准地转大洋风生环流的格子Boltzmann数值模拟

建立了求解准地转相当正压涡度方程的格子Boltzmann (LB)模型. 该模型将准地转相当正压涡度方程作为一个平流-扩散-反应方程来加以处理,在整体二阶精度下,通过Chapman_Enskog多尺度分析法,可将格子Boltzmann方程还原到相当正压涡度方程. 在不同Reynolds数、不同边界条件以及不同风应力驱动下的数值解表明,该模型正确反映了风生环流的基本结构和不同边界的耗散特征,并得到风生环流的多平衡态解等非线性特征. 此外,不同Rossby变形半径下的实验证明,小Rossby变形半径更容易激发环流的非线性模态. 通过与同等类型有限差方案的比较,表明本文的LB模型具有稳定性好、精度高等优点.     

3D多孔介质渗透率的格子Boltzmann模拟

多孔介质结构的复杂性使其内部的流动非常复杂,通常不加简化就难以求解。格子Boltzmann方法以其无需简化就能处理复杂孔隙结构的优势,成为研究多孔介质流动的一种有效的数值计算方法。从现场采集的彩色铸体剖面图中提取孔隙信息重构了一种接近真实岩石的3D孔隙介质数字岩心。在此基础上,使用格子Boltzmann方法进一步得到能准确求解多孔介质中流动问题的Navier-Stokes方程,用以研究孔隙岩石的渗流特性。该方法对简单模型渗透率的模拟结果与相应的解析解或实验测量结果吻合良好,对某油田6个样品的模拟结果与实验结果的误差不大,说明格子Boltzrnann方法可以用来计算实际问题的渗透率。     

基于Biot-Squirt方程的波场模拟

Biot流动和喷射流动是含流体多孔隙介质中流体流动的两种重要力学机制,对地震波和声波的传播均产生重要影响. Dvorkin和Nur提出了同时包含Biot流动和喷射流动力学机制的统一的BISQ(Biot-Squirt)模型,基于这一模型,尽管有关弹性波在多孔隙介质中的衰减和频散问题已被广泛研究,然而,基于BISQ波传播方程的波场数值模拟至今仍未见报道. 本文从同时包含两种力学机制的孔隙弹性波方程出发,利用FCT有限差分法对含流体孔隙各向同性介质中的地震波和声波进行了数值模拟,并与基于Biot流动的Biot理论之模拟结果进行比较. 数值模拟结果表明:同时包含Biot流动和喷射流动影响的地震波和声波速度比仅包含Biot流动作用的地震波和声波速度慢,慢P波的衰减比根据Biot理论模拟的慢P波衰减更强.     

陆地下垫面与环境气流对锋面气旋发展过程影响的理想试验

地面摩擦和大尺度流场是影响锋面气旋结构演变的重要因子,本文使用WRF模式并采用湿物理方案,通过理想化试验,综合考虑陆面摩擦、气旋式扰动相对于急流位置和大尺度流场对锋面气旋结构变化的影响.结果表明：当仅考虑单一因子时,气旋式扰动位于急流南侧和辐合流流场有利于气旋形成Shapiro-Keyser（S-K）模型结构.当同时考虑地面摩擦和大尺度辐合时,气旋式扰动位于急流北侧的气旋发展整体向经典的挪威气旋模型转变;扰动位于急流南侧的的气旋发展则整体呈现S-K模型结构,此时辐合流场有利于S-K模型结构出现.当同时考虑地面摩擦和大尺度辐散时,扰动处于急流北侧的气旋呈现挪威气旋模型结构;由于气旋式扰动穿越急流和辐散流场同时有利于暖锋后弯发展以及冷暖锋距离加大和锋消,扰动处于急流南侧的气旋呈现典型S-K气旋模型结构.这个结果解释了在东亚大陆地区辐散场形势下出现的S-K模型结构气旋个例.     

旋转变径管内螺旋流相干结构的大涡模拟研究

旋转管式分离设备的主分离段一般为变径管结构,针对其内部螺旋流的研究主要集中在平均统计量的分布规律上,缺乏从流动结构角度的描述。本文采用大涡模拟方法对不同旋转条件下变径管内螺旋流开展数值模拟研究,分别以Q准则与基于SVD方法的POD分解法,对数值计算的速度场进行了分析。Q准则等值面显示,螺旋涡从大锥段开始发生破碎,旋转效应能够减弱外涡流区的漩涡强度;POD分解重构后脉动速度场显示,脉动速度场的1阶模态为主模态,包含了湍流的大部分能量,5阶模态之后的流动为由小尺度涡构成的复杂湍动结构。旋转效应抑制了径向涡,促进了轴向涡。从流场结构的角度而言,旋转效应对分离起到了积极的作用。     

求解弹性波动方程的频率域近似解析离散化波场模拟方法

为提高频率域弹性波动方程数值求解的计算效率,本文引入近似解析离散化(NAD)方法将其进行数值离散并得到大型线性代数方程组.在详细分析了相应系数矩阵的稀疏分块结构与数学性质之后,本文提出采用不精确旋转分块三角预处理子加速Krylov子空间迭代方法来快速求解该线性方程组,并利用数值试验证实这种方法在弹性波场模拟方面的数值效率.通过与另外两种经典数值方法(常规有限差分方法和交错网格有限差分方法)对多种介质模型进行波场模拟、数值频散分析以及与解析解的波形对比,NAD方法显示了其在压制数值频散和提高计算效率方面的优势以及对复杂介质模型弹性波场数值模拟的有效性.     

二维地震波场的组合型紧致有限差分数值模拟

地震波场数值模拟在地球物理勘探和地震学中具有重要的支撑作用.本文将组合型紧致差分格式用于声波和弹性波方程的数值模拟中.根据泰勒级数展开和声波方程,建立了位移场时间四阶离散格式,并将组合型紧致差分格式用于位移场空间导数的求取,然后对该差分格式进行了精度分析、误差分析、频散分析和稳定性分析.理论研究结果表明：①该差分格式为时间四阶、空间六阶精度,与常规七点六阶中心差分和五点六阶紧致差分相比,具有更小的截断误差和更高的模拟精度;②每个波长仅需要5.6个采样点,且满足稳定性条件的库郎数为0.792,可以使用粗网格和较大时间步长进行计算.所以该方法具有占用内存少、计算效率高和低数值频散等优势.最后,本文进行了二维各向同性完全弹性介质的声波和弹性波方程的数值模拟,实验结果表明本文提出的方法具有更高的计算精度,能够大幅度的节约计算量和内存需求,对于三维大尺度模型问题具有更好的适应性.     

Biot流动和喷射流动耦合作用下波传播的FCT紧致差分模拟

本文从含流体多孔隙介质中同时包含Biot流动和喷射流动两种力学机制的BISQ(Biot-Squirt)方程出发,利用FCT(Flux-Corrected Transport)紧致差分方法数值模拟了在Biot流和喷射流共同作用下的波在含流体多孔隙各向同性介质中的传播.通过与仅受Biot流动作用下的波场结果对比,我们研究了...     

用格子玻尔兹曼方法模拟非均匀介质中的电场响应

介绍了用格子玻尔兹曼方法模拟非均匀介质中的电场响应的数值模拟方法. 格子玻尔兹曼方法是从微观领域出发进行数值计算的一种全新的正演模拟方法;从玻尔兹曼碰撞模型出发,利用泰勒展开和Chapman Enskog展开,在基本力学守恒条件和约束条件的限制下,导出了电场响应的扩散方程,得到了局部平衡分布函数的表达式,给出了若干正演模拟的结果;其结果表明,利用这种方法进行非均匀介质中的电场响应正演模拟具有灵活、方便和简单等优点.     

基于横向各向同性BISQ方程的弹性波传播数值模拟

Biot流动和喷射流动是含流体多孔隙介质中流体流动的两种重要力学机制. 近年来，利用同时处理这两种力学机制的BISQ(Biot-Squirt)模型，弹性波衰减和频散的问题已被广泛研究；然而基于BISQ方程的波场数值模拟尚未见到公开的报道．本文从BISQ方程出发，利用交错网格方法对横向各向同性孔隙介质中不同频率和相界情况，以及双层介质中的弹性波传播进行数值模拟，研究了在同时考虑两种流动机制作用情况下地震波和声波的传播特性及传播过程中出现的各种波动现象．      

Energetic scaling of the geodynamo

The typical scales, velocities, and magnetic fields in the liquid core of the Earth are determined by using the analysis results of the magnitude of energy that is available for the geodynamo, physical regularities, and observational data. In this work, it is justified that the geomagnetic field is mainly generated in a regime where the magnetic Lorentz force is equilibrated by the Archimedean buoyancy force and by the Coriolis rotational force and the force of inertia is considerably less than these forces. The characteristic periods obtained in the course of this justification permit one to clarify not only the physical nature of secular geomagnetic variations but also that of jerks. In another regime, which is less probable for the present-day Earth, the main balance of forces is determined by inertia and buoyancy; the magnetic field has no significant effect on the typical rate and scale of convection. This regime seems to be probable in the liquid core of the Earth during inversions or digressions, as well as in depths of Mercury, Mars, Uranus, and Neptune.     

A reduced model for nonlinear dispersive waves in a rotating environment

Abstract

The simplest model for geophysical flows is one layer of a constant density fluid with a free surface, where the fluid motions occur on a scale in which the Coriolis force is significant. In the linear shallow water limit, there are non-dispersive Kelvin waves, localized near a boundary or near the equator, and a large family of dispersive waves. We study weakly nonlinear and finite depth corrections to these waves, and derive a reduced system of equations governing the flow. For this system we find approximate solitary Kelvin waves, both for waves traveling along a boundary and along the equator. These waves induce jets perpendicular to their direction of propagation, which may have a role in mixing. We also derive an equivalent reduced system for the evolution of perturbations to a mean geostrophic flow.     

Divergent-rotational Nonlinear Energy Conversions in Wavenumber-frequency Domain During Summer Monsoon

--This work deals with computational modelling designed to understand the dynamical mechanism of low frequency monsoonal transients that results from nonlinear divergent-rotational (&gif1;) kinetic energy (KE) conversions due to the effects of Coriolis force, vorticity and divergence during the summer monsoon 1988 over the latitudinal belt 20°S-30°N at 850 hPa and 200 hPa. The results show two distinct spectral peaks spanning 30-45 days and 18-25 days in the energy conversions from the transient divergent motions to rotational motions. Due to the latitudinal variation of the earth's rotational effects, the conversion from the transient divergent to rotational motions, associated mainly with wavenumbers 1 and 2, tend to be more pronounced to the north of 15°N on the 30-45-day and 18-25-day time scales in the upper and lower tropospheres, respectively. The contribution of the stationary waves to maintenance of the low frequency rotational flow due to the effect of divergence through barotropic instability is significant at the upper troposphere. Divergent to rotational KE conversion by wave-wave interaction due to divergence is identified as an important mechanism for maintenance of low frequency oscillations in the lower troposphere. The upper tropospheric planetary scale divergent motions associated with 30-45-day oscillation gain substantial energy through nonlinear &gif1; interaction due to vorticity.     

Longitudinal variation in lateral trapping of fine sediment in tidal estuaries: observations and a 3D exploratory model

This study investigates the longitudinal variation of lateral entrapment of suspended sediment, as is observed in some tidal estuaries. In particular, field data from the Yangtze Estuary are analysed, which reveal that in one cross-section, two maxima of suspended sediment concentration (SSC) occur close to the south and north sides, while in a cross-section 2 km down-estuary, only one SSC maximum on the south side is present. This pattern is found during both spring tide and neap tide, which are characterised by different intensities of turbulence. To understand longitudinal variation in lateral trapping of sediment, results of a new three-dimensional exploratory model are analysed. The hydrodynamic part contains residual flow due to fresh water input, density gradients and Coriolis force and due to channel curvature-induced leakage. Moreover, the model includes a spatially varying eddy viscosity that accounts for variation of intensity of turbulence over the spring-neap cycle. By imposing morphodynamic equilibrium, the two-dimensional distribution of sediment in the domain is obtained analytically by a novel procedure. Results reveal that the occurrence of the SSC maxima near the south side of both cross-sections is due to sediment entrapment by lateral density gradients, while the second SSC maximum near the north side of the first cross-section is by sediment transport due to curvature-induced leakage. Coriolis deflection of longitudinal flow also contributes the trapping of sediment near the north side. This mechanism is important in the upper estuary, where the flow due to lateral density gradients is weak.     

Meridional circulation from differential rotation in an adiabatically stratified solar/stellar convection zone

Meridional circulation in stellar convection zones is not generally well observed, but may be critical for the workings of MHD dynamos operating in these domains. Coriolis forces from differential rotation play a large role in determining what the meridional circulation is. Here, we consider the question of whether a stellar differential rotation that is constant on cylinders concentric with the rotation axis can drive a meridional circulation. Conventional wisdom says that it can not. Using two related forms of the governing equations that respectively estimate the longitudinal components of the curl of the meridional mass flux and the vorticity, we show that such differential rotation will drive a meridional flow. This is because to satisfy anelastic mass conservation, non-spherically symmetric pressure contours must be present for all differential rotations, not just ones that depart from constancy on cylinders concentric with the rotation axis. Therefore, the fluid is always baroclinic if differential rotation is present. This is because, in anelastic systems, the perturbation pressure must satisfy a Poisson type equation, as well as an equation of state and a thermodynamic equation. We support our qualitative reasoning with numerical examples, and show that meridional circulation is sensitive to the magnitude and form of departures from rotation constant on cylinders. The effect should be present in 3D global anelastic convection simulations, particularly those for which the differential rotation driven by global convection is nearly cylindrical in profile. For solar-like differential rotation, Coriolis forces generally drive a two-celled circulation in each hemisphere, with a second, reversed flow at high latitudes. For solar like turbulent viscosities, the meridional circulation produced by Coriolis forces is much larger than observed on the Sun. Therefore, there must be at least one additional force, probably a buoyancy force, which opposes the meridional flow to bring its amplitude down to observed values.     

Development of a simplistic vegetative filter strip model for sediment and nutrient retention at the field scale

Vegetative filter strips (VFSs) are a commonly used conservation measure to remove pollutants from agricultural runoff. The effectiveness of VFSs has been widely studied at the plot scale, yet researchers generally agree that field scale implementations are far less effective. The purpose of this research was to develop a field scale VFS submodel for the Soil and Water Assessment Tool (SWAT). A model for the retention of sediments and nutrients in VFSs was developed from experimental observations derived from 22 publications. A runoff retention model was developed from Vegetative Filter Strip MODel (VFSMOD) simulations. This model was adapted to operate at the field scale by considering the effects of flow concentration generally absent from plot scale experiments. Flow concentration through 10 hypothetical VFSs was evaluated using high resolution (2 m) topographical data and multipath flow accumulation. Significant flow concentration was predicted at all sites, on average 10% of the VFS received half of the field runoff. As implemented in SWAT, the VFS model contains two sections, a large section receiving relatively modest flow densities and a smaller section treating more concentrated flow. This field scale model was incorporated into SWAT and verified for proper function. This model enhances the ability of SWAT to evaluate the effectiveness of VFSs at the watershed scale. Published in 2009 by John Wiley & Sons, Ltd.     

Kinematic turbulent dynamo in a shear flow

Abstract

We consider the turbulent dynamo action in a differentially rotating flow by making use of a kinematic approach when the effect of a generated magnetic field on turbulent motions is neglected. The mean electromotive force is calculated in a quasilinear approximation. Differential rotation can stretch turbulent magnetic field lines and break the symmetry of turbulence in such a way that turbulent motions become suitable for the generation of a large scale magnetic field. The presence of shear changes the type of an equation governing the mean magnetic field. Due to shear stresses the mean magnetic field can be generated by a turbulent dynamo action even in a uniform turbulence. The growth rate depends on the length scale of the mean field being faster for the field with a smaller length scale.     

Multi-scale waves in sound-proof global simulations with EULAG

EULAG is a computational model for simulating flows across a wide range of scales and physical scenarios. A standard option employs an anelastic approximation to capture nonhydrostatic effects and simultaneously filter sound waves from the solution. In this study, we examine a localized gravity wave packet generated by instabilities in Held-Suarez climates. Although still simplified versus the Earth’s atmosphere, a rich set of planetary wave instabilities and ensuing radiated gravity waves can arise. Wave packets are observed that have lifetimes ≤ 2 days, are negligibly impacted by Coriolis force, and do not show the rotational effects of differential jet advection typical of inertia-gravity waves. Linear modal analysis shows that wavelength, period, and phase speed fit the dispersion equation to within a mean difference of ∼ 4%, suggesting an excellent fit. However, the group velocities match poorly even though a propagation of uncertainty analysis indicates that they should be predicted as well as the phase velocities. Theoretical arguments suggest the discrepancy is due to nonlinearity — a strong southerly flow leads to a critical surface forming to the southwest of the wave packet that prevents the expected propagation.     

Modeling depth-averaged velocity and bed shear stress in compound channels with emergent and submerged vegetation

This paper presents an approach to modeling the depth-averaged velocity and bed shear stress in compound channels with emergent and submerged vegetation. The depth-averaged equation of vegetated compound channel flow is given by considering the drag force and the blockage effect of vegetation, based on the Shiono and Knight method (1991) [40]. The analytical solution to the transverse variation of depth-averaged velocity is presented, including the effects of bed friction, lateral momentum transfer, secondary flows and drag force due to vegetation. The model is then applied to compound channels with completely vegetated floodplains and with one-line vegetation along the floodplain edge. The modeled results agree well with the available experimental data, indicating that the proposed model is capable of accurately predicting the lateral distributions of depth-averaged velocity and bed shear stress in vegetated compound channels with secondary flows. The secondary flow parameter and dimensionless eddy viscosity are also discussed and analyzed. The study shows that the sign of the secondary flow parameter is determined by the rotational direction of secondary current cells and its value is dependent on the flow depth. In the application of the model, ignoring the secondary flow leads to a large computational error, especially in the non-vegetated main channel.     

Strong intrusions of the Northern Mediterranean Current on the eastern Gulf of Lion: insights from in-situ observations and high resolution numerical modelling

The Northern Mediterranean Current is the return branch of the cyclonic circulation of the northwestern Mediterranean Sea. Because of geostrophic constraints, this warm and oligotrophic current is forced to flow westward along the continental slope of the Gulf of Lion. But, occasionally, it penetrates on the shelf and strongly impacts the local biogeochemistry and in turn the primary production. By combining in situ observations and high-resolution modelling, it is shown that intrusions on the eastern part of the gulf are mainly forced by easterly or northwesterly wind events, through physical mechanisms that are very different in nature. Easterlies induce a piling of water along the Gulf of Lion coast that drives, through geostrophy, an alongshore shelf-intruding current. This intrusive current occurs independently of the stratification and is concomitant with the wind forcing. On the other hand, intrusions due to northwesterlies only occur during stratified conditions and are related to the development of upwellings along the Gulf of Lion coasts. When the upwelling develops, a northwestward alongshore pressure force balances the Coriolis force associated with the onshore flow at depth. When the winds drop, the upwelling relaxes and the onshore flow weakens. Consequently, the Coriolis force no longer counterbalances the pressure force that ultimately dominates the momentum balance, causing the displacement of the Northern Current on the Gulf of Lion shelf approximately 1 day after the wind relaxation. This time lag between the northwesterlies decrease and the intrusions permits to anticipate possible changes in the biogeochemistry of the Gulf of Lion.