强迫耗散正压大气中四波共振

本文首次研究了含Ekman摩擦和非绝热加热的四波共振动力学．使用新的双时间尺度和新的时间变换式，由四波共振的广义Landau方程，导得普遍的非线性低频周期解，Ekman摩擦使得低频周期具有滞后和突变返回两个重要特征，而非绝热加热作用与中高纬准双周振荡有关，中高纬的30－50天振荡则与自由Rossby波准共振有关．本文还研究了四波共振产生的爆发性不稳定，指出较大振幅波产生的爆发性不稳定可能是阻塞迅速形成的又一重要原因，还首次得到在正压大气中Ekman摩擦能够激发爆发性不稳定．本文结果纠正了Craik于1985年提出的在流体力学中广泛应用的两个错误论断．     

球面长波模式的设计和应用

本文介绍一两层准地转的球面长波谱模式(LWM)。它包括非绝热加热、地表摩擦和山脉分布。试验表明,由于引进瞬变涡旋输送特征参数化,LWM较低阶谱模式(LOM)有显著改进。它除具有LOM经济简明的优点外,还更合理地描述大气的能量循环和角动量平衡,更准确地模拟纬向西风和定常波。因而适于理论研究和数值模拟。     

DESIGNATION AND APPLICATION OF A SPHERICAL LONG-WAVE SPECTRAL MODEL

A two-level,quasi-geostrophic long-wave model based on spherical coordinates was developed with theexplicit part belonging to a low-order model.However,it includes not only diabatic heating,Ekman fric-tion and mountain distribution,but also parameterized forcing effects of transfer properties of transienteddies.Experiment results showed that,due to the introduction of the parameterization of transfer propertiesof transient eddies,remarkable improvements on characters of low-order model had been obtained.Inaddition to its economization in calculation and conciseness in physics as in a low-order model,the long-wave model was shown to describe the energetics and angular momentum balance of the atmosphere much morereasonably,and to present the features of zonal mean westerlies and stationary waves much more correctlythan the corresponding low-order model.This kind of long-wave model was therefore regarded as suitablefor theoretical research and numerical modelling of some aspects of the general circulation of the atmosphere.     

线性准地转模型中副热带感热加热强迫的定常波

通过求取定常线性准地转位涡模式的解析解,研究了感热加热强迫所激发的副热带定常波的结构特征,讨论了基本流、牛顿冷却及地面摩擦等对定常波振幅和位相的影响。结果表明,东风时定常波在垂直方向上表现为上、下层反位相的第一斜压结构,且地面系统远强于中高层;西风时定常波呈现出向上的传播特征,在高层,随着风速增大振幅随高度的升高有增大趋势。在近地层,东风时气旋（反气旋）主体位于加热西（东）侧;西风时气旋（反气旋）主体位于加热东（西）侧,近地层以上相反。此外,发现东、西风基本流的作用具有对称特征,这与潜热加热显著不同。研究结果还表明,牛顿冷却对定常波有重要影响,基本流越弱影响越显著。在静止大气中,感热加热强迫下无斯韦尔德鲁普（Sverdrup）解,考虑牛顿冷却时,感热强迫在热源范围内的近地层和中高层分别激发出气旋式和反气旋式环流,气旋中心位于加热中心略偏西的位置。在非静止大气中,牛顿冷却项使地面系统中心向上风方向移动,东风时向东移。牛顿冷却对高、低层系统均有削弱作用。地面摩擦则明显不同,它总会使低层系统减弱,高层系统增强。     

Ekman动量近似下中间边界层模式中的风场结构

发展了一个准三维的、中等复杂的边界层动力学模式，该模式包含了EKman动量近似下的惯性加速度和Blackadar的非线性湍流粘性系数，它进一步改进了Tan和Wu(1993）提出的边界层理论模型。该模型在数值计算复杂性上与经典Ekman模式相类似，但由于包含了Ekman动量近似下的惯性项，使得该模式比传统Ekman模式更近于实际过程。中详细地比较了该模式与其他简化边界层模式在动力学上的差异，结果表明：在经典的Ekman模式中，由于忽略了流动的惯性项作用，导致在气旋性切变气流（反气旋性切变气流）中风速和边界层顶部的垂直速度的高估（低估），而在半地转边界层模式中，由于高估了流动惯性项的作用，结果与经典Ekman模式相反。同样，该模式可以应用于斜压边界层，对于Ekman动量下的斜压边界层风场同时具有经典斜压边界层和Ekman动量近似边界层的特征。     

The Ekman momentum approximation and its application

In the boundary layer, the flow is basically an equilibrium of three forces: Coriolis, pressure gradient and frictional. This means that it is an Ekman flow while the basic flow in the free atmosphere is an equilibrium of two forces: Coriolis and pressure gradient, and is a geostrophic flow. Therefore, it is natural to try to modify the geostrophic momentum approximation in the free atmosphere to become an Ekman momentum approximation in the boundary layer. The physical explanation and foundation of the Ekman momentum approximation are discussed.     

台风移速突变的数值研究

用准地转正压模式，在无环境气流的情况下，实施了８组时间积分大于５个模式日的试验。在模式大气台风移动的过程中，清楚地显示了移速突然变化的现象。台风移速突然变化与前期台风环流的非对称结构之间存在着密切的联系。最后分析了台风环流非规则结构对路径的影响。     

A NUMERICAL SIMULATION OF TYPHOON GENERATION

By using a two-dimensional axisymmetrical PEM in which two physical processes (the Ekman pumping and the vertical transportation of cumulus momentum) are included, the genesis and development of typhoons have been simulated. The results of numerical simulation show that the generation and structure of the typhoon simulated by the model involving both the physical processes are much close to a real one in the atmosphere as compared with that involving either the Ekman pumping or the cumulus momentum transport. Therefore, it can be suggested that the cumulus momentum transport and Ekman pumping together play an important role in the genesis and development of typhoons through the CISK mechanism.     

Dynamic Impact of the Vertical Shear of Gradient Wind on the Tropical Cyclone Boundary Layer Wind Field

This work studies the impact of the vertical shear of gradient wind （VSGW） in the free atmosphere on the tropical cyclone boundary layer （TCBL）. A new TCBL model is established, which relies on five- force balance including the pressure gradient force, Coriolis force, centrifugal force, turbulent friction, and inertial deviation force. This model is then employed to idealize tropical cyclones （TCs） produced by DeMaria＇s model, under different VSGW conditions （non-VSGW, positive VSGW, negative VSGW, and VSGW increase/decrease along the radial direction）. The results show that the free-atmosphere VSGW is particularly important to the intensity of TC. For negative VSGW, the total horizontal velocity in the TCBL is somewhat suppressed. However, with the maximum radial inflow displaced upward and outward, the radial velocity notably intensifies. Consequently, the convergence is enhanced throughout the TCBL, giving rise to a stronger vertical pumping at the TCBL top. In contrast, for positive VSGW, the radial inflow is significantly suppressed, even with divergent outflow in the middle-upper TCBL. For varying VSGW along the radial direction, the results indicate that the sign and value of VSGW is more important than its radial distribution, and the negative VSGW induces stronger convergence and Ekman pumping in the TCBL. which favors the formation and intensification of TC.     

On the instability of a planetary boundary layer with Rossby-number similarity

The formation of longitudinal vortex rolls in the planetary boundary layer (PBL) is investigated by means of perturbation analysis. The method is the same as that used by previous authors who have investigated the instability of a laminar Ekman layer. To study the instability of the turbulent boundary layer of the atmosphere, vertical profiles are needed of the eddy viscosity and of the two components of the basic flow. These profiles have been obtained by a numerical PBL-model; they are universal for zz ₀. (However, the stability equations are not completely universal, i.e., independent of the external parameters). For each thermal stratification, expressed by the internal stratification parameter , one has a set of three consistent profiles.The numerical solution of the stability equations gives the critical values and the perturbation growth rates as functions of thermal stratification and of the surface Rossby number Ro₀. This is in contrast to the case of a laminar Ekman layer, where the instability depends on a Reynolds number only, which makes atmospheric applications difficult. The most unstable perturbations are found for Ro₀ = 1 × 10⁶ approximately, which is in the range of surface Rossby numbers observed in the atmosphere. However, considering vortex rolls oriented in the direction of the surface stress, the instability is found to be universal, i.e., independent of the external parameters combined in the surface Rossby number. With respect to thermal stratification, the results show that the instability of the perturbations increases with increasing static stability.     

''98南海季风(SCSMEX)和高原科学试验(TIPEX)边界层

使用1998年南海季风(SCSMEX)试验和青藏高原科学试验(TIPEX)的边界层资料对Ekman特征进行了动力学研究。得到如下结果：(1)在青藏高原和南海及其周围区域有类似的Ekman动力学特征。(2)比较研究表明，边界层厚度在青藏高原约为2250m且考虑到它的摆动特性，其厚度可在2250-2750m之间。在热带西南太平洋边界层厚度约为2000m，其厚度摆动较小，在平原地区边界层厚度较低。（3）由于高原和热带海域海拔高度的不同，尽管在高原和热带海区有着几乎同样的边界层厚度，但边界层对大气的影响是相当不同的。考虑到海拔高度的影响，在这两个地区摩擦力作用的空间部位的高度有相当大的差别。(4)这两个区域的湍流摩擦的垂直结构差异较大。使用’98SCSMEX和TIPEX边界层资料计算结果表明，即使在低层，平均湍流粘性力在高原上是热带海域的2．3倍。     

A BAROTROPIC QUASI-GEOSTROPHIC MODEL WITH LARGE-SCALE TOPOGRAPHY, FRICTION AND HEATING

Based on the barotropic equations including large-scale topography, friction and heat factor, a barotropic quasi-geostrophic model with large-scale topography, friction and heating is obtained by means of scale analysis and small parameter method. It is shown that this equation is a basic one, which is used to study the influence of the Tibetan Plateau on the large-scale flow in the atmosphere. If the friction and heating effect of large-scale topography are neglected, this model will degenerate to the general barotropic quasi-geostrophic one.     

Turbulent Helicity in the Atmospheric Boundary Layer

We consider the assumption postulated by Deusebio and Lindborg (J Fluid Mech 755:654–671, 2014) that the helicity injected into the Ekman boundary layer undergoes a cascade, with preservation of its sign (right- or alternatively left-handedness), which is a signature of the system rotation, from large to small scales, down to the Kolmogorov microscale of turbulence. At the same time, recent direct field measurements of turbulent helicity in the steppe region of southern Russia near Tsimlyansk Reservoir show the opposite sign of helicity from that expected. A possible explanation for this phenomenon may be the joint action of different scales of atmospheric flows within the boundary layer, including the sea-breeze circulation over the test site. In this regard, we consider a superposition of the classic Ekman spiral solution and Prandtl’s jet-like slope-wind profile to describe the planetary boundary-layer wind structure. The latter solution mimics a hydrostatic shallow breeze circulation over a non-uniformly heated surface. A 180°-wide sector on the hodograph plane exists, within which the relative orientation of the Ekman and Prandtl velocity profiles favours the left rotation with height of the resulting wind velocity vector in the lowermost part of the boundary layer. This explains the negative (left-handed) helicity cascade toward small-scale turbulent motions, which agrees with the direct field measurements of turbulent helicity in Tsimlyansk. A simple turbulent relaxation model is proposed that explains the measured positive values of the relatively minor contribution to turbulent helicity from the vertical components of velocity and vorticity.     

A STUDY ON TYPHOON MOVEMENT PARTⅡ:DYNAMICAL ROLE OF SMALL TOPOGRAPHY AND THE PLANETARY BOUNDARY LAYER

The dynamic effects of small topography (in the sense of the characteristic height of the topography as compared with the vertical thickness of the system of motion) and the Ekman pumping caused by the frictional convergence in the bounary layer on the motion of a typhoon have been qualitatively discussed in this part based on the governing equation of typhoon motion derived in part I of this paper. The results show that a topographical ridge tends to attract the typhoon approaching it and this explains at least partially the phenomenon that the typhoon over the western Pacific tends to accelerate just before their making land fall over the coastal areas. It is also shown that the Ekman pumping at the top of the boundary layer favors the typhoon acceleration along the local steering current.     

Parameterizations of the daytime friction velocity,temperature scale,and upslope flow over gently inclined terrain in calm synoptic conditions

A set of new parameterizations for the friction velocity and temperature scale over gently sloped terrain and in calm synoptic conditions are theoretically derived. The friction velocity is found to be proportional to the product of the square root of the total accumulated heating in the boundary layer and the sinusoidal function of the slope angle, while the temperature scale is proportional to the product of the boundary layer depth, the sinusoidal function of the slope angle and the potential temperature gradient in the free atmosphere. Using the new friction velocity parameterization, together with a parameterization of eddy diffusivity and an initial potential temperature profile around sunrise, an improved parameterization for the thermally induced upslope flow profile is derived by solving the Prandtl equations. The upslope flow profile is found to be simply proportional to the friction velocity.     

台风的数值模拟研究——积云动量输送作用

本文用一个考虑积云动量垂直输送作用的二维轴对称原始方程模式,模拟了台风的生成和发展过程。数值试验所得到的“模式台风”比考虑Ekman抽吸作用所得结果在其结构上更接近实际台风。因此,同Ekman抽吸一样,积云动量垂直输送作用也可以激发第二类条件不稳定(CISK),促使台风的生成和发展。而且,积云动量垂直输送作用,在台风的形成和维持中可能比Ekman抽吸更为重要。     

Impact of resolving the diurnal cycle in an ocean–atmosphere GCM. Part 1: a diurnally forced OGCM

The diurnal cycle is a fundamental time scale in the climate system, at which the upper ocean and atmosphere are routinely observed to vary. Current climate models, however, are not configured to resolve the diurnal cycle in the upper ocean or the interaction of the ocean and atmosphere on these time scales. This study examines the diurnal cycle of the tropical upper ocean and its climate impacts. In the present paper, the first of two, a high vertical resolution ocean general circulation model (OGCM), with modified physics, is developed which is able to resolve the diurnal cycle of sea surface temperature (SST) and current variability in the upper ocean. It is then validated against a satellite derived parameterization of diurnal SST variability and in-situ current observations. The model is then used to assess rectification of the intraseasonal SST response to the Madden–Julian oscillation (MJO) by the diurnal cycle of SST. Across the equatorial Indo-Pacific it is found that the diurnal cycle increases the intraseasonal SST response to the MJO by around 20%. In the Pacific, the diurnal cycle also modifies the exchange of momentum between equatorially divergent Ekman currents and the meridionally convergent geostrophic currents beneath, resulting in a 10% increase in the strength of the Ekman cells and equatorial upwelling. How the thermodynamic and dynamical impacts of the diurnal cycle effect the mean state, and variability, of the climate system cannot be fully investigated in the constrained design of ocean-only experiments presented here. The second part of this study, published separately, addresses the climate impacts of the diurnal cycle in the coupled system by coupling the OGCM developed here to an atmosphere general circulation model.     

Inertia and diurnal oscillations of Ekman layers in atmosphere and ocean

A 1D model, including a time variation of eddy viscosity and mixed layer depth, is applied to study Ekman spirals. It simulates a weak velocity in the atmosphere but a jet in the upper oceanic mixed layer during daytime; and a strong velocity in the atmosphere but a weak, uniform velocity in the ocean at night. The mean spirals in both atmosphere and ocean are close to the average spirals at midday and midnight, they are not flat as suggested by previous studies but consistent with the observations of Polton et al (2013). Our results also show shorter length scale for magnitude decay than for rotation of mean velocity as observed in the ocean, which comes from the combined effects of the diurnal variation of PBL and the Coriolis force. The latter becomes more important away from the surface. In the upper oceanic mixed layer, the mean velocity mainly comes from the strong jets in the late afternoon and early evening. Near and below the depth of Ekman depth, the weak velocities change with time and cancel out each other if averaged timing is longer than the inertia period. It results in diminishing of magnitude of the mean velocity, but the amplitude of individual parcel oscillating can still be quite large near the Ekman depth. Meanwhile, the change of velocity angle from the surface is near or less than 90 degree. Hence, shorter length scale for magnitude decay than for rotation of the mean velocity is not controlled by viscosity alone. Meanwhile, the model does not need two viscosities as suggested previously.The results also show that either the diurnal variation of surface stress or eddy viscosity alone can create a diurnal oscillation of velocity in the ocean. The interactions between PBL force and the Coriolis force can create a weak instability in the atmosphere and ocean at 30° and 90°. This weak instability may explain the observed nocturnal LLJ near 30 °N on the lee of the Rocky Mountains and the intensification of mesoscale circulation simulated by Sun and Wu (1992).     

One-Equation Turbulence Modelling for Atmospheric and Engineering Applications

A new algebraic turbulent length scale model is developed, based on previous one-equation turbulence modelling experience in atmospheric flow and dispersion calculations. The model is applied to the neutral Ekman layer, as well as to fully-developed pipe and channel flows. For the pipe and channel flows examined the present model results can be considered as nearly equivalent to the results obtained using the standard k– model. For the neutral Ekman layer, the model predicts satisfactorily the near-neutral Cabauw friction velocities and a dependence of the drag coefficient versus Rossby number very close to that derived from published (G. N. Coleman) direct numerical simulations. The model underestimates the Cabauw cross-isobaric angles, but to a less degree than the cross-isobar angle versus Rossby dependence derived from the Coleman simulation. Finally, for the Cabauw data, with a geostrophic wind magnitude of 10 ms^–1, the model predicts an eddy diffusivity distribution in good agreement with semi-empirical distributions used in current operational practice.     

Nonlinear resonance interactions and index cycles in the atmosphere

A barotropic spectral model is used to study the planetary-scale motions of an atmosphere whose wave ensemble modes are externally driven. Pertubations are induced by a barotropic analogue of thermal driving and by Ekman friction, bottom topography, and the vanished internal dissipation. The use of complete spectral expansions without truncation leads to that the nonlinear coupling equations between the low-index mode and the high-index mode are obtained by means of the random phase approximation and the projec-tion operator techniques. The nonlinear coupling equations are entirely equivalent to the Volterra systems in ecology.In the phase-plane, the orbits of the nonlinear coupling equations are the family of closed curves, indicat-ing a bound, and periodic motion. The qualitative behaviors of low-index and high-index modes as functions of time picture the motion of atmospheric flows, with exchanges of energy between the low-index mode and the high-index mode by nonlinear resonance interaction. It is suggested that the phenomenon of blocking be exponentially grown of the low-index mode, the atmospheric motion then evolved to the high-index mode due to relaxation process. The results therefore lead to a plausible hypothesis concerning index cycles in the atmosphere discussed by Lorenz’s early works.