Compressibility,core dynamics and the subseismic wave equation

It is shown that in the dynamics of a deep fluid of planetary scale such as the Earth's core, compressibility, stratification and self-gravitation are all important as well as rotation. The existing proof of Cowling's theorem prohibiting non-stationary axisymmetric dynamos, and the application of the Proudman-Taylor theorem to core flows, both based on the assumption of solenoidal flow, need to be reconsidered. For sufficiently small (subacoustic) frequencies or reciprocal time scales, an approximation which neglects the effect of flow pressure on the density is valid. We call this the “subseismic approximation” and show that it leads to a new second-order partial differential equation in a single scalar variable describing the low frequency dynamical behaviour. The new “subseismic wave equation” allows a direct connection to be made between the various possible physical regimes of core structure and its dynamics.     

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.     

How does the bed surface impact low-magnitude bedload transport rates over gravel-bed rivers?

Bedload transport is a complex phenomenon that is not well understood, especially for poorly sorted sediment and low transport rates, which is what is typically found in alpine gravel-bed rivers. In this paper, the interaction between bedload rate, bed stability and flow is investigated using flume experiments. Significant differences in bedload rates were observed for experiments conducted on beds formed with the same gravel material but presenting diverse arrangements and bedforms. Tests were performed under regimes of low transport rate, which are mainly controlled by gravel-bed roughness. Different scales of roughness were identified using the statistical characteristics of detailed bed elevation measurements: grain, structure and large bedform scales. The role played by these different roughness scales in bedload dynamics was examined. For quasi-flat beds, bed stability was quantified using a combination of bed surface criteria describing grain and structure scales. It was found that bed stability affects the bedload rate directly and not only through its influence on the flow or on the incipient motion. For beds with large bedforms, the analysis of bedload dynamics also showed the importance of accounting for effective bed shear stress distributions. An empirical bedload model for low transport regimes was suggested. Compared with previous formulae developed for alpine rivers, this model accounts for bed stability and distribution of effective bed shear stress. It significantly improves the understanding of gravel dynamics over complex beds such as arranged beds or those with large bedforms. However, further tests are needed to use the model outside the range of conditions of this study. © 2019 John Wiley & Sons, Ltd.     

Modal base forces in structures having a straight-line mode of vibration

The modal base forces in structures having a straight-line mode of vibration are investigated. Making use of the orthogonality relationship between the different modes, a relation between the modal base shears and base moments is found in all but the straight-line mode. This relation states that the contribution of the inertia forces to the modal overturning moments referred to the centre of rotation of the straight-line mode is identically null. The contributions of the vertical forces and lateral constraints must, however, be accounted for. For the special case of the straight-line mode being proportional to the height of each storey, the centre of rotation coincides with the base of the structure. For the case of the straight-line mode being a uniform displacement, the centre of rotation is at infinity and the contribution of the inertia forces to the modal base shears identically disappears in all but the straight-line mode.     

Combining the management of water level regimes and plant structures for waterbird habitat provision in wetlands

The survival of waterbirds depends heavily on habitat, particularly aquatic plants. For each kind of aquatic plant, there are specific water level regime requirements to meet its germination and growth. Previous studies usually focused on the use of water level management to achieve protection and restoration of aquatic plants. However, the water level regimes in many wetlands have been greatly changed and their ecological objectives usually cannot be achieved by water level management alone. Accordingly, this study combined water level management and artificial planting for waterbird habitat provision in wetlands. The Hongze Lake National Wetland Nature Reserve was taken as the research area. In this study, we considered the needs of waterbirds for nesting and foraging, and determined the aquatic plant species to be planted. According to the seasonal water level requirements of these plants, we simulated the plantable areas of different aquatic plants under different water level regimes. We then further optimized the water level regimes according to the needs of waterbirds, and determined the optimal water level management scheme. In addition, we formulated planting principles, explored the planting structure under each water level regime, so that the plant structure can better serve the waterbirds. The results showed that the current water level regime of Hongze Lake is not consistent with the growth rhythm of aquatic plants. Because of the human regulation, the water level of the wetland is high in winter and low in summer, which is contrary to the requirements of aquatic plant growth. A combination of water level regimes and plant structure management, however, could effectively expand the area for waterbird habitat. The results of this study will help wetland managers to make informed decisions about how to restore the waterbird habitat in other similar regulated wetlands.     

A comparison of the asymptotic and no-z approximations for galactic dynamos

Abstract

The asymptotic and the no-z approximation methods of solving the axisymmetric mean field αΩ dynamo equation in a galactic disc are compared. The behaviour of the solutions is explored in both the linear and nonlinear regimes for a variety of dynamo parameters and two different rotation curves. The solutions obtained from the two different approaches are found to be in good agreement.     

On the theory of the geomagnetic dynamo based on mean field electrodynamics

A survey is given on the present state of the geomagnetic dynamo theory which is based on the electrodynamics of mean fields in electrically conducting turbulent media. Models of both the ²-type and the ω-type are taken into consideration, i.e. models where the -effect alone, or together with a differential rotation, gives rise to the regeneration of magnetic fields. Results of special investigations are given and discussed. Models of the ²-type apply to the Earth provided that it shows no noticeable differential rotation. It is pointed out that such models can explain not only the generation of a magnetic field with an axisymmetric dipole-like structure, but also the occurrence of non-axisymmetric components and their westward drift. If, however, a noticeable differential rotation exists, models of the ω-type have to be envisaged. Such models also allow an understanding of the existence of a magnetic field with an axisymmetric dipole-like structure, but they do not provide for a straightforward interpretation of the occurrence and behaviour of the non-axisymmetric components.     

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.     

On the dynamical structure of the midshelf water column off northwest Africa

K undu (1977, Bottom turbulence, pp. 187–207) showed that the upwelling system off northwest Africa is dominated by turbulent friction and suggested that over such broad and shallow continental shelves, the surface and bottom frictional boundary layers overlap in the water column. Different estimates for the thickness of the boundary layers have been proposed more recently, which take into account, amongst other things, the effects of stratification. The application of these various estimates and the direct computation of the transports within the resulting layers provide a qualitatively consistent picture of the time-dependent structure of the water column on the northwest African continental shelf, with the observed cross-shelf transports in reasonable agreement with the expected Ekman transports. The only exceptions are two instances when the passage of upwelling fronts by the mooring appear to introduce an appreciable difference between the observed and the expected transports. Our results confirm those of K undu (1977), but only for times when the wind is strongly upwelling favourable. For periods of weak winds, our calculations suggest that a non-turbulent interior region develops. Thus, the structure of the water column is dynamically non-stationary, fluctuating between non-turbulent and frictionally dominated regimes, as a function of the intensity of the wind. This implies that the study of currents through a stationary time-series approach at individual depths may not be applicable in these regions.     

西北太平洋俯冲带日本本州至中国东北段应力场反演

本研究基于Global CMT提供的1196个1976年11月-2017年1月M_W>4.6地震矩心矩张量解,对西北太平洋俯冲带日本本州至中国东北段的应力场进行反演计算,得到了从浅表到深部俯冲带应力状态的完整分布.结果显示：俯冲带浅表陆壳一侧应力场呈现水平挤压、垂向拉伸状态,洋壳一侧的应力状态则相反,即近水平拉张、近垂向压缩.沿着俯冲板片向下,应力主轴逐渐向俯冲板片轮廓靠拢,其中位于双地震层（120 km深度附近）之上的部分,主张应力轴沿俯冲板片轮廓展布而又比其更为陡倾;双地震层内的应力模式同典型Ⅰ型双层地震带内的应力模式一致,即上层沿俯冲板片轮廓压缩、下层沿俯冲板片轮廓拉伸;双地震层之下,应力模式逐步转变为主压应力轴平行于俯冲板片轮廓.通观所研究的整个俯冲系统,水平面内主压和主张应力轴基本保持了与西北太平洋板片俯冲方向上的一致性,同经典俯冲板片的应力导管模型所预言的俯冲带应力模式相符;而主张应力轴在俯冲板片表面之下的中源地震深度范围内转向海沟走向,或许同研究区域横跨日本海沟与千岛海沟结合带,改变的浅部海沟形态致使完整俯冲板片下部产生横向变形有关.

     

Rapid formation of taylor columns: Obstacles against sidewalls

Abstract

The problem of topographic forcing by an obstacle against the boundary of a rotating flow is considered in various parameter regimes. The timescale for the motion is the topographic vortex-stretching time, which is inversely proportional to the background rotation rate and the fractional height of the obstacle. For slow flows this time is short compared with the advection time and the governing equation of conservation of potential vorticity is linear. The final state satisfies the non-linear equation for the advection of potential vorticity, however, and so time dependence has given a specific solution to a non-linear problem. The presence of the sidewall causes a stagnant Taylor column to be set up far more rapidly than cases with no sidewall. It is shown that viscosity and mixing arrests the inviscid evolution at some stage, thus some fluid still crosses the obstacle in the steady state. These solutions suggest that experimental results on separation obtained by Griffiths and Linden (1983) can tentatively be ascribed to entrainment and expulsion of fluid through vertical shear layers at the edge of the topography.     

Generation of 3D Spatially Variable Anisotropy for Groundwater Flow Simulations

Sedimentary units generally present anisotropy in their hydraulic properties, with higher hydraulic conductivity along bedding planes, rather than perpendicular to them. This common property leads to a modeling challenge if the sedimentary structure is folded. In this paper, we show that the gradient of the geological potential used by implicit geological modeling techniques can be used to compute full hydraulic conductivity tensors varying in space according to the geological orientation. For that purpose, the gradient of the potential, a vector normal to the bedding, is used to construct a rotation matrix that allows the estimation of the 3D hydraulic conductivity tensor in a single matrix operation. A synthetic 2D cross section example is used to illustrate the method and show that flow simulations performed in such a folded environment are highly influenced by this rotating anisotropy. When using the proposed method, the streamlines follow very closely the folded formation. This is not the case with an isotropic model.     

Structure of numerically simulated katabatic and anabatic flows along steep slopes

Direct numerical simulation (DNS) is applied to investigate properties of katabatic and anabatic flows along thermally perturbed (in terms of surface buoyancy flux) sloping surfaces in the absence of rotation. Numerical experiments are conducted for homogeneous surface forcings over infinite planar slopes. The simulated flows are the turbulent analogs of the Prandtl (1942) one-dimensional laminar slope flow. The simulated flows achieve quasi-steady periodic regimes at large times, with turbulent fluctuations being modified by persistent low-frequency oscillatory motions with frequency equal to the product of the ambient buoyancy frequency and the sine of the slope angle. These oscillatory wave-type motions result from interactions between turbulence and ambient stable stratification despite the temporal constancy of the surface buoyant forcing. The structure of the mean-flow fields and turbulence statistics in simulated slope flows is analyzed. An integral dynamic similarity constraint for steady slope/wall flows forced by surface buoyancy flux is derived and quantitatively verified against the DNS data.     

Sublimation-driven evolution of the local radius and the moment of inertia of short-period comets

This article is a continuation of the previous one considering the evolution of a long-period comet. The changes of the local radius and the moment of inertia as well as the orientation of the rotation axis are calculated. With reference to the previous model, the time-dependent orbital parameters are introduced. The procedure of sublimation-driven evolution is implemented to the comets 67P/Churyumov-Gerasimenko, 9P/Tempel 1, and 81P/Wild. The inclination of the rotation axis of Comet Ch-G is calculated. The position of the rotation axis is a result of the best fit of the water production rate curve received from modelling to the observational water production rate curve. The method is verified through application to Comets 9P/Tempel 1 and 81P/Wild with well-known positions of the rotation axes. The best fit is for inclination of the rotation axis which is close to the position of the rotation axis with minimum energy (maximum of the moment of inertia). For the best fitted position of the rotation axis I = 90° and Φ = 60°, the largest decrease of radius was about 5.6 m in the northern polar region. The smallest decrease of radius, of about 0.3 m, was noticed on cometographic latitudes between 39° and 46°.     

我国主要地形上空理想定常流的流域分界分析

本文根据旋转层结流体过山的基本理论,从总体上对影响我国天气、气候形成和发展的主要地形进行了动力学分析,定性地给出了中纬度典型的东西、南北向气流过我国主要地形的整体特征：以绕流还是爬流为主以及地形流动的准地转动力学性质.结果表明我国地形大致可以分成三类：第一类是以爬流为主,满足准地转平衡动力学;第二类是以爬流为主,不满足准地转平衡动力学;第三类以绕流为主,不满足准地转动力学平衡.具体地形流动的整体特征取决于地形特征尺度、过山气流方向、地形高度以及地形的几何形状等.数值模拟的验证结果表明定性分析是可信的.     

Equivalent time-average and effective medium for periodic layers

The propagation of acoustic waves through a periodic layered medium is analyzed by an eigenvalue decomposition of the propagator matrix. This reveals how the velocity and attenuation of the layered medium vary as function of the periodic structure, material parameters and frequency. There are two important parameters which control the wave propagation in the periodic medium: the reflection coefficient and the ratio between one‐way traveltimes of the two parts of the cyclic layered medium. For low frequencies (large values of wavelength to layer thickness), the layered structure behaves as an effective medium, then there is a transition zone, and for higher frequencies (small values of wavelength to layer thickness) the medium is described by the time‐average velocity. In this paper we mostly concentrate on the transition zone between an effective medium and time‐average medium regimes. The width of the transition zone increases with larger values of the reflection coefficient. The transition zone corresponds to a blocking regime for which the transmission response of the layered structure is close to zero. For even higher frequencies, the time‐average medium is replaced by a new transition zone, and then again a time‐average medium. This pattern is periodically repeated with higher frequencies. For small values of the reflection coefficient, the transition between effective medium and time‐average medium occurs around a value of wavelength to layer thickness equal to 4.     

Some new possibilities for diagnosing the magnetosphere based on whistler characteristics

Different types of natural electromagnetic emissions are generated in the Earth’s electronic radiation belts. The conditions for generation of these emissions depend on the plasma parameters, geometry of the system, wave transfer processes, and regularities of particle accumulation and precipitation from the magnetic trap. Effective interaction between waves and particles can often be described by the plasma magnetospheric maser theory. A plasma magnetospheric maser actually operates in several main regimes. These regimes are responsible for the generation of VLF emissions with different frequency spectrum dynamics. The regimes replace each other as a result of variations in the local and global characteristics of the magnetosphere. For example, the cyclotron generation dynamics largely depends on the the source power of energetic particles. Several new methods for diagnosing the near-Earth plasma can be implemented if the plasma magnetospheric maser theory is known.     

川滇地区地震活动与地球自转速率变化之间的关系

利用川滇地区1962—2016年间发生的MS≥6.0地震资料,在去除余震的情况下,分析了其发生与地球自转速率变化极值点之间的关系。得到以下结果:川滇地区MS≥6.0地震的发生与地球自转速率变化极值点具有显著关系,对于不同震级范围的地震,其与不同周期的地球自转速率变化有关。对于MS≥7.0的地震,有90%发生在地球自转速率季节性变化极值点前14天至后37天时间段内;对于6.0≤MS≤6.4的地震,有80%发生在地球自转速率短周期变化极值点前68小时至后30小时的时间段内;对于6.5≤MS≤6.9的地震,有87.5%发生在地球自转速率短周期变化极值点前36小时至后64小时的时间段内。地震发生在特定时间段的显著性检验结果表明,川滇地区MS≥6.0地震与地球自转速率变化极值点的关系都可以在α=0.05的显著性水平下通过显著性检验。这个结果表明,在地球自转速率发生转折的期间容易触发地震,对川滇地区地震发生时间预测具有参考意义。     

Gravity potential of the normal body in the outer and inner space

Summary The level rotational ellipsoid, best fitting the actual Earth, rotating with the same angular velocity around a common axis of rotation, is assumed to be a mathematical model of the real Earth. The gravity potential of this body and its derivatives in the outer space are derived by means of the generalized Pizzetti method[1]. For some analyses of the structure of the Earth we need to know the gravity anomaly and thus the gravity potential and its derivatives inside the mathematical model. These values are not defined in the classical conception. In this paper, the normal potential and its derivatives in the inner space are derived up to a certain depth, which is still of significance for gravimetric research.Dedicated to RNDr Jan Pícha, CSc., on his 60th Birthday     

Structure constraints and instability leading to the post-perovskite phase transition of MgSiO3

Recent experience with Rietveld refinement of structural analogues and literature surveys, suggests anion–anion repulsion limits the stability of the perovskite phase, including in the MgSiO₃ perovskite to post-perovskite transition. Assuming rigid octahedral coordination, still to be tested experimentally, the critical point where intra- and inter-octahedral anion–anion distances are equal provides a useful metric for predicting the pressure of the perovskite/post-perovskite transition and the Clapeyron slope of the phase boundary, once pressure and temperature derivatives of relevant structure parameters are known. The inter-octahedral anion–anion distances and the polyhedral volume ratio are rigorously formulated as a function of octahedral rotation in this work, assuming the orthorhombic (Pbnm) perovskite structure, where regular octahedra share each corner and conform to the in- and anti-phase rotation schemes designated by space group symmetry. These mathematical expressions are consistent with structure data from 70 perovskite-structured materials surveyed in the literature at ambient as well as extreme conditions and define structure constraints, such as the minimum polyhedral volume ratio, which must be reached before the phase transition to the post-perovskite structure-type can proceed. The formalism we present is general for perovskite (Pbnm) and dependent on the accuracy with which structures can be determined from, sometimes compromised, high pressure diffraction data.