On some of the relations for vertical velocity in the atmosphere

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Rossby-Haurwitz's equation for the conservation of vertical vorticity component in the baroclinic atmosphere

Summary It is shown that the conservation equation of potential vorticity in the barotropic atmosphere holds good, even in the baroclinic atmosphere, if it is permissible to introduce the isentropic and mass-conservation approximations.     

A simple theory for the vertical structure of the tropical atmosphere

It is suggested that the gross mean vertical structure of the undisturbed tropical atmosphere may be understood in terms of convective boundary layers driven in different ways and on different time scales by the evaporation of water from the sea surface. The mixed layer on a short time scale is driven partly by the buoyancy produced by the light weight of the water vapor; the trade cumulus layer on an intermediate time scale by the buoyancy (but not heating) produced by the condensation of the water vapor in shallow trade cumulus clouds; and the troposphere itself on a long time scale by the buoyancyand heating produced by the condensation of the water vapor in the deep cumulonimbus clouds.May 1985This paper was issued as a Harvard University report in 1974. For this version only Section 5 has been rewritten. There has been sufficient interest in this work over the years to warrant making it more widely available through the open literature.Contribution No. 783 from NOAA/Pacific Marine Environmental Laboratory     

On the vertical transport of angular momentum in the atmosphere

Summary The possible modes of vertical transport of angular momentum in the atmosphere are considered. Momentum balance calculations for both hemispheres show the possibility of countergradient transport by vertical eddies in the region of the mid-latitude jet. As a consequence, it is pointed out that the transport of momentum downward from the region of maximum westerlies would have to be accomplished by the mean meridional motions, through the action of Coriolis torques. The same mechanism may account for a large part of the upward transport in the tropics. The very approximate nature of the calculations must, however, be borne clearly in mind.     

60年来大气中二氧化碳浓度数据的趋势方程研究

通过讨论已有的60年来大气中CO₂浓度数据的分布状态,采用趋势分析方法,给出了具体趋势方程形式.与冰芯分析或观测数据对比结果表明,趋势方程曲线与已有数据基本符合,随后初步给出了2010年至2016年间大气中CO₂浓度预测值.     

Advanced insights into sources of vertical velocity in the ocean

Estimating vertical velocity in the oceanic upper layers is a key issue for understanding ocean dynamics and the transport of biogeochemical elements. This paper aims to identify the physical sources of vertical velocity associated with sub-mesoscale dynamics (fronts, eddies) and mixed-layer depth (MLD) structures, using (a) an ocean adaptation of the generalized Q-vector form of the ω-equation deduced from a primitive equation system which takes into account the turbulent buoyancy and momentum fluxes and (b) an application of this diagnostic method for an ocean simulation of the Programme Océan Multidisciplinaire Méso Echelle (POMME) field experiment in the North-Eastern Atlantic. The approach indicates that w-sources can play a significant role in the ocean dynamics and strongly depend on the dynamical structure (anticyclonic eddy, front, MLD, etc.). Our results stress the important contribution of the ageostrophic forcing, even under quasi-geostrophic conditions. The turbulent w-forcing was split into two components associated with the spatial variability of (a) the buoyancy and momentum (Ekman pumping) surface fluxes and (b) the MLD. Process (b) represents the trapping of the buoyancy and momentum surface energy into the MLD structure and is identified as an atmosphere/oceanic mixed-layer coupling. The momentum-trapping process is 10 to 100 times stronger than the Ekman pumping and is at least 1,000 times stronger than the buoyancy w-sources. When this decomposition is applied to a filamentary mixed-layer structure simulated during the POMME experiment, we find that the associated vertical velocity is created by trapping the surface wind-stress energy into this structure and not by Ekman pumping.     

A mixing-length model for predicting vertical velocity distribution in flows through emergent vegetation

Abstract

The vertical profiles of streamwise velocities are computed on flood plains vegetated with trees. The calculations were made based on a newly developed one-dimensional model, taking into account the relevant forces acting on the volumetric element surrounding the considered vegetation elements. A modified mixing length concept was used in the model. An important by-product of the model is the method for evaluating the friction velocities, and consequently bed shear stresses, in a vegetated channel. The model results were compared with the relevant experimental results obtained in a laboratory flume in which flood plains were covered by simulated vegetation.     

Pattern of vertical velocity in the Lofoten vortex (the Norwegian Sea)

Mean radial distributions of various dynamic characteristics of the permanently existing anticyclonic Lofoten vortex (LV) in the Norwegian Sea are obtained from an eddy-permitting regional hydrodynamic MIT general circulation model. It is shown that the model adequately reproduces the observed 3D thermohaline and dynamic structure of the vortex. The obtained radial distribution of the mean vertical velocity is found to form a complex structure: with the upward fluxes along the axis in and above the anticyclonically rotating LV core, compensated by the downward fluxes in the vortex skirt. These vertical motions maintain the vortex potential energy anomaly against dissipation. This secondary circulation is generated by the centrifugal force and, to a lesser extent, by the horizontal dispersion of the vortex energy, both intensified towards the sea surface. Below the vortex core, the maximum downward vertical velocity converges towards the vortex axis with depth. At these depth levels, the secondary circulation is forced by Ekman divergence in the bottom mixed layer. The theory of columnar vortices with helical structure, applied to the LV, relate the radial profiles of the vertical velocity with those of the horizontal circulation. The theoretically predicted the radial patterns of the mean vertical velocity in the LV were close to those, obtained from the primitive equation ocean model, when approximating the radial patterns of the azimuthal velocity with the Rayleigh profile.     

Large scale vertical eddies in the atmosphere and the energy of the mean zonal flow

Summary The zonal eddy stress across horizontal surfaces due to large scale vertical motions was evaluated for two months from data for the northern hemisphere for a number of levels up to 50 mb. From this information and from the corresponding distributions for each of the two months of the mean zonal winds, the rate of transformation of kinetic energy from eddy to mean zonal form was calculated. The two sets of data gave rather small values for the hemisphere which were of opposite sign.     

Vertical velocity due to mean baroclinicity and diabatic heating of the atmosphere

Summary Vertical velocities at the 800, 600 and 400 mbar surfaces over India have been calculated, making use of a 3-level geostrophic baroclinic model. Further, the effects of non-adiabatic heating is included into the model and vertical velocity due to diabatic heating is obtained for the same period. A numerically obtained vertical velocity field due to baroclinicity and diabatic heating is seen to be in agreement with the observed weather patterns.     

风的垂直切变对滞弹性大气中静力适应过程的影响

本文基于描写滞弹性大气静力适应过程的线性方程组,从波动频散关系、气团运动规律和能量转换的角度出发,研究了水平基流及其垂直切变对该模式大气静力适应过程的影响.构造四种水平基流垂直分布模型进行比较,分别为常数型、线性切变型、反气旋切变型和气旋切变型,得到结论：（1）具有重力波性质的波动是滞弹性大气静力适应过程中扰动能量传播的方式,当垂直折射指数大于零时,基本气流及其垂直切变的存在,不仅改变了波动频率的大小,而且改变波动传播的方向;（2）在静力适应过程中气块的运动轨迹呈椭圆形,水平基流及其垂直切变影响椭圆的扁率,同时也影响扰动物理量之间的偏振关系;（3）水平基流的垂直切变是扰动能量和水平基流能量发生转换的媒介,当存在垂直向上的动量输送时,正的垂直风切变对应扰动能量的衰减,水平基流能量的增加,负的垂直风切变对应扰动能量的增加,水平基流能量的衰减;（4）不同的风的垂直切变模型,对静力适应过程的影响不同;对于水平基流呈反气旋切变型和气旋切变型,扰动发展的波动垂直结构为,急流轴上方波动等相位线自下而上向西倾斜,急流轴下方波动等相位线自下而上向东倾斜,反之亦然.

     

Three-layer model for vertical velocity distribution in open channel flow with submerged rigid vegetation

Based on the detailed laboratory experiments and theoretical analysis, a new three-layer model is proposed to predict the vertical velocity distribution in an open channel flow with submerged vegetation. The time averaged velocity and turbulence behaviour of a steady uniform flow with fully submerged artificial rigid vegetation was measured using a 3D Micro ADV, and the vertical distribution of velocity and Reynolds shear stress at different vegetation height, vegetation density and measuring positions were obtained. The results show that the velocity profile consists of three hydrodynamic regimes (i.e. the upper non-vegetated layer, the outer and bottom layer within vegetation); accordingly different methods had been adopted to describe the vertical velocity distribution. For the upper non-vegetated layer, a modified mixing length theory combined with the concept of ‘the new vegetation boundary layer’ was adopted, and an analytical model was presented to predict the vertical velocity distribution in this region. For the bottom layer within vegetation, the depth average velocity was obtained by numerically solving the momentum equations. For the upper layer within vegetation, the analytical solution was presented by expressing the shear stress as a formula fitted to the experimental data. Finally, the analytical predictions of the vertical velocity over the whole flow depth were compared with the results obtained by other researchers, and the good agreement proved that the three-layer model can be used to predict the velocity distribution of the open channel flow with submerged rigid vegetation.     

A model for tectonic rotations about a vertical axis

The rotation of a rigid ellipsoidal inclusion within a highly viscous fluid, orientated so that two of the principal axes remain horizontal, is used as a model for the rotation of crustal inclusions in wide zones of continental deformation. This model is also applicable to other geological problems involving the rotation of inclusions in a matrix. The pattern of behaviour in such a model is shown to be complex. In general the rotation rate of the inclusion is a function of all components of the velocity field of the deforming medium and the horizontal aspect ratio of the inclusion. However, for a given velocity field, this aspect ratio must exceed a critical value before the inclusion can rotate continuously. Inclusions with lower aspect ratios will rotate, for a certain range of orientations, in an opposite direction to the sense of shear in the deforming zone. The possibility of the inclusion changing shape during rotation adds to the complexity of behaviour.     

Look-ahead vertical seismic profiling inversion approach for density and compressional wave velocity in Bayesian framework

To reduce drilling uncertainties, zero-offset vertical seismic profiles can be inverted to quantify acoustic properties ahead of the bit. In this work, we propose an approach to invert vertical seismic profile corridor stacks in Bayesian framework for look-ahead prediction. The implemented approach helps to successfully predict density and compressional wave velocity using prior knowledge from drilled interval. Hence, this information can be used to monitor reservoir depth as well as quantifying high-pressure zones, which enables taking the correct decision during drilling. The inversion algorithm uses Gauss–Newton as an optimization tool, which requires the calculation of the sensitivity matrix of trace samples with respect to model parameters. Gauss–Newton has quadratic rate of convergence, which can speed up the inversion process. Moreover, geo-statistical analysis has been used to efficiently utilize prior information supplied to the inversion process. The algorithm has been tested on synthetic and field cases. For the field case, a zero-offset vertical seismic profile data taken from an offshore well were used as input to the inversion algorithm. Well logs acquired after drilling the prediction section was used to validate the inversion results. The results from the synthetic case applications were encouraging to accurately predict compressional wave velocity and density from just a constant prior model. The field case application shows the strength of our proposed approach in inverting vertical seismic profile data to obtain density and compressional wave velocity ahead of a bit with reasonable accuracy. Unlike the commonly used vertical seismic profile inversion approach for acoustic impedance using simple error to represent the prior covariance matrix, this work shows the importance of inverting for both density and compressional wave velocity using geo-statistical knowledge of density and compressional wave velocity from the drilled section to quantify the prior covariance matrix required during Bayesian inversion.     

京津冀城市群地区夏季低层大气风速谱特征分析

利用京津冀城市群地区6个观测站风廓线雷达夏季一个月同步观测资料,对其进行了风功率谱和小波分析.越接近地面,测站之间风的周期变化特征差异越明显,离地面越远,差异不显著.各站大于1天周期的频谱特征差异小,而小于1天周期的频谱特征差异大.各站频谱在几百米高度有明显日变化.不同位置的测站其日变化周期信号随高度分布表现为不同程度的地形影响效应.部分测站1 km高度以下风功率谱在大于1天高频区近似满足-5/3幂分布规律.降水过程风频谱在低层普遍有小于1天的高频周期,这与降水过程高低空风速起伏和变化密切相关.各站平均风矢量日变化在5:00—6:00、20:00—21:00有明显风速变化和风向转换,1500 m以下风向变化差异显著,偏南风出现时间及影响高度与该地区的山谷风和海陆风相联系.各站之间风速相关系数随高度分布呈现出低层低、上层高的特点.最后还给出了风廓线雷达布网建议.     

Travel time computations using a compact eikonal equation for vertical transverse isotropic media

Eikonal solvers often have stability problems if the velocity model is mildly heterogeneous. We derive a stable and compact form of the eikonal equation for P‐wave propagation in vertical transverse isotropic media. The obtained formulation is more compact than other formulations and therefore computationally attractive. We implemented ray shooting for this new equation through a Hamiltonian formalism. Ray tracing based on this new equation is tested on both simple as well as more realistic mildly heterogeneous velocity models. We show through examples that the new equation gives travel times that coincide with the travel time picks from wave equation modelling for anisotropic wave propagation.     

Generalized Dix equation and analytic treatment of normal-moveout velocity for anisotropic media*

Despite the complexity of wave propagation in anisotropic media, reflection moveout on conventional common-midpoint (CMP) spreads is usually well described by the normal-moveout (NMO) velocity defined in the zero-offset limit. In their recent work, Grechka and Tsvankin showed that the azimuthal variation of NMO velocity around a fixed CMP location generally has an elliptical form (i.e. plotting the NMO velocity in each azimuthal direction produces an ellipse) and is determined by the spatial derivatives of the slowness vector evaluated at the CMP location. This formalism is used here to develop exact solutions for the NMO velocity in anisotropic media of arbitrary symmetry. For the model of a single homogeneous layer above a dipping reflector, we obtain an explicit NMO expression valid for all pure modes and any orientation of the CMP line with respect to the reflector strike. The contribution of anisotropy to NMO velocity is contained in the slowness components of the zero-offset ray (along with the derivatives of the vertical slowness with respect to the horizontal slownesses) — quantities that can be found in a straightforward way from the Christoffel equation. If the medium above a dipping reflector is horizontally stratified, the effective NMO velocity is determined through a Dix-type average of the matrices responsible for the ‘interval’ NMO ellipses in the individual layers. This generalized Dix equation provides an analytic basis for moveout inversion in vertically inhomogeneous, arbitrarily anisotropic media. For models with a throughgoing vertical symmetry plane (i.e. if the dip plane of the reflector coincides with a symmetry plane of the overburden), the semi-axes of the NMO ellipse are found by the more conventional rms averaging of the interval NMO velocities in the dip and strike directions. Modelling of normal moveout in general heterogeneous anisotropic media requires dynamic ray tracing of only one (zero-offset) ray. Remarkably, the expressions for geometrical spreading along the zero-offset ray contain all the components necessary to build the NMO ellipse. This method is orders of magnitude faster than multi-azimuth, multi-offset ray tracing and, therefore, can be used efficiently in traveltime inversion and in devising fast dip-moveout (DMO) processing algorithms for anisotropic media. This technique becomes especially efficient if the model consists of homogeneous layers or blocks separated by smooth interfaces. The high accuracy of our NMO expressions is illustrated by comparison with ray-traced reflection traveltimes in piecewise-homogeneous, azimuthally anisotropic models. We also apply the generalized Dix equation to field data collected over a fractured reservoir and show that P-wave moveout can be used to find the depth-dependent fracture orientation and to evaluate the magnitude of azimuthal anisotropy.     

Effect of source parameters on forward-directivity velocity pulse for vertical strike slip fault in half space

It has been found that the large velocity pulse is one of the most important characteristics of near-fault strong ground motions. Some statistical relationships between pulse period and the moment magnitude for near-fault strong ground motions have been established by Somerville （1998）; Alavi and Krawinkler （2000）; and Mavroeidis and Papageorgiou （2003）, where no variety of rupture velocity, fault depth, and fault distance, etc. were considered. Since near-fault ground motions are significantly influenced by the rupture process and source parameters, the effects of some source parameters on the amplitude and the period ofa forward-directivity velocity pulse in a half space are analyzed by the finite difference method combined with the kinematic source model in this paper. The study shows that the rupture velocity, fault depth, position of the initial rupture point and distribution of asperities are the most important parameters to the velocity pulse. Generally, the pulse period decreases and the pulse amplitude increases as the rupture velocity increases for shallow crustal earthquakes. In a definite region besides the fault trace, the pulse period increases as the fault depth increases. For a uniform strike slip fault, rupture initiating from one end of a fault and propagating to the other always generates a higher pulse amplitude and longer pulse period than in other cases.