A model of a homogeneous isotropic turbulent flow and its application for the simulation of cloud drop tracks

Abstract

A model of a homogeneous isotropic turbulent flow is presented. The model provides different realizations of the random velocity field component with given correlation latitudinal and lateral functions and a spatial structure which obeys the Kolmogorov theory of homogeneous and isotropic turbulence. For the generation of the turbulent flow the structural function of the flow in the form suggested by Batchelor (Monin and Yaglom, 1975) was used. This function describes the spectrum of turbulence both in the viscous and inertial ranges. The isotropy and homogeneity of the velocity field of the model are demonstrated.

The model is aimed at simulating the ‘‘fine'’ features of drop's (aerosol particles') motion, such as the deviations of drops’ velocity from the velocity of the flow, detailed structures of drops’ tracks, related to drops’ (particles') inertia. The model is intended also for the purpose of studying cloud drops’ and aerosol particles’ motion and their diffusional spreading utilizing the Monte Carlo methods.

Some examples of drop tracks for drops of different size are presented. Drops’ tracks are very sophisticated, so that the relative position of drops falling initially from the same point can vary drastically. In some cases drops’ tracks diverge very quickly, in other cases all drops move within a turbulent eddy along nearly the same closed tracks, but with different speed. The concentration of drop tracks along isolated paths is found in spite of the existence of a large number of velocity harmonics. It is shown that drops (aerosol particles) tend to leave some areas of the turbulent flow apparently due to their inertia. These effects can possibly contribute to inhomogeneity of drops’ concentration in clouds at different spatial scales.     

Spatial growth of gulf stream meanders

Abstract

An attractive explanation for the observed spatial growth of the Gulf Stream meanders is that the meanders are spatially growing unstable waves. The results of a calculation based on a simple two-layer model of baroclinically unstable flow presented here support this idea. The model is a familiar one with the energy for the growth of the meander perturbations coming from the potential energy available in the geostrophic tilt of the interface between the two layers due to their velocity shear. In order to distinguish between spatial and temporal growth, it IS necessary to assume that the meanders are generated in a localized region, or equivalently, that the meanders are upstream disturbances which are amplified as they enter a region of unstable flow. This assumption is implemented mathematically through the use of a Green's function which governs the propagation of the meanders. Analysis of the spatial and temporal characteristics of the Green's function leads to a criterion which must he satisfied if the meanders arc to grow spatially. This criterion is that the mean flow velocity must be sufficiently greater than the velocity shear, U_m > √2 U_s, in order to have spatial growth. This simply means that the growing meanders must be washed downstream faster than they spread upstream, or equivalently the spatial growth is due to downstream advection of growing disturbances. The actual Gulf Stream flow is in fair agreement with this criterion.     

Hydrological characteristics of vegetated river flows: a laboratory flume study

Abstract

Laboratory flume experiments were undertaken to measure the vertical profiles of mean flow velocity for three different flow discharges and four different stem densities of Hydrilla verticillata. The data were used to calculate three parameters, namely Manning's roughness coefficient, the Reynolds number and the Froude number. In addition, empirical equations were obtained for the vertical distribution of measured flow velocity within the transitional zone and above the plant canopy. The results show that: (a) the vertical distribution of measured flow velocity exhibits three zone profiles; (b) Manning's roughness coefficient decreases with increasing depth-averaged flow velocity; (c) the relationship between Manning's roughness coefficient and the depth-averaged flow velocity is within the smooth left inverse curve; (d) Manning's roughness coefficient significantly changes with increasing density of Hydrilla; (e) the Froude number is independent of the density of Hydrilla; and (f) both the Reynolds number and the Froude number increase with increasing depth-averaged flow velocity.

Citation Shi, J.Z., Li, Y.-H., Hughes, J.M.R., and Zhao, M., 2013. Hydrological characteristics of vegetated river flows: a laboratory flume study. Hydrological Sciences Journal, 58 (5), 1047–1058.

Editor Z.W. Kundzewicz     

基于GPS数据分析渭河盆地现今地壳形变特征

基于2001—2015年流动及连续GPS观测资料,借助多面函数拟合法建立渭河盆地水平速度场模型,并计算球面坐标下的应变特征参数。结合陕西地区地质构造背景,分析渭河盆地水平速度场及应变场分布特征。结果表明:(1)渭河盆地西部GPS速度场受青藏块体及鄂尔多斯块体共同作用明显,西部GPS速度场大于中东部,且GPS速度场有顺时针旋转的运动特征。(2)渭河盆地西部主应力场变化复杂,中部的西安地区主应变差异变化明显,与2009年11月5日高陵M_S4.4地震对应;渭河盆地西部出现最大剪应变及面应变高值区及差异变化高梯度带,在西安附近出现最大剪应变及面应变差异变化梯度带,高陵地震震中位于零值线附近。(3)2001—2010年的主应变、最大剪应变、面应变变化比2011—2015年显著,表明高陵地震发生后,应力场进行了释放调整,近期渭河盆地地震紧迫性相对较低。     

A double-porosity model for a fractured aquifer with non-Darcian flow in fractures

Abstract

Non-Darcian flow in a finite fractured confined aquifer is studied. A stream bounds the aquifer at one side and an impervious stratum at the other. The aquifer consists of fractures capable of transmitting water rapidly, and porous blocks which mainly store water. Unsteady flow in the aquifer due to a sudden rise in the stream level is analysed by the double-porosity conceptual model. Governing equations for the flow in fractures and blocks are developed using the continuity equation. The fluid velocity in fractures is often too high for the linear Darcian flow so that the governing equation for fracture flow is modified by Forcheimer's equation, which incorporates a nonlinear term. Governing equations are coupled by an interaction term that controls the quasi-steady-state fracture—block interflow. Governing equations are solved numerically by the Crank-Nicolson implicit scheme. The numerical results are compared to the analytical results for the same problem which assumes Darcian flow in both fractures and blocks. Numerical and analytical solutions give the same results when the Reynolds number is less than 0.1. The effect of nonlinearity on the flow appears when the Reynolds number is greater than 0.1. The higher the rate of flow from the stream to the aquifer, the higher the degree of nonlinearity. The effect of aquifer parameters on the flow is also investigated. The proposed model and its numerical solution provide a useful application of nonlinear flow models to fractured aquifers. It is possible to extend the model to different types of aquifer, as well as boundary conditions at the stream side. Time-dependent flow rates in the analysis of recession hydrographs could also be evaluated by this model.     

On the Structures Observed in Thin Rotating Layers of a Conductive Fluid and the Anomalies of the Geomagnetic Field

The results of the laboratory and numerical experiments in circular rotating trays with thin layers of a conductive fluid under the MHD generation of small-scale velocity fields are presented. The configurations of constant magnets for MHD generation were determined based on the numerical calculations with shallow water equations. Both the laboratory and numerical experiments with rotating trays demonstrate the emergence of nonaxisymmetric structures and large-scale near-circular vortices caused by the energy transfer from the system of the externally generated small-scale vortices to the large-scale velocity fields under the action of the Coriolis force. The near-circular vortex has areas with differential rotation when the angular velocity of rotation decreases with the radius. The single large-scale vortices and wide jet flows arise in the regimes of subrotation and superrotation relative to the external rotation depending on its angular velocity. The emergence of the flow structures with the azimuthal wave number m = 2 is demonstrated, and their probable relation to the anomalies of the geomagnetic field observed on the Earth’s surface is considered.     

江苏盐城盐纺井地球化学异常信息提取及机理分析

依据江苏省盐城市纺织厂井Ca²⁺和Cl^-月均值浓度,利用从属函数和自适应阈值法对该井进行了地球化学异常信息提取与分析;结合波速比和地磁谐波振幅比数据,利用膨胀扩容模式开展了映震机理讨论。结果表明,2008～2016年Ca²⁺浓度出现6次从属函数异常和5次自适应阈值异常,Cl^-浓度出现4次从属函数异常和5次自适应阈值异常,较好地对应了台站200km范围内M_L≥4.0的地震。此外,根据波速比、地磁谐波振幅比和该井地下水地球化学成因等分析结果,判断Ca²⁺、Cl^-浓度在震前的快速上升与深部流体上涌有关。     

The instability of barotropic circular vortices

Abstract

The linear, normal mode instability of barotropic circular vortices with zero circulation is examined in the f-plane quasigeostrophic equations. Equivalents of Rayleigh's and Fjortoft's criteria and the semicircle theorem for parallel shear flow are given, and the energy equation shows the instability to be barotropic. A new result is that the fastest growing perturbation is often an internal instability, having a finite vertical scale, but may also be an external instability, having no vertical structure. For parallel shear flow the fastest growing perturbation is always an external instability; this is Squire's theorem. Whether the fastest growing perturbation is internal or external depends upon the profile: for mean flow streamfunction profiles which monotonically decrease with radius, the instability is internal for less steep profiles with a broad velocity extremum and external for steep profiles with a narrow velocity extremum. Finite amplitude, numerical model calculations show that this linear instability analysis is not valid very far into the finite amplitude range, and that a barotropic vortex, whose fastest growing perturbation is internal, is vertically fragmented by the instability.     

A Reynolds-averaged turbulence modelling approach to the maintenance of the Venus superrotation

Abstract

A maintenance mechanism of an approximately linear velocity profile of the Venus zonal flow or superrotation is explored, with the aid of a Reynolds-averaged turbulence modelling approach. The basic framework is similar to that of Gierasch (Meridional circulation and maintenance of the Venus atmospheric rotation. J. Atmos. Sci. 1975, 32, 1038–1044) in the sense that the mechanism is examined under a given meridional circulation. The profile mimicking the observations of the flow is initially assumed, and its maintenance mechanism in the presence of turbulence effects is investigated from a viewpoint of the suppression of energy cascade. In the present work, the turbulent viscosity is regarded as an indicator of the intensity of the cascade. A novelty of this formalism is the use of the isotropic turbulent viscosity based on a non-local time scale linked to a large-scale flow structure. The mechanism is first discussed qualitatively. On the basis of these discussions, the two-dimensional numerical simulation of the proposed model is performed, with an initially assumed superrotation, and the fast zonal flow is shown to be maintained, compared with the turbulent viscosity lacking the non-local time scale. The relationship of the present model with the current general circulation model simulation is discussed in light of a crucial role of the vertical viscosity.     

Point dilution tests to calculate groundwater velocity: an example in a porous aquifer in northeast Italy

ABSTRACT

The point dilution test is a single-well technique for estimating horizontal flow velocity in the aquifer surrounding a well. The test is conducted by introducing a tracer into a well section and monitoring its decreasing concentration over time. When using a salt tracer, the method is easy and inexpensive. Traditionally, the horizontal Darcy velocity is calculated as a function of the rate of dilution and is based on the simple assumption that the decreasing tracer concentration is proportional both to the apparent velocity into the test section and to the Darcy velocity in the aquifer. In this article, an alternative approach to analyse the results of point dilution tests is proposed and verified using data acquired at a test site in the middle Venetian plain, northeast Italy. In this approach, the one-dimensional equilibrium advection–dispersion equation is inverted using the CXTFIT model to estimate the apparent velocity inside the test section. Analysis of the field data obtained by the two approaches shows good agreement between the methods and suggests that it is possible to use the equilibrium advection–dispersion equation to estimate apparent velocity over a wide range of velocities.

Editor D. Koutsoyiannis; Associate editor K. Heal     

Combined geothermal-geophysical models of the earth's crust and upper mantle for the European continent

An attempt is made to obtain a combined geophysical model along two regional profiles: Black Sea— White Sea and Russian Platform—French Central Massif. The process of the model construction had the following stages: 1. The relation between seismic velocity (V_p, km/s) and density (σ, g/cm³) in crustal rocks was determined from seismic profiles and observed gravity fields employing the trial and error method. 2. Relations between heat production HP (μW/m³), velocity and density were established from heat flow data and crustal models of old platforms where the mantle heat flow HF_M is supposed to be constant. The HF_M value was also determined to 11 ± 5 mW/m². 3. A petrological model of the old platform crust is proposed from the velocity-density models and the observed heat flow. It includes 10–12 km of acid rocks, 15–20 km of basic/metamorphic rocks and 7–10 km of basic ones. 4. Calculation of the crustal gravity effects; its substraction from the observed field gave the mantle gravity anomalies. Extensively negative anomalies have been found in the southern part of Eastern Europe (50–70 mgal) and in Western Europe (up to 200 mgal). They correlate with high heat flow and lower velocity in the uppermost mantle. 5. A polymorphic advection mechanism for deep tectonic processes was proposed as a thermal model of the upper mantle. Deep matter in active regions is assumed to be transported (advected) upwards under the crust and in its place the relatively cold material of the uppermost mantle descends. The resulting temperature distribution depends on the type of endogeneous regime, on the age and size of geostructure. Polymorphic transitions were also taken into account.     

Uncertainty analysis of flow velocity estimation by a simplified entropy model

The velocity field in a river flow cross‐sectional area can be determined by applying entropy as done in 1978 by Chiu, who developed a two‐dimensional model of flow velocity based on the knowledge of maximum velocity, u_max, and the dimensionless entropic parameter, characteristic of the river site. This is appealing in the context of discharge monitoring, particularly for high floods, considering that u_max occurs in the upper portion of flow area and can be easily sampled, unlike velocity in the lower portion of flow area. The simplified form of Chiu's entropy‐based velocity model, proposed in 2004 by Moramarco et al., has been found to be reasonably accurate for determining mean flow velocity along each vertical sampled in the flow area, but no uncertainty analysis has been reported for this simplified entropy‐based velocity model. This study, therefore, performed uncertainty analysis of the simplified model following a procedure proposed by Misirli et al. in 2003. The flow velocity measurements at the Rosciano River section along the Chiascio River, central Italy, carried out for a period spanning 20 years were used for this purpose. Results showed that the simplified entropy velocity model was able to provide satisfactory estimates of velocity profiles in the whole flow area and the 95% confidence bands for the computed estimated mean vertical velocity were quite representative of observed values. In addition, using these 95% confidence bands, it was possible to have an indication of the uncertainty in the determination of mean cross‐sectional flow velocity as well. Copyright © 2012 John Wiley & Sons, Ltd.     

Rayleigh wave phase velocity tomography and strong earthquake activity on the southeastern front of the Tibetan Plateau

To investigate the relationship between velocity structure and earthquake activity on the southeastern front of the Tibetan Plateau, we make use of continuous observations of seismic ambient noise data obtained at 55 broadband stations from the regional Yunnan Seismic Network. These data are used to compute Rayleigh wave Green's Functions by cross-correlating between two stations, extracting phase velocity dispersion curves, and finally inverting to image Rayleigh wave phase velocity with periods between 5 and 34 s by ambient noise tomography. The results show significant lateral variations in crustal and uppermost mantle structures in the studied region. Phase velocity anomalies at short periods(5–12 s) are closely related to regional tectonic features such as sediment thickness and the depth of the crystalline basement. The Sichuan-Yunnan rhombic block, enclosed by the Honghe, Xiaojiang and Jianchuan faults, emerges as a large range of low-velocity anomalies at periods of 16–26 s, that inverts to high-velocity anomalies at periods of 30–34 s. The phase velocity variation in the vicinity of the Sichuan-Yunnan rhombic block suggests that the low-velocity anomaly area in the middle-lower crust may correspond to lower crustal channelized flow of the Tibetan Plateau. The spatial distribution of strong earthquakes since 1970 reveals that the Yunnan region is inhomogeneous and shows prominent characteristics of block motion. However, earthquakes mostly occur in the upper crust, with the exception of the middle-Yunnan block where earthquakes occur at the interface zone between high and low velocity as well as in the low-velocity zones, with magnitudes being generally less than 7. There are few earthquakes of magnitude 5 at the depths of 15–30 km, where gather earthquakes of magnitude 7 or higher ones which mainly occur in the interface zone between high and low velocities with others extending to the high-velocity abnormal zone.     

On the inadequacies of Long's model for steady two-dimensional stratified flows

Nonlinear analysis of two-dimensional steady flows with density stratification in the presence of gravity is considered. Inadequacies of Long's model for steady stratified flow over topography are explored. These include occurrence of closed streamline regions and waves propagating upstream. The usual requirements in Long's model of constant dynamic pressure and constant vertical density gradient in the upstream condition are believed to be the cause of these inadequacies. In this article, we consider a relaxation of these requirements, and also provide a systematic framework to accomplish this. As illustrations of this generalized formulation, exact solutions are given for the following two special flow configurations: the stratified flow over a barrier in an infinite channel; the stratified flow due to a line sink in an infinite channel. These solutions exhibit again closed-streamline regions as well as waves propagating upstream. The persistence of these inadequacies in the generalized Long's model appears to indicate that they are not quite consequences of the assumptions of constant dynamic pressure and constant vertical density gradient in Long's model, contrary to previous belief.

On the other hand, solutions admitted by the generalized Long's model show that departures from Long's model become small as the flow becomes more and more supercritical. They provide a nonlinear mechanism for the generation of columnar disturbances upstream of the obstacle and lead in subcritical flows to qualitatively different streamline topological patterns involving saddle points, which may describe the lee-wave-breaking process in subcritical flows and could serve as seats of turbulence in real flows. The occurrences of upstream disturbances in the presence of lee-wave-breaking activity described by the present solution are in accord with the experiments of Long (Long, R.R., “Some aspects of the flow of stratified fluids, Part 3. Continuous density gradients”, Tellus 7, 341--357 (1955)) and Davis (Davis, R.E., “The two-dimensional flow of a stratified fluid over an obstacle”, J. Fluid Mech. 36, 127–143 ()).     

山东地区地壳P波三维速度结构及其与地震活动的关系

利用山东及周边区域地震台网1975—2014年1月期间记录到的1369个地震的13781个P波到时数据对山东地区地壳结构进行了层析成像研究.结果表明,山东地区地壳速度结构存在明显的不均匀性.沂沭断裂带介质速度结构复杂,呈现明显的分段特征,两侧块体速度存在差异,具有块体边界的构造特征.鲁西断块20km以下深度处存在大规模的低速异常区,这与该地区始新世发生的大规模滑脱拆离构造有关,可能产生于太平洋板块的西向俯冲导致地幔热物质沿沂沭断裂带向上并向西涌动.历史大震及ML4.0以上中强震大部分为走滑型地震,主要发生于高低速异常过渡带且有深大断裂穿过的地区.震群主要发生于低速体上部或周边,且震源深度优势分布在中上地壳,这与地下介质富含流体并导致应力集中有关.     

Deep tectonic setting of the 2008 Wenchuan <Emphasis Type="Italic">M</Emphasis><Subscript>s</Subscript>8.0 earthquake in southwestern China

Teleseismic P-wave receiver functions at 20 broadband seismic stations in the Longmenshan fault zone (LMFZ) and its vicinity were extracted, and the crustal thickness and the P- and S-wave velocity ratio were calculated by use of the H-k stacking algorithm. With the results as constraints, the S-wave velocity structures beneath each station were determined by the inversion of receiver functions. The crustal structure of the Rear-range zone is similar to that of the Songpan-Garze Block, whereas the velocity structure of the Fore-range zone resembles that of Sichuan Basin, implying that the Central Principal Fault of LMFZ is the boundary between the eastern Tibetan Plateau and the Yangtze Block. Lower velocity zone exists in lower crust of the Songpan-Garze Block and the central-southern segment of the Rear-range zone, which facilitates the detachment of the material in upper and middle crust. Joint analysis of the receiver functions and the Bouguer gravity anomalies supports the thesis on the detachment-thrust mode of the LMFZ. A double-detachment pattern is suggested to the tectonic setting in the Songpan-Garze Block. The upper detachment occurs at the depth of 10-15 km, and represents a high-temperature ductile shear zone. There is a lower detachment at the depth of about 30 km, below which the lower crust flow exists in the eastern Tibetan Plateau. Interpretation of the Bouguer gravity anomalies indicates that the Sichuan Basin is of higher density in upper and middle crust in comparison with that of the Songpan-Garze Block. The LMFZ with higher density is the result from the thrusting of the Songpan-Garze Block over the Sichuan Basin. In the lower crust, higher P velocity and higher density in the Sichuan Basin are related to more rigid material, while lower S velocity and lower density in the Songpan-Garze Block are related to the softened and weakened material. The higher density block beneath the Sichuan Basin obstructs the eastward flow of lower crustal material from the Tibetan Plateau, which is driven by the compression of northward movement of Indian Plate. The eastward movement of upper and middle crustal material is also obstructed by the rigid Yangtze Block, resulting in the stress concentrated and accumulated along the LMFZ. When the stress releases sharply, the Wenchuan M _s8.0 earthquake occurs. Supported by the National Natural Science Foundation of China (Grant Nos. 40334041, 40774037) and Joint Foundation of Earthquake Science (Grant No. 1040062)     

Comparing the stream re-aeration coefficient estimated from ANN and empirical models / Comparaison d'estimations par un RNA et par des modèles empiriques du coefficient de réaération en cours d'eau

Abstract

Dissolved oxygen (DO) is one of the most useful indices of river's health and the stream re-aeration coefficient is an important input to computations related to DO. Normally, this coefficient is expressed as a function of several variables, such as mean stream velocity, shear stress velocity, bed slope, flow depth, and Froude number. However, in free surface flows, some of these variables are interrelated, and it is possible to obtain simplified stream re-aeration equations. In recent years, different functional forms have been advanced to represent the re-aeration coefficient for different data sets. In the present study, the artificial neural network (ANN) technique has been applied to estimate the re-aeration coefficient (K ₂) using data sets measured at different reaches of the Kali River in India and values obtained from the literature. Observed stream/channel velocity, bed slope, flow depth, cross-sectional area and re-aeration coefficient data were used for the analysis. Different combinations of variables were tested to obtain the re-aeration coefficient using an ANN. The performance of the ANN was compared with other estimation methods. It was found that the re-aeration coefficient estimated by using an ANN was much closer to the observed values as compared with the other techniques.     

Accelerating shear velocity in gravel-bed channels

Abstract

The behaviour of the shear velocity along a gravel-bed channel is investigated experimentally in the presence of a negative pressure gradient (accelerating flow). Different methods of estimation of the shear velocity, derived from vertical profiles of the mean longitudinal point velocity, are examined and a new method is proposed. Results show that the proposed method of estimation is comparable to the St Venant and Clauser's methods. At a specific cross section, for constant bottom slope and relative roughness, shear velocity increases with discharge.     

Hydraulic properties affected by litter and stem cover under overland flow

Vegetation stems and litter cover have different effects on sediment transport capacity under the same experimental conditions, which in essence, may be due to differences in their hydraulic properties, but the availability of comparative studies is limited. This study aimed to compare the hydraulic properties affected by litter and stem cover, compare differences in the drag forces exerted by litter and stems on overland flow, and develop new Manning's n and flow velocity equations for litter cover. Two series of flume experiments were conducted with the same slope gradients (8.8%, 17.6%, 26.8%) and flow discharge rates (0.5, 1.0 × 10⁻³ m³ s⁻¹). Artificial Gramineae stems with a 0%–30% cover level and Pinus tabulaeformis litter with a 0%–70% cover level were used in series 1 and series 2, respectively. The flow velocity and depth were measured. The results showed that the Froude number and flow velocity affected by stem cover were much lower than those affected by litter cover, while the opposite trend was observed in the relative magnitude of the Reynolds number, flow depth and shear stress. The form resistance caused by stems was 22–57 times greater than that caused by litter for the same cover level, which suggests that stem cover contributes more than litter cover to increasing the flow resistance and reducing the flow's ability for sediment detachment and transport. Two new equations for calculating Manning's n and flow velocity under the influence of litter cover were developed, with R² and NSE values of 0.96. The results of this study contribute to revealing the mechanisms of the differences of the effects of stem and litter cover on soil erosion.