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1.
A numerical study has been made of the heat transfer through a fluid layer with recirculating flow. The outer fluid surface was assumed to be spherical, while the inner surface consisted of a sphere concentrically or eccentrically located with respect to the outer spherical surface. The recirculating flow was assumed to be driven by a gas flow creating stress on the fluid's outer surface so that creeping (low Reynolds number) flow developed in its interior. The present study solves the Stokes equation of motion and the convective diffusion equation in bispherical coordinates and presents the streamline and isotherm patterns.Nomenclature a i inner sphere radius - a d outer sphere radius - A 1 defined by equation (5) - A 2 defined by equation (6) - B 1 defined by equation (7) - B 2 defined by equation (8) - c dimensional factor for bispherical coordinates - C constant in equation (4) - d narrowest distance between the two eccentric spheres - E 2 operator defined by equation (1) in spherical coordinates and by equation (21) in bispherical coordinates - G modified vorticity, defined in equation (22) - G * non-dimensional modified vorticity, defined in equation (28) - h metric coefficient of bispherical coordinate system, defined in equation (18) - k w thermal conductivity of water - K 1 defined by equation (9) - K 2 defined by equation (10) - N Re Reynolds number=2a dU/gn - N Pe,h Peclet number=2a dU/ - n integer counter - q heat flux - r radius - r * non-dimensional radius=r/a d - S surface area - t time - t * non-dimensional time=t/a d 2 - T temperature - T o temperature at inner sphere surface - T a temperature at outer sphere surface - T * non-dimensional temperature;=(T–T o)/(Ta–To) - u velocity - u r radial velocity in spherical coordinates - u angular velocity in spherical coordinates - u radial velocity in bispherical coordinates - u angular velocity in bispherical coordinates - U free stream velocity - u r * =u r/U - u * =u /U - u * =u /U - u * =u /U Greek symbols a 1 small displacement - vorticity, defined in equation (17) - * non-dimensional vorticity, defined in equation (27) - radial bispherical coordinates - o bispherical coordinate of inner sphere - a bispherical coordinate of outer sphere - angular coordinate in spherical coordinates - thermal diffusivity - w thermal diffusivity of water - kinematic viscosity - angular bispherical coordinate - spherical coordinate - streamfunction - non-dimensional streamfunction for spherical coordinates, = /(U a d 2 ) - * non-dimensional streamfunction for bispherical coordinates, defined in equation (26)  相似文献   

2.
Abstract

This paper analyzes the linear stability of a rapidly-rotating, stratified sheet pinch in a gravitational field, g, perpendicular to the sheet. The sheet pinch is a layer (O ? z ? d) of inviscid, Boussinesq fluid of electrical conductivity σ, magnetic permeability μ, and almost uniform density ρ o; z is height. The prevailing magnetic field. B o(z), is horizontal at each z level, but varies in direction with z. The angular velocity, Ω, is vertical and large (Ω ? VA/d, where VA = B0√(μρ0) is the Alfvén velocity). The Elsasser number, Λ = σB2 0/2Ωρ0, measures σ. A (modified) Rayleigh number, R = gβd2/ρ0V2 A, measures the buoyancy force, where β is the imposed density gradient, antiparallel to g. A Prandtl number, PK = μσK, measures the diffusivity, k, of density differences.  相似文献   

3.
Shear flow instability arising from the velocity shear between the inner and the outer central plasma sheet regions is studied by treating the plasma as compressible. Based on the linearized MHD equations, dispersion relations for the surface wave modes occurring at the boundary of the inner central plasma sheet (ICPS) and the outer central plasma sheet (OCPS) are derived. The growth rates and the eigenmode frequencies are obtained numerically. Three data sets consisting of parameters relevant to the earth’s magnetotail are considered. The plasma sheet region is found to be stable for constant plasma flows unless MA>9.6, where MA is the Alfvén Mach number in the ICPS. However, for a continuously varying flow velocity profile in the ICPS, the instability is excited for MA\geq1.4. The excited modes have oscillation periods of 2–10 min and 1.5–6 s, and typical transverse wavelengths of 30–100 RE and 0.5–6 RE for data sets 1 and 2 (i.e., case of no neutral sheet) respectively. For the data set 3, which corresponds to a neutral sheet at the center of the plasma sheet, the excited oscillations have periods of 2 s-1 min with transverse wavelengths of 0.02–1 RE.  相似文献   

4.
Sustainable water management in semi-arid agriculture practices requires quantitative knowledge of water fluxes within the soil-vegetation-atmosphere system. Therefore, we used stable-isotope approaches to evaluate evaporation (Ea), transpiration (Ta), and groundwater recharge (R) at sites in Senegal's Groundnut basin and Ferlo Valley pasture region during the pre-monsoon, monsoon, and post-monsoon seasons of 2021. The approaches were based upon (i) the isothermal evaporation model (for quantifying Ea); (ii) water and isotope mass balances (to partition Ea and Ta for groundnut and pasture); and (iii) the piston displacement method (for estimating R). Ea losses derived from the isothermal evaporation model corresponded primarily to Stage II evaporation, and ranged from 0.02 to 0.09 mm d−1 in the Groundnut basin, versus 0.02–0.11 mm d−1 in Ferlo. At the groundnut site, Ea rates ranged from 0.01 to 0.69 mm d−1; Ta was in the range 0.55–2.29 mm d−1; and the Ta/ETa ratio was 74%–90%. At the pasture site, the ranges were 0.02–0.39 mm d−1 for Ea; 0.9–1.69 mm d−1 for Ta; and 62–90% for Ta/ETa. The ETa value derived for the groundnut site via the isotope approach was similar to those from eddy covariance measurements, and also to the results from the previous validated HYDRUS-1D model. However, the HYDRUS-1D model gave a lower Ta/ETa ratio (23.2%). The computed groundwater recharge for the groundnut site amounted to less than 2% of the local annual precipitation. Recommendations are made regarding protocols for preventing changes to isotopic compositions of water in samples that are collected in remote arid regions, but must be analysed days later. The article ends with suggestions for studies to follow up on evidence that local aquifers are being recharged via preferential pathways.  相似文献   

5.
A 3D kinematic geodynamo model in a sphere with the conductive solid inner core is considered. The 3D magnetic field and velocity field are resolved in the physical space for r- and -coordinates, whereas the sin- and cos-decomposition is applied to the -coordinate. The additional boundary conditions for the case of non-zero velocity field on the boundaries of the liquid spherical shell and for different magnetic diffusivities of the inner and outer core are applied. The computer code was tested by free decay mode solutions and comparisons were made also with results reported by other authors. This work is a part of a project to study 3D inviscid geodynamo models.  相似文献   

6.
Lava balloons—peculiar products of basaltic submarine eruptions   总被引：1，自引：1，他引：0  
Between December 1998 and April 2001, a submarine basaltic eruption occurred west of Terceira Island, Azores (Portugal) in water depths between 300 and 1,000?m. Physical evidence for the eruption was provided by the periodic occurrence of hot lava “balloons” floating on the sea surface. The balloons consisted of a large gas-filled cavity surrounded by a thin shell (a few centimetres thick). The shells of the collected balloons are composed of two layers, termed the outer layer and the inner layer, defined by different bubble number density, bubble sizes and crystal content. The inner layer is further divided into three sublayers defined by more subtle differences in vesicularity. The outer layer is glassy, golden-coloured and highly porous. It shows signs of fluidal deformation and late-stage extension cracks. Interstitial glass contains 0.29?wt% H2O and CO2 is below detection. Melt inclusions contain up to 1.18?wt% H2O and 1,500?ppm CO2 (from different inclusions). Cooling rates of the outermost glass of the outer layer are found to be as high as 1,259?K/s. During ascent of low viscosity magma to the ocean floor, volatiles, dominated by CO2, exsolved from the magma (melt + crystals). The buoyancy of the vapour phase that accumulated below a thin crust on lava ponded at the vent caused bulging and ultimately cracking of the crust. This allowed large bubbles (central cavity) surrounded by a film of vesicular magma (balloon shell) to leak into the water column. On contact with the seawater, the outermost part of the outer layer of the shell hyperquenched. If an entirely closed shell was produced during detachment, the trapped gas inside allowed buoyant rise. Only balloons with the right balance of physical properties (e.g. size and bulk density) rose all the way to the sea surface.  相似文献   

7.
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8.
The water retention curve (θ(ψ)), which defines the relationship between soil volumetric water content (θ) and matric potential (ψ), is of paramount importance in characterizing the hydraulic behaviour of soils. However, few methods are so far available for estimating θ(ψ) in undisturbed soil samples. We present a new design of TDR‐pressure cell (TDR‐Cell) for estimating θ(ψ) in undisturbed soil samples. The TDR‐Cell consists of a 50‐mm‐long and 50‐mm internal diameter stainless steel cylinder (which constitutes the outer frame of a coaxial line) attached to a porous ceramic disc and closed at the ends with two aluminium lids. A 49‐mm‐long and 3‐mm‐diameter stainless steel rod, which runs longitudinally through the centre of the cylinder, constitutes the inner rod of a coaxial TDR probe. The TDR‐Cell was used to determine the θ(ψ) curves of a packed sand and seven undisturbed soil samples from three profiles of agricultural soils. These θ(ψ) curves were subsequently compared to those obtained from the corresponding 2‐mm sieved soils using the pressure plate method. Measurements of bulk electrical conductivity, σa, as a function of the water content, σa(θ), of the undisturbed soil samples were also performed. An excellent correlation (R2 = 0·988) was found between the θ values measured by TDR on the different undisturbed soils and the corresponding θ obtained from the soil gravimetric water content. A typical bimodal θ(ψ) function was found for most of the undisturbed soil samples. Comparison between the θ(ψ) curves measured with the TDR‐Cell and those obtained from the 2‐mm sieved soils showed that the pressure plate method overestimates θ at low ψ values. The σa(θ) relationship was well described by a simple power expression (R2 > 0·95), in which the power factor, defined as tortuosity, ranged between 1·18 and 3·75. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

9.
长江中下游大型湖泊水体固有光学特性:Ⅰ.吸收   总被引：1，自引：0，他引：1  
吸收系数是水体固有光学特性的重要组成部分,也是构建水色参数高精度遥感模型的基础,具有重要的研究意义.本文针对长江中下游三大淡水湖——鄱阳湖(2010 10、2011 08)、太湖(2008 10、2011 08)和巢湖(2009 10)进行5次野外实验,以International Ocean Colour Coordinating Group(IOCCG)2000年报告"Remote Sensing of Ocean Colour in Coastal,and Other Optically-Complex,Waters"为基础,对水体不同光学主导类型进行分类;并根据ad(非色素颗粒物吸收)、aph(浮游植物色素吸收)、ag(有色可溶性有机物吸收)等不同主导类型光谱曲线特征差异,引入ad-g(主导类型ad、ag、ad-ag的合并类型)和aph-related(主导类型ad-aph、ad-aph-ag的合并类型)类型,对主导类型进行归纳合并.结果显示:秋季,鄱阳湖、太湖、巢湖的主导类型较为单一,分别为ad、ad-ag、ad-aph-ag;夏季,鄱阳湖和太湖同为两种类型共同主导,分别为ad、ad-ag,ad-aph-ag、ad-aph.总体来说,鄱阳湖夏、秋季和太湖秋季主导类型都属于ad-g类型,而太湖夏季和巢湖秋季则属于aph-related类型.另外,分别针对Gons和Gitelson叶绿素a模型假设条件进行验证,发现不同湖泊水体及不同主导类型下其适用性程度不一致.  相似文献   

10.
Abstract

Finite amplitude convection in spherical shells with spherically symmetric gravity and heat source distribution is considered. The nonlinear problem of three-dimensional convection in shells with stress-free and isothermal boundaries is solved by expanding the dependent variables in terms of powers of the amplitude of convection. The preferred mode of convection is determined by a stability analysis in which arbitrary infinitesimal disturbances are superimposed on the steady solutions. The shell is assumed to be thick and only shells for which the ratio ζ of outer radius to inner radius is 2 or 3 are considered. Three cases, two of which lead to a self adjoint problem, are treated in this paper. The stable solutions are found to be l=2 modes for ζ=3 where l is the degree of the spherical harmonics and an l=3 non-axisymmetric mode which exhibits the symmetry of a tetrahedron for ζ=2. These stable solutions transport the maximum amount of heat. The Prandtl number dependence of the heat transport is computed for the various solutions analyzed in the paper.  相似文献   

11.
Abstract

Numerical simulations of thermal convection in a rapidly rotating spherical fluid shell heated from below and within have been carried out with a nonlinear, three-dimensional, time-dependent pseudospectral code. The investigated phenomena include the sequence of transitions to chaos and the differential mean zonal rotation. At the fixed Taylor number T a =106 and Prandtl number Pr=1 and with increasing Rayleigh number R, convection undergoes a series of bifurcations from onset of steadily propagating motions SP at R=R c = 13050, to a periodic state P, and thence to a quasi-periodic state QP and a non-periodic or chaotic state NP. Examples of SP, P, QP, and NP solutions are obtained at R = 1.3R c , R = 1.7 R c , R = 2R c , and R = 5 R c , respectively. In the SP state, convection rolls propagate at a constant longitudinal phase velocity that is slower than that obtained from the linear calculation at the onset of instability. The P state, characterized by a single frequency and its harmonics, has a two-layer cellular structure in radius. Convection rolls near the upper and lower surfaces of the spherical shell both propagate in a prograde sense with respect to the rotation of the reference frame. The outer convection rolls propagate faster than those near the inner shell. The physical mechanism responsible for the time-periodic oscillations is the differential shear of the convection cells due to the mean zonal flow. Meridional transport of zonal momentum by the convection cells in turn supports the mean zonal differential rotation. In the QP state, the longitudinal wave number m of the convection pattern oscillates among m = 3,4,5, and 6; the convection pattern near the outer shell has larger m than that near the inner shell. Radial motions are very weak in the polar regions. The convection pattern also shifts in m for the NP state at R = 5R c , whose power spectrum is characterized by broadened peaks and broadband background noise. The convection pattern near the outer shell propagates prograde, while the pattern near the inner shell propagates retrograde with respect to the basic rotation. Convection cells exist in polar regions. There is a large variation in the vigor of individual convection cells. An example of a more vigorously convecting chaotic state is obtained at R = 50R c . At this Rayleigh number some of the convection rolls have axes perpendicular to the axis of the basic rotation, indicating a partial relaxation of the rotational constraint. There are strong convective motions in the polar regions. The longitudinally averaged mean zonal flow has an equatorial superrotation and a high latitude subrotation for all cases except R = 50R c , at this highest Rayleigh number, the mean zonal flow pattern is completely reversed, opposite to the solar differential rotation pattern.  相似文献   

12.
Abstract

Numerical simulations of thermal convection in a rapidly rotating spherical fluid shell with and without inhomogeneous temperature anomalies on the top boundary have been carried out using a three-dimensional, time-dependent, spectral-transform code. The spherical shell of Boussinesq fluid has inner and outer radii the same as those of the Earth's liquid outer core. The Taylor number is 107, the Prandtl number is 1, and the Rayleigh number R is 5Rc (Rc is the critical value of R for the onset of convection when the top boundary is isothermal and R is based on the spherically averaged temperature difference across the shell). The shell is heated from below and cooled from above; there is no internal heating. The lower boundary of the shell is isothermal and both boundaries are rigid and impermeable. Three cases are considered. In one, the upper boundary is isothermal while in the others, temperature anomalies with (l,m) = (3,2) and (6,4) are imposed on the top boundary. The spherically averaged temperature difference across the shell is the same in all three cases. The amplitudes of the imposed temperature anomalies are equal to one-half of the spherically averaged temperature difference across the shell. Convective structures are strongly controlled by both rotation and the imposed temperature anomalies suggesting that thermal inhomogeneities imposed by the mantle on the core have a significant influence on the motions inside the core. The imposed temperature anomaly locks the thermal perturbation structure in the outer part of the spherical shell onto the upper boundary and significantly modifies the velocity structure in the same region. However, the radial velocity structure in the outer part of the shell is different from the temperature perturbation structure. The influence of the imposed temperature anomaly decreases with depth in the shell. Thermal structure and velocity structure are similar and convective rolls are more columnar in the inner part of the shell where the effects of rotation are most dominant.  相似文献   

13.
An analytical formulation is developed for the resultant electromagnetic field of an oscillating vertical magnetic dipole located over a thin conductive sheet of infinite extent. The sheet is characterized by a conductivity-thickness product or conductance d that may be a function of the horizontal coordinates. The system of integral equations arising in the general formulation is simplified greatly when azimuthal symmetry prevails. Numerical results for a Gaussian variation of d in the radial direction are presented for the case of a symmetrically located source. These results are for the fields at the level of the source dipole over the conductive sheet. It is shown that the quadrature response of the sheet is enhanced when there is rapid variation of the conductance. The null in the resultant wave tilt is also found to be shifted toward the direction of increasing conductance.  相似文献   

14.
Measurements with the ion charge-energy-mass spectrometer CHEM on the AMPTE/CCE spacecraft were used to investigate the origin of energetic He+ and He++ ions observed in the equatorial plane at 3\leqL\leq9. Special emphasis was laid on the dependence of long-term average distributions on magnetic local time (MLT) and the geomagnetic activity index Kp. The observations are described in terms of the phase space densities f1 (for He+) and f2 (for He++). They confirm preliminary results from a previous study: f1 is independent of MLT, whereas f2 is much larger on the nightside than on the dayside. They show, furthermore, that f1 increases slightly with Kp on intermediate drift shells, but decreases on high drift shells (L\geq7). f2 increases with Kp on all drift shells outside the premidnight sector. Within this sector a decrease is observed on high drift shells. A simple ion tracing code was developed to determine how and from where the ions move into the region of observations. It provides ion trajectories as a function of the ion charge, the magnetic moment and Kp. The ion tracing enables a distinction between regions of closed drift orbits (ring current) and open convection trajectories (plasma sheet). It also indicates how the outer part of the observation region is connected to different parts of the more distant plasma sheet. Observations and tracing show that He++ ions are effectively transported from the plasma sheet on convection trajectories. Their distribution in the observation region corresponds to the distribution of solar wind ions in the plasma sheet. Thus, energetic He++ ions most likely originate in the solar wind. On the other hand, the plasma sheet is not an important source of energetic He+ ions. Convection trajectories more likely constitute a sink for He+ ions, which may diffuse onto them from closed drift orbits and then get lost through the magnetopause. An ionospheric origin of energetic He+ ions is unlikely as well, since the source mechanism should be almost independent of Kp. There is considerable doubt, however, that a plausible mechanism also exists during quiet periods that can accelerate ions to ring current energies, while extracting them from the ionosphere. It is concluded, therefore, that energetic He+ ions are mainly produced by charge exchange processes from He++ ions. This means that most of the energetic He+ ions constituting the average distributions also very likely originate in the solar wind. Additional ionospheric contributions are possible during disturbed periods.  相似文献   

15.
During July and August 1981 subsurface intrusion of upwelled nutrient-rich Gulf Stream water was the dominant process affecting temporal and spatial changes in phytoplankton biomass and productivity of the southeastern United States continental shelf between 29 and 32°N latitude. Intruded waters in the study area covered as much as 101 km including virtually all of the middle and outer shelf and approximately 50% of the inner shelf area.Within 2 weeks following a large intrusion event in late July, middle shelf primary production and Chl a reached 3 to 4 gC m− d−1 and 75 mg m−, respectively. At the peak of the bloom 80% of the water column primary production occurred below the surface mixed-layer, and new primary production (i.e., NO3-supported) exceeded 90% of the total. Chl a-normalized photosynthetic rates were very high as evidenced by high mean assimilation number (15.5 mg C mg Chl a−1 h−1), high mean α (14 mg C mg Chl a−1 Ein−1 m), and no photoinhibition. As a result of the high photosynthetic rates, mean light-utilization index (Ψ) was 2 to 3 times higher than reported for temperature sub-arctic and arctic waters.The results imply a seasonal (June to August) middle shelf production of 150 g C m−1, about 15% higher than previous estimates of annual production on the middle shelf. Intrusions of the scale we observed in 1981 may not occur every summer. However, when such events do occur, they are by far the most important processes controlling summer phytoplankton dynamics of the middle and outer shelf and of the inner shelf in the southern half of the study area.  相似文献   

16.
官厅水库秋季悬浮颗粒物和CDOM吸收特性   总被引：2，自引：0，他引：2  
雷霞  郭子祺  田野  谢飞  秦静欣 《湖泊科学》2013,25(6):883-891
利用2012年9月5日在官厅水库采集的水体吸收系数数据,对总悬浮颗粒物、浮游植物色素颗粒物、非色素颗粒物和有色可溶性有机物的吸收特性进行研究.结果表明:秋季官厅水库的颗粒物吸收以浮游植物色素吸收为主,总颗粒物吸收光谱与浮游藻类吸收光谱相似;非色素颗粒物和有色可溶性有机物的吸收系数随波长的增大接近指数规律衰减;ad(440)、ad(675)与CChl.a呈显著相关,表明官厅水库秋季的非色素颗粒物主要来源于浮游藻类降解产物,陆源性输入较少;a ph(440)、a ph(675)与CChl.a存在显著线性关系,但其比吸收系数较为恒定,与CChl.a基本无关;不同采样点的不同组分吸收系数对总吸收系数的贡献不同,大致有4种表现类型.在富营养程度较高的妫库区,浮游植物色素是水体光谱吸收的主导因子;在富营养程度较低的中库区,颗粒物与有色可溶性有机物共同主导水体光谱吸收.  相似文献   

17.
This paper presents a response spectrum analysis procedure for the calculation of the maximum structural response to three translational seismic components that may act at any inclination relative to the reference axes of the structure. The formula GCQC3, a generalization of the known CQC3‐rule, incorporates the correlation between the seismic components along the axes of the structure and the intensity disparities between them. Contrary to the CQC3‐rule where a principal seismic component must be vertical, in the GCQC3‐rule all components can have any direction. Besides, the GCQC3‐rule is applicable if we impose restrictions to the maximum inclination and/or intensity of a principal seismic component; in this case two components may be quasi‐horizontal and the third may be quasi‐vertical. This paper demonstrates that the critical responses of the structure, defined as the maximum and minimum responses considering all possible directions of incidence of one seismic component, are given by the square root of the maximum and minimum eigenvalues of the response matrix R , of order 3×3, defined in this paper; the elements of R are established on the basis of the modal responses used in the well‐known CQC‐rule. The critical responses to the three principal seismic components with arbitrary directions in space are easily calculated by combining the eigenvalues of R and the intensities of those components. The ratio rmax/rSRSS between the maximum response and the SRSS response, the latter being the most unfavourable response to the principal seismic components acting along the axes of the structure, is bounded between 1 and √(3γa2/(γa2 + γb2 + γc2)), where γa?γb?γc are the relative intensities of the three seismic components with identical spectral shape. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

18.
A study on the transient response of a circular cylindrical shell of finite length embedded in a homogeneous, isotropic and linear elastic half-space is presented. The soil-structure system is subjected to suddenly applied explosion waves. The numerical method employed is a combination of the time domain semi-analytical boundary element method used for the semi-infinite soil medium and the finite strip method used for the circular cylindrical shell. The two methods are combined through equilibrium and compatibility conditions at the soil-structure interface. The dynamic responses at the interface between the soil medium and the structure for every time step are obtained. Numerical examples are presented in detail to demonstrate the use and versatility of the proposed method. The following parameters are found to affect the response: (1) the slenderness ratio of the length over the diameter of the shell, L/D; (2) the relative wall thickness, h/a; (3) the relative stiffness ratio between the shell and the medium, Es/Em; and (4) the incidence angle of the explosion wave, α.  相似文献   

19.
Abstract

This paper is concerned with a three-dimensional spherical model of a stationary dynamo that consists of a convective layer with a simple poloidal flow of the S2c 2 kind between a rotating inner body core and solid outer shell. The rotation of the inner core and the outer shell means that there are regions of concentrated shear or differential rotation at the convective layer boundaries. The induction equation for the inside of the convective layer was solved numerically by the Bullard-Gellman method, the eigenvalue of the problem being the magnetic Reynolds number of the poloidal flow (R M2) and it was assumed that the magnetic Reynolds number of the core (R M1) and of the shell (R M3) were prescribed parameters. Hence R M2 was studied as a function of R M1 and R M3, along with the orientation of the rotation axis, the radial dependence of the poloidal velocity and the relative thickness of the layers for the three different situations, (i) the core alone rotating, (ii) the shell alone rotating and (iii) the core and the shell rotating together. In all three cases it was found that, at definite orientations of the rotation axis, there is a good convergence of both the eigenvalues and the eigenfunctions of the problem as the number of spherical harmonics used to represent the problem increases. For R M1 =R M3= 103, corresponding to the westward drift velocity and the parameters of the Earth's core, the critical values of R M2 are found to be three orders of magnitude lower than R M1, R M3 so that the poloidal flow velocity sufficient for maintaining the dynamo process is 10-20 m/yr. With only the core or the shell rotating, the velocity field generally differs little from the axially symmetric case. However, for R M2 (or R M3) lying in the range 102 to 105, the self-excitation condition is found to be of the form R M2˙R ½ M1=constant (or R M2˙R½ M3=constant) and the solution does not possess the properties of the Braginsky near-axisymmetric dynamo. We should expect this, in particular, in the Braginsky limit R M2˙R?½; M1=constant.

An analysis of known three-dimensional dynamo models indicates the importance of the absence of mirror symmetry planes for the efficient generation of magnetic fields.  相似文献   

20.
Data from flume studies are used to develop a model for predicting bed‐load transport rates in rough turbulent two‐dimensional open‐channel flows moving well sorted non‐cohesive sediments over plane mobile beds. The object is not to predict transport rates in natural channel flows but rather to provide a standard against which measured bed‐load transport rates influenced by factors such as bed forms, bed armouring, or limited sediment availability may be compared in order to assess the impact of these factors on bed‐load transport rates. The model is based on a revised version of Bagnold's basic energy equation ibsb = ebω, where ib is the immersed bed‐load transport rate, ω is flow power per unit area, eb is the efficiency coefficient, and sb is the stress coefficient defined as the ratio of the tangential bed shear stress caused by grain collisions and fluid drag to the immersed weight of the bed load. Expressions are developed for sb and eb in terms of G, a normalized measure of sediment transport stage, and these expressions are substituted into the revised energy equation to obtain the bed‐load transport equation ib = ω G 3·4. This equation applies regardless of the mode of bed‐load transport (i.e. saltation or sheet flow) and reduces to ib = ω where G approaches 1 in the sheet‐flow regime. That ib = ω does not mean that all the available power is dissipated in transporting the bed load. Rather, it reflects the fact that ib is a transport rate that must be multiplied by sb to become a work rate before it can be compared with ω. It follows that the proportion of ω that is dissipated in the transport of bed load is ibsb/ω, which is approximately 0·6 when ib = ω. It is suggested that this remarkably high transport efficiency is achieved in sheet flow (1) because the ratio of grain‐to‐grain to grain‐to‐bed collisions increases with bed shear stress, and (2) because on average much more momentum is lost in a grain‐to‐bed collision than in a grain‐to‐grain one. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

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