Quasi-geostrophic motions in a galactic flow

Summary We continue the theoretical investigation of geostrophically balanced motions of a star gas in a rotating galaxy. The method of small perturbations is employed to derive a quasi geostrophic vorticity equation suitable for solving initial value problems for slow galactic eddying motions. The results derived for this simple theoretical model are then generalized to obtain approximate geostrophic forecast equations suitable for study of nonlinear galactic motions over a whole disk galaxy. A simple discussion of the stability of our approximate vorticity equation is presented. It is expected that in the absence of rapid gravitational instabilities, actual eddy motions observed in spiral galaxies will be at least approximately of the type of motion discussed in this paper. The Rossby adjustment problem is investigated in this context.     

Experimental and computational verification of reasonable design formulae for base‐isolated structures

It is clear that base isolation is a sensible strategic design in attenuating the responses of a structural system induced by ground motions. The design of seismically isolated structures is mainly governed by the Uniform Building Code (UBC) published by the International Conference of Building Officials. The UBC code emphasizes a simple, statically equivalent design method that displacements of an isolated structure are concentrated at the isolation level. Therefore, the superstructure nearly moves as a rigid body and the design forces of elements above isolators are based on the behaviour of isolators at the design displacement. However, in the UBC code, the distribution of inertial (or lateral) forces over the height of the superstructure above isolation has been found to be too conservative for most isolated structures. In view of this, two simple and reasonable design formulae for the lateral force distribution on isolated structures have been proposed in this paper. Results obtained from a full‐scale isolated structure tested on the shaking table and numerical analyses of two additional examples verify the suitability of design formulae. It is illustrated that the proposed formulae can predict well the lateral force distribution on isolated structures during earthquakes. Copyright © 2003 John Wiley & Sons, Ltd.     

An explanation for salinity- and SPM-induced vertical countergradient buoyancy fluxes

Measurements of turbulent fluctuations of velocity, salinity, and suspended particulate matter (SPM) are presented. The data show persistent countergradient buoyancy fluxes. These countergradient fluxes are controlled by the ratio of vertical turbulent kinetic energy (VKE) and available potential energy (APE) terms in the buoyancy flux equation. The onset of countergradient fluxes is found to approximately coincide with larger APE than VKE. It is shown here that the ratio of VKE to APE can be written as the square of a vertical Froude number. This number signifies the onset of the dynamical significance of buoyancy in the transport of mass. That is when motions driven by buoyancy begin to actively determine the vertical turbulent transport of mass. Spectral and quadrant analyses show that the occurrence of countergradient fluxes coincides with a change in the relative importance of turbulent energetic structures and buoyancy-driven motions in the transport of mass. Furthermore, these analyses show that with increasing salinity-induced Richardson number (Ri), countergradient contributions expand to the larger scales of motions and the relative importance of outward and inward interactions increases. At the smaller scales, at moderate Ri, the countergradient buoyancy fluxes are physically associated with an asymmetry in transport of fluid parcels by energetic turbulent motions. At the large scales, at large Ri, the countergradient buoyancy fluxes are physically associated with convective motions induced by buoyancy of incompletely dispersed fluid parcels which have been transported by energetic motions in the past. Moreover, these convective motions induce restratification and enhanced settling of SPM. The latter is generally the result of salinity-induced convective motions, but SPM-induced buoyancy is also found to play a role.     

Seismic demand in medium- and long-period structures

Based on the results of an extensive parametric study of elastic and inelastic response of SDOF systems, in which the most important structural parameters were varied and ground motions of very different characteristics were taken into account, simple formulae for determining the seismic demand in SDOF systems with natural periods in the medium- and long-period range are proposed. Seismic demand is expressed in terms of the mean values of maximum relative displacements and maximum input energy. These results can be used to provide rough estimates of structural behaviour when different damage models are applied. As well as this, the proposed formulae can be used to construct design spectra of the Newmark-Hall type.     

The kinematics of hexagonal magnetoconvection

Abstract

Calculations are presented for the evolution of a magnetic field which is subject to the effect of three-dimensional motions in a convecting layer of highly conducting fluid with hexagonal symmetry. The back reaction of the field on the motions via the Lorentz force is neglected. We consider cases where the imposed field is either vertical or horizontal. In the former case, flux accumulates at cell centres, with subsidiary concentrations at the vertices of the pattern. In the latter, topological asymmetries between up- and down-moving fluid regions generate positive flux at the base of the layer and negative flux at the top, though the system is actually an amplifier rather than a self-excited dynamo. Spiral field lines form in the interiors of the cells, and the phenomenon of “flux expulsion” found in two-dimensional solutions is somewhat altered when the imposed field is horizontal. Applications for stellar magnetic fields include a possible mechanism for burying flux at the base of a convection zone.     

Internal waves in a rotating stratified fluid in an arbitrary gravitational field

Abstract

Small amplitude oscillations of a uniformly rotating, density stratified, Boussinesq, non-dissipative fluid are examined. A mathematical model is constructed to describe timedependent motions which are small deviations from an initial state that is motionless with respect to the rotating frame of reference. The basic stable density distribution is allowed to be an arbitrary prescribed function of the gravitational potential. The problem is considered for a wide class of gravitational fields. General properties of the eigenvalues and eigenfunctions of square integrable oscillations are demonstrated, and a bound is obtained for the magnitude of the frequencies. The modal solutions are classified as to type. The eigenfunctions for the pressure field are shown to satisfy a second-order partial differential equation of mixed type, and the equation is obtained for the critical surfaces which delineate the elliptic and hyperbolic regions. The nature of the problem is examined in detail for certain specific gravitational fields, e.g., a radially symmetric field. Where appropriate, results are compared with those of other investigations of waves in a rotating fluid of spherical configuration and the novel aspects of the present treatment are emphasized. Explicit modal solutions are obtained in the specific example of a fluid contained in a rigid cylinder, stratified in the presence of vertical gravity, with the buoyancy frequency N being an arbitrary prescribed function of depth.     

采用剪切波分裂方向约束的板块绝对运动模型研究

板块绝对运动(即岩石圈板块相对于深部地幔的运动)导致软流圈深度存在较强的剪切作用,为软流圈呈现较强的地震波速各向异性提供了一种物理解释.相应地,软流圈地震各向异性的实测数据为反演板块绝对运动提供了一种定量的约束.本文利用前人发表的由474个剪切波分裂数据组成的全球软流圈地震各向异性方向数据集,结合板块相对运动模型MORVEL,通过加权最小二乘法反演板块绝对运动.计算结果表明,由实测数据约束的板块绝对运动模型不能将观测数据拟合到原始数据测量误差要求的统计水平上,反映出以地震各向异性方向指示板块绝对运动方向存在原始数据测量误差之外的系统性误差.该误差或可归因于板块绝对运动控制软流圈地震各向异性的物理机制复杂性以及小尺度地幔流动的区域复杂性.因此,地震各向异性方向只能从统计平均的意义上约束板块绝对运动方向,两者间的差别除了测量误差外还应包含复杂物理成因的模型误差.在原始数据测量误差的基础上增加20°的模型误差并且剔除一个离群数据后,本文得到了最优拟合剪切波分裂数据集的SKS473模型,并与由热点数据反演得到的板块绝对运动模型进行对比.由于约束板块绝对运动的地震各向异性数据和热点数据都存在误差较大、地理分布不均的局限性,结合两类数据的联合反演或可成为未来建立更高精度板块绝对运动模型的有效途径.     

Coupled motions of the inner core and possible geomagnetic implications

As the inner core is a good electrical conductor any ambient magnetic field would diffuse into it on a time scale long compared to several thousand years, and conversely be frozen there on shorter time scales. From the observations that the dipole component of the Earth's magnetic field has been inclined persistently to the spin axis over hundreds of thousands of years, and that the dipole drifts and decays significantly more slowly than the nondipole field, it is suggested that the external dipole is simply a manifestation of a field frozen in an inclined inner core. It is shown that the much neglected gravitational restoring torque can be significant for an inclined inner core, so much so that its motion is in the main determined by gravity, with electromagnetic and inertial coupling effects being of secondary importance. A regular precession of the inner core is shown to be possible where its spin axis drifts westward relative to the mantle with a period of ～ 7000 y. Some preliminary calculations of the possible motions of a gravitationally coupled mantle-inner core system are shown.     

Etude des transferts verticaux dans la zone non saturee et de l'emmagasinement d'une nappe libre (dans le cas d'un pompage,dans les conditions naturelles)

A 1-month pumping test has been carried out during the summer of 1970 in order to study the desaturation of the cone of depression and the restoration of the water level and the re-wetting during the recovery phase. The observations were continued in order to evaluate the water movements during an annual cycle.The water flux resulting from a potential difference was evaluated. A slow and long-continued drainage is due to the low permeability of the water-bearing formations. Less than half the gravitational water was removed. The specific yields obtained from nuclear methods and other more classical methods based on transient flow formulae are quite different, being, in the latter case, 10–15 times smaller.The interaction between the saturated and unsaturated zones has been determined: contrary to what we would expect, in the unsaturated zone the capillary fringe has contributed only a small part to the water flux. Measurements of soil-water content show that in the cone of depression the resaturation is not complete.During the recharge period, we have noticed a water-level rise in the absence of vertical fluxes, due to an increase of the level in the river; the water movement is controlled by the nature of the formation and the influence of the water content on the permeability. The water balance obtained from the water content measurements is close to that found by the generalized Darcy law and it gives an acceptable approximation of infiltration and evapotranspiration components. The evapotranspiration estimated by this method is, however, very different from that derived from the climatic method.A continuous inflow to the water table has been determined, but it is often insignificant. Most of the groundwater recharge is obtained by a few periods of intense precipitation during which the daily fluxes reach values 100 times higher than normal inflow. Summer rains can reach the groundwater table when their intensity and timing create conditions favourable for downward flow in the upper soil horizons.     

Numerical study of characteristics of underground blast induced surface ground motion and their effect on above-ground structures. Part I. Ground motion characteristics

Current codes of practice in assessing the blast ground motion effect on structures are mainly based on the ground peak particle velocity (PPV) or PPV and the principal frequency (PF) of the ground motion. PPV and PF of ground motion from underground explosions are usually estimated by empirical formulae derived from field blast tests. Not many empirical formulae for PF, but many empirical formulae for PPV are available in the literature. They were obtained from recorded data either on ground surface or in the free field (inside the geological medium). Owing to the effect of surface reflection, blast motions on ground surface and in the free field are very different. But not many publications in the open literature discuss the differences of blast motions on ground surface and in the free field. Moreover, very few publications discuss the blast ground motion spatial variation characteristics. As ground motion directly affects structural responses, it is very important to study its characteristics in order to more reliably assess its effects on structures. In this paper, a validated numerical model is used to simulate stress wave at a granite site owing to explosion in an underground chamber. Using the simulated stress wave, the relations such as PPV and PF attenuation as well as spatial variation of motions on ground surface and in the free field are derived. Discussions on the differences of the characteristics of surface and free field motions are made. Results presented in this paper can be used in a more detailed assessment of ground motion effect on structures.     

On the accuracy of the bathymetry-generated gravitational field quantities for a depth-dependent seawater density distribution

In geophysical studies investigating the lithosphere structure, the gravitational field generated by the ocean density contrast (i.e., bathymetry-generated gravitational field) represents a significant amount of the signal to be modelled and subsequently removed from the Earth’s gravity field. The ocean density contrast is typically calculated as the difference between the mean density values of the Earth’s crust and seawater. The approximation of the actual seawater density distribution by its mean value yields relative errors up to about 2% in computed quantities of the gravitational field. To reduce these errors, a more realistic model of the seawater density distribution is utilized based on the analysis of existing oceanographic data of salinity, temperature, and pressure (depth). We study the accuracy of the bathymetry-generated gravitational field quantities formulated for a depth-dependent model of the seawater density distribution. This density distribution approximates the seawater density variations due to an increasing pressure with depth, whereas smaller lateral density variations caused by salinity, temperature, and other oceanographic factors are not taken into consideration. The error analysis reveals that the approximation of the seawater density by the depth-dependent density model reduces the maximum errors to less than 0.6%. The corresponding depth-averaged errors are below 0.1%. The depth-dependent seawater density model is further facilitated in expressions for computing the bathymetry-generated gravitational field quantities by means of the spherical bathymetric (ocean bottom depth) functions. The numerical realization reveals large differences in the results obtained with and without consideration of the depth-dependent seawater density distribution. The maxima of absolute differences reach 201 m²/s² and 16.5 mGal in computed values of the potential and attraction, respectively. The application of the depth-dependent seawater density model thus significantly improves the accuracy in the forward modelling of the bathymetric gravitational field quantities.     

Thermal histories of the core and mantle

Recognition that the cooling of the core is accomplished by conduction of heat into a thermal boundary layer (D″) at the base of the mantle, partly decouples calculations of the thermal histories of the core and mantle. Both are controlled by the temperature-dependent rheology of the mantle, but in different ways. Thermal parameters of the Earth are more tightly constrained than hitherto by demanding that they satisfy both core and mantle histories. We require evolution from an early state, in which the temperatures of the top of the core and the base of the mantle were both very close to the mantle solidus, to the present state in which a temperature increment, estimated to be ～ 800 K, has developed across D″. The thermal history is not very dependent upon the assumption of Newtonian or non-Newtonian mantle rheology. The thermal boundary layer at the base of the mantle (i.e., D″) developed within the first few hundred million years and the temperature increment across it is still increasing slowly. In our preferred model the present temperature at the top of the core is 3800 K and the mantle temperature, extrapolated to the core boundary without the thermal boundary layer, is 3000 K. The mantle solidus is 3860 K. These temperatures could be varied within quite wide limits without seriously affecting our conclusions. Core gravitational energy release is found to have been remarkably constant at ～ 3 × 10¹¹ W. nearly 20% of the core heat flux, for the past 3 × 10⁹ y, although the total terrestrial heat flux has decreased by a factor of 2 or 3 in that time. This gravitational energy can power the “chemical” dynamo in spite of a core heat flux that is less than that required by conduction down an adiabatic gradient in the outer core; part of the gravitational energy is used to redistribute the excess heat back into the core, leaving 1.8 × 10¹¹ W to drive the dynamo. At no time was the dynamo thermally driven and the present radioactive heating in the core is negligibly small. The dynamo can persist indefinitely into the future; available power 10¹⁰ y from now is estimated to be 0.3 × 10¹¹ W if linear mantle rheology is assumed or more if mantle rheology is non-linear. The assumption that the gravitational constant decreases with time imposes an implausible rate of decrease in dynamo energy. With conventional thermodynamics it also requires radiogenic heating of the mantle considerably in excess of the likely content of radioactive elements.     

On the excitation of the earth's seismic normal modes

Summary The excitation of the earth's normal modes is formulated as an initial value problem. The static state of the earth, stressed from its hydrostatic reference situation, is considered as the initial state. The initial state is relaxed, at the time of the earthquake, by the removal of the forces maintaining the departure from hydrostatic equilibrium. Expressions are derived for the coefficients giving the relative excitation of the individual modes for the cases where these forces are compensating volume forces or compensating tractions on the faces of a dislocation. It is demonstrated that a point slip dislocation has a body force equivalent in the form of a double couple with a deviatoric moment tensor. However, for a source with volume change no moment tensor equivalent can be found. The volume change, apart from an elastic effect which can be represented by an isotropic moment tensor, has a direct gravitational effect on the excitation. This effect is due to a balanced force field consisting of a point force at the source and a continuous distribution of volume forces throughout the earth. The latter distribution, if not taken into account, may give rise to artificial phases in the frequency spectrum of the normal modes.     

Seasonal variations between sampling and classical mean turbulent heat flux estimates in the eastern North Atlantic

The two commonly used statistical measures of the air-sea heat flux, the sampling and classical means, have been compared using hourly reports over a 7-year-period from a weather ship stationed in the NE Atlantic. The sampling mean is the average over all flux estimates in a given period, where individual flux estimates are determined from ship reports of meteorological variables using the well-known bulk formulae. The classical mean is the flux derived by substituting period-averaged values for each of the meteorological variables into the bulk formula (where the averaging period employed is the same as that over which the fluxes are to be determined). Monthly sampling and classical means are calculated for the latent and sensible heat fluxes. The monthly classical mean latent heat flux is found to overestimate the sampling mean by an amount which increases from 1–2 W m⁻² in summer to 7 W m⁻² in winter, on average, over the 7-year-period. In a given winter month, the excess may be as great as 15 W m⁻², which represents about 10% of the latent heat flux. For the sensible heat flux, any seasonal variation between the two means is of the order of 1 W m⁻² and is not significant compared to the interannual variation. The discrepancy between the two means for the latent heat flux is shown to arise primarily from a negative correlation between the wind speed and sea-air humidity difference, the effects of which are implicitly included in the sampling method but not in the classical. The influence of the dominant weather conditions on the sign and magnitude of this correlation are explored, and the large negative values that it takes in winter are found to depend on the typical track of the mid-latitude depressions with respect to the position sampled. In conclusion, it is suggested that sampling means should be employed where possible in future climatological studies.     

从偶层位出发建立曲面上的位场转换解释系统

本文从偶层位公式出发,导出了曲面上位场转换所需的基本公式:偶层场强分量及偶层场强分量的一阶导数、二阶导数的表达式;并导出了一条称之为“磁化方向与磁场分量方向互换”的定理,从而建立了一个多功能的曲面上的位场转换解释系统.     

Peak displacement patterns for the performance-based seismic design of steel eccentrically braced frames

Performance-based seismic design(PBSD) aims to assess structures at different damage states. Since damage can be directly associated to displacements, seismic design with consideration of displacement seems to be logical. In this study, simple formulae to estimate the peak floor displacement patterns of eccentrically braced frames(EBFs) at different performance levels subjected to earthquake ground motions are proposed. These formulae are applicable in a PBSD and especially in direct displacement-based design(DDBD). Parametric study is conducted on a group of 30 EBFs under a set of 15 far field and near field accelerograms which they scaled to different amplitudes to adapt various performance levels. The results of thousands of nonlinear dynamic analyses of EBFs have been post-processed by nonlinear regression analysis in order to recognize the major parameters that influence the peak displacement pattern of these frames. Results show that suggested displacement patterns have relatively good agreement with those acquired by an exact nonlinear dynamic analysis.     

Molecular transport in fracture processes

The Asymmetric Continuum Theory based on deformation fields includes the strain rotation as an equally important deformation part as the shear and confining strains; all these fields can be related to their origin in the fracture processes by some displacement motions in a source. Some of these motions may belong to an individual process, some to complex correlated events; in this latter case the displacements related to these strains could be shifted in phase. Moreover, we may expect an appearance of some molecular transport motions; the molecular transport may be helpful for understanding an interaction of the molecular processes and related molecular momentum flux. These correlated events should be mutually related in a source by the release-rebound mechanism. In particular, we consider the point fracture events as associated with a confining load or/and with the shear and rotation processes; we discuss the related effects and their meaning when discussing the fault plane mechanism and emitted waves. It is to be pointed out that such molecular motions are too small to be observed by the existing seismological networks.     

Characterization of seismic hazard and structural response by energy flux

Seismic safety of structures depends on the structure's ability to absorb the seismic energy that is transmitted from ground to structure. One parameter that can be used to characterize seismic energy is the energy flux. Energy flux is defined as the amount of energy transmitted per unit time through a cross-section of a medium, and is equal to kinetic energy multiplied by the propagation velocity of seismic waves. The peak or the integral of energy flux can be used to characterize ground motions. By definition, energy flux automatically accounts for site amplification. Energy flux in a structure can be studied by formulating the problem as a wave propagation problem. For buildings founded on layered soil media and subjected to vertically incident plane shear waves, energy flux equations are derived by modeling the building as an extension of the layered soil medium, and considering each story as another layer. The propagation of energy flux in the layers is described in terms of the upgoing and downgoing energy flux in each layer, and the energy reflection and transmission coefficients at each interface. The formulation results in a pair of simple finite-difference equations for each layer, which can be solved recursively starting from the bedrock. The upgoing and downgoing energy flux in the layers allows calculation of the energy demand and energy dissipation in each layer. The methodology is applicable to linear, as well as nonlinear structures.     

Experimental study of near-bed concentration and sediment vertical mixing parameter for vertical concentration distribution in the surf zone

Two formulae for the near-bed concentration(C_a) and the sediment vertical mixing parameter(m) are established based on a large scale wave flume experiment.The advantage of the new formulae is that the turbulent kinetic energy induced by wave breaking can be taken into account;the formula for C_a is in terms of the near-bed,time-averaged turbulent kinetic energy,and the formula for m is in terms of depth-and time-averaged turbulent kinetic energy.A new expression for suspended sediment load also is established by depth integration of the vertical distribution of the suspended sediment concentration obtained on basis of the new formulae.Equation validation is done by comparing the predicted C_a and m to measurements for different types of waves(regular wave,wave group,and irregular wave),and good agreement is found.The advantages of the proposed formulae over previous formulae also are discussed.