclinic adjustment to an initial basin-scale step height discontinuity in the density interface of a two-layer fluid. The dimensionless parameters that are important in determining the observed response are the Burger number S=R/R₀ (where R is the baroclinic Rossby radius of deformation and R₀ is the basin radius) and the initial forcing amplitude (H₁ is the upper layer depth). Experimental observations and a numerical approach, using contour dynamics, are used to identify the mechanisms that result in the dominance of nonlinear behaviour in the long time evolution, τ>2⁻¹ (where τ is time scaled by the inertial period T_I=2π/f). When the influence of rotation is moderate (0.25≤S≤1), the instability mechanism is associated with the finite amplitude potential vorticity (PV) perturbation introduced when the double gyre is established. On the other hand, when the influence of rotation is strong (S≤0.1), baroclinic instability contributes to the nonlinear behaviour. Regardless of the mechanism, nonlinearity acts to transfer energy from the geostrophic double gyre to smaller scales associated with an eddy field. In the lower layer, Ekman damping is pronounced, resulting in the dissipation of the eddy field after only 40T_I. In the upper layer, where dissipative effects are weak, the eddy field evolves until it reaches a symmetric distribution of potential vorticity within the domain consisting of cyclonic and anticyclonic eddy pairs, after approximately 100T_I. The functional dependence of the characteristic eddy lengthscale L_E on S is consistent with previous laboratory studies on continuously forced geostrophic turbulence. The cyclonic and anticyclonic eddy pairs are maintained until viscous effects eventually dissipate all motion in the upper layer after approximately 800T_I. The outcomes of this study are considered in terms of their contribution to the understanding of the energy pathways and transport processes associated with basin-scale motions in large stratified lakes.     

地形对低空地转气流上重力惯性波稳定性的影响

研究指出,对西风地转气流,地形的南坡有利于重力惯性波的不稳定,北坡不利于波动的不 稳定发展;对东风气流,情况与此相反.重力惯性波不稳定的条件是(u+g~*A/f)~2≥g~*H.     

Comments on ‘the influence of geostrophic shear on the cross-isobar angle of the surface wind’

Boundary-Layer Meteorology -     

Zonal and meridional circulations in the equatorialzone as deduced from the divergence field of the surface wind

The zonal and meridional circulations and their variability are examined on the basis of the surface wind data for 1950-1979. The climatological mean zonal wind and its divergence are examined in reference to the Walker Circulation. The role played by the meridional circulation in contributing to convergence of the surface wind field within the equatorial zone is emphasized. Regression coefficients are used to infer seasonal mean anomalies of divergence of the surface wind in years when the sea level pressure is 1 hPa above normal at Darwin, a condition representative of El Nino events. It is shown that anomalies in the divergence associated with the meridional wind component are primarily responsible for the heavy precipitation in the Central Pacific, while the anomalous divergence associated with the zonal wind component may cause the drought in the Western Pacific near Indonesia. A similar pattern of divergence anomalies is evident during three consecutive seasons beginning in northern summer and ending in northern winter. The reinforcement of the Hadley Circulation during El Nino episodes is noted. It is shown that the circulations over the Atlantic Ocean and Pacific Ocean are relatively uncorrelated. The interrelation between the dipole anticyclones and the meridional cir-culation over the central Pacific is discussed.     

The influences of orography upon the flow within Ekman boundary layer under the approximation of geostrophic momentum

In this paper, the influences of orography on the boundary layer flow with the approximation of geostrophic momentum are studied. The wind velocity at the lower boundary will not always be zero when the orography exists. So the structure of the boundary layer flow, as well as the vertical velocity at the top of the boundary layer, is affected. There are three factors affecting the vertical motion at the top of the boundary layer: lifting due to orography; divergence due to Ekman flow, and advection of the geostrophic momentum. These effects and the features of the flow within the boundary layer are discussed in detail.     

斜压大气中的特征波动和地转适应过程

本文对斜压大气的小扰动方程作了严格和全面的数学分析:论证了关于垂直边界条件的正确提法以及初始场一些特殊问题,澄清了迄今不正确的和混乱的提法;给出了解的存在、唯一和稳定性的证明。在这基础上,对大气的特征波动作了分类,并证明内波的能量总是向宇宙空间弥散掉,最终强度趋于零。因此,即使扰动的水平范围为无限,或者严格地考虑到地球表面为球面,也有地转适应过程,这是以在未研究过的机理。     

A theoretical test of the geostrophic momentum approximation

A previously developed model of a 2-dimensional air flow with constant horizontal shear is used to estimeate the accuracy of the geostrophic momentum approximation by comparison of exact solutions when exist with approxi-mate ones.     

Development of sea surface temperature,surface wind and divergence anomalies during a composite ENSO episode

Summary The interannual variations in sea surface temperature (SST) in the equatorial east Pacific, which are dominated by the El Niño phenomenon, are shown for the period 1870–1983. Since 1870 25 significant warm events have occurred. These events are classified as weak, moderate, strong and very strong, according to the normalized SST anomalies in the region 130° W–80° W, 0°–5° S.The spatial and temporal development of a composite El Niño/Southern Oscillation (ENSO) episode, based on 10 very strong or strong events, is presented in terms of SST, surface wind and divergence anomalies for the tropical Pacific (10° N–30° S). During its evolution the following phases are distinguished: Antecedent Conditions, Onset Phase, Peak Phase, Mature Phase and Dissipation Stage.Some aspects of ocean-atmosphere interaction associated with this evolution and, more specifically, the initiation of the composite event, are described. Seasonally varying feedback processes between SST, surface wind and convergence anomaly patterns in the western Pacific/Indonesian region suggest a possible mechanism for the initiation of typical ENSO events.

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Zusammenfassung Die interannuären Variationen der Meeresoberflächentemperatur (SST) im äquatorialen Ostpazifik, die von dem El Niño-Phänomen dominiert werden, werden für die Periode 1870–1983 aufgezeigt. Seit 1870 traten 25 signifikante Ereignisse auf. Diese Ereignisse werden entsprechend den normierten SST-Anomalien in der Region 130° W–80° W, 0°–5° S als schwach, mittel, stark und sehr stark klassifiziert.Die räumliche und zeitliche Entwicklung einer Komposit-El Niño/Southern Oscillation (ENSO)-Episode, die auf 10 sehr starken bzw. starken Ereignissen basiert, wird anhand von SST-, Bodenwind- und Divergenzanomalien für den tropischen Pazifik (10° N–30° S) dargestellt. Während ihrer Entwicklung werden die folgenden Phasen unterschieden: Vorausgehende Bedingungen, Einsetzphase, Spitzenphase, Reifestadium und Auflösungsstadium.Einige Aspekte der Wechselbeziehungen Ozean—Atmosphäre werden im Zusammenhang mit der Entwicklung und insbesondere der Auslösung des Komposit-Ereignisses beschrieben. Jahreszeitlich variierende Rückkopplungsprozesse zwischen SST-, Bodenwind- und Konvergenzanomalien in der westpazifischen/indonesischen Region stellen einen möglichen Mechanismus für die Auslösung typischer ENSO-Ereignisse dar.

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With 9 Figures     

A numerical study of geostrophic adjustment and frontogenesis

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A numerical experiment of the PBL with geostrophic momentum approximation

In this paper, a numerical experiment of the motion in the PBL (planetary boundary layer) is perform-ed with geostrophic momentum approximation, in which a nonlinear eddy transfer coefficient is used. Some results are obtained for the boundary layer winds in cyclone-anticyclone and trough-ridge systems. This treat-ment improves W-B’s work. The effects of geostrophic wind tendency and the advection of the geostrophic wind on the winds in the PBL are also discussed.