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1.
Abstract

We investigate the influence of differential rotation on magnetic instabilities for an electrically conducting fluid in the presence of a toroidal basic state of magnetic field B 0 = BMB0(r, θ)1 φ and flow U0 = UMU0 (r, θ)1φ, [(r, θ, φ) are spherical polar coordinates]. The fluid is confined in a rapidly rotating, electrically insulating, rigid spherical container. In the first instance the influence of differential rotation on established magnetic instabilities is studied. These can belong to either the ideal or the resistive class, both of which have been the subject of extensive research in parts I and II of this series. It was found there, that in the absence of differential rotation, ideal modes (driven by gradients of B 0) become unstable for Ac ? 200 whereas resistive instabilities (generated by magnetic reconnection processes near critical levels, i.e. zeros of B0) require Ac ? 50. Here, Λ is the Elsasser number, a measure of the magnetic field strength and Λc is its critical value at marginal stability. Both types of instability can be stabilised by adding differential rotation into the system. For the resistive modes the exact form of the differential rotation is not important whereas for the ideal modes only a rotation rate which increases outward from the rotation axis has a stabilising effect. We found that in all cases which we investigated Λc increased rapidly and the modes disappeared when Rm ≈ O(ΛC), where the magnetic Reynolds number Rm is a measure of the strength of differential rotation. The main emphasis, however, is on instabilities which are driven by unstable gradients of the differential rotation itself, i.e. an otherwise stable fluid system is destabilised by a suitable differential rotation once the magnetic Reynolds number exceeds a certain critical value (Rm )c. Earlier work in the cylindrical geometry has shown that the differential rotation can generate an instability if Rm ) ?O(Λ). Those results, obtained for a fixed value of Λ = 100 are extended in two ways: to a spherical geometry and to an analysis of the effect of the magnetic field strength Λ on these modes of instability. Calculations confirm that modes driven by unstable gradients of the differential rotation can exist in a sphere and they are in good agreement with the local analysis and the predictions inferred from the cylindrical geometry. For Λ = O(100), the critical value of the magnetic Reynolds number (Rm )c Λ 100, depending on the choice of flow U0 . Modes corresponding to azimuthal wavenumber m = 1 are the most unstable ones. Although the magnetic field B 0 is itself a stable one, the field strength plays an important role for this instability. For all modes investigated, both for cylindrical and spherical geometries, (Rm )c reaches a minimum value for 50 ≈ Λ ≈ 100. If Λ is increased, (Rm )c ∝ Λ, whereas a decrease of Λ leads to a rapid increase of (Rm )c, i.e. a stabilisation of the system. No instability was found for Λ ≈ 10 — 30. Optimum conditions for instability driven by unstable gradients of the differential rotation are therefore achieved for ≈ Λ 50 — 100, Rm ? 100. These values lead to the conclusion that the instabilities can play an important role in the dynamics of the Earth's core.  相似文献   

2.
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   

3.
Linear α2Ω-dynamo waves are investigated in a thin turbulent, differentially rotating convective stellar shell. A simplified one-dimensional model is considered and an asymptotic solution constructed based on the small aspect ratio of the shell. In a previous paper Griffiths et al. (Griffiths, G.L., Bassom, A.P., Soward, A.M. and Kuzanyan, K.M., Nonlinear α2Ω-dynamo waves in stellar shells, Geophys. Astrophys. Fluid Dynam., 2001, 94, 85–133) considered the modulation of dynamo waves, linked to a latitudinal-dependent local α-effect and radial gradient of the zonal shear flow. These effects are measured at latitude θ by the magnetic Reynolds numbers R α f(θ) and R Ω g(θ). The modulated Parker wave, which propagates towards the equator, is localised at some mid-latitude θp under a Gaussian envelope. In this article, we include the influence of a latitudinal-dependent zonal flow possessing angular velocity Ω*(θ) and consider the possibility of non-axisymmetric dynamo waves with azimuthal wave number m. We find that the critical dynamo number D c?=?R α R Ω is minimised by axisymmetric modes in the αΩ-limit (Rα→0). On the other hand, when Rα?≠?0 there may exist a band of wave numbers 0?m?m ? for which the non-axisymmetric modes have a smaller D c than in the axisymmetric case. Here m ? is regarded as a continuous function of R α with the property m?→0 as R α→0 and the band is only non-empty when m??>1, which happens for sufficiently large R α. The preference for non-axisymmetric modes is possible because the wind-up of the non-axisymmetric structures can be compensated by phase mixing inherent to the α2Ω-dynamo. For parameter values resembling solar conditions, the Parker wave of maximum dynamo activity at latitude θp not only propagates equatorwards but also westwards relative to the local angular velocity Ω*(θ p ). Since the critical dynamo number D c?=?R α R Ω is O (1) for small R α, the condition m ??>?1 for non-axisymmetric mode preference imposes an upper limit on the size of |dΩ*/dθ|.  相似文献   

4.
Abstract

A linear analysis is used to study the stability of a rapidly rotating, electrically-conducting, self-gravitating fluid sphere of radius r 0, containing a uniform distribution of heat sources and under the influence of an azimuthal magnetic field whose strength is proportional to the distance from the rotation axis. The Lorentz force is of a magnitude comparable with that of the Coriolis force and so convective motions are fully three-dimensional, filling the entire sphere. We are primarily interested in the limit where the ratio q of the thermal diffusivity κ to the magnetic diffusivity η is much smaller than unity since this is possibly of the greatest geophysical relevance.

Thermal convection sets in when the temperature gradient exceeds some critical value as measured by the modified Rayleigh number Rc. The critical temperature gradient is smallest (Rc reaches a minimum) when the magnetic field strength parameter Λ ? 1. [Rc and Λ are defined in (2.3).] The instability takes the form of a very slow wave with frequency of order κ/r 2 0 and its direction of propagation changes from eastward to westward as Λ increases through Λ c ? 4.

When the fluid is sufficiently stably stratified and when Λ > Λm ? 22 a new mode of instability sets in. It is magnetically driven but requires some stratification before the energy stored in the magnetic field can be released. The instability takes the form of an eastward propagating wave with azimuthal wavenumber m = 1.  相似文献   

5.
In this article we study the linear instability of the two-dimensional strongly stratified model for global MHD in the diffusive solar tachocline. Gilman and Fox [Gilman, P.A. and Fox, P., Joint instability of the latitudinal differential rotation and toroidal magnetic fields below the solar convection zone. Astrophys. J., 1997, 484, 439–454] showed that for ideal MHD, the observed surface differential rotation becomes more unstable than is predicted by Watson's [Watson, M., Shear instability of differential rotation in stars. Geophys. Astrophys. Fluid Dyn., 1981, 16, 285–298] nonmagnetic analysis. They showed that the solar differential rotation is unstable for essentially all reasonable values of the differential rotation in the presence of an antisymmetric toroidal field. They found that for the broad field case B φ～sinθcosθ, θ being the co-latitude, instability occurs only for the azimuthal m?=?1 mode, and concluded that modes which are symmetric (meridional flow in the same direction) about the equator onset at lower field strengths than the antisymmetric modes. We study the effect of viscosity and magnetic diffusivity in the strongly stably stratified case where diffusion is primarily along the level surfaces. We show that antisymmetric modes are now strongly preferred over symmetric modes, and that diffusion can sometimes be destabilising. Even solid body rotation can be destabilised through the action of magnetic field. In addition, we show that when diffusion is present, instability can occur when the longitudinal wavenumber m?=?2.  相似文献   

6.
Abstract

Convection in a rotating spherical shell has wide application for understanding the dynamics of the atmospheres and interiors of many celestial bodies. In this paper we review linear results for convection in a shell of finite depth at substantial but not asymptotically large Taylor numbers, present nonlinear multimode calculations for similar conditions, and discuss the model and results in the context of the problem of solar convection and differential rotation. Detailed nonlinear calculations are presented for Taylor number T = 105, Prandtl number P = 1, and Rayleigh number R between 1 |MX 104 and 4 |MX 104 (which is between about 4 and 16 times critical) for a shell of depth 20% of the outer radius. Sixteen longitudinal wave numbers are usually included (all even wave numbers m between 0 and 30) the amplitudes of which are computed on a staggered grid in the meridian plane.

The kinetic energy spectrum shows a peak in the wave number range m = 12–18 at R = 104, which straddles the critical wave number m = 14 predicted by linear theory. These are modes which peak near the equator. The spectrum shows a second strong peak at m = 0, which represents the differential rotation driven by the peak convective modes. As R is increased, the amplitude of low wave numbers increases relative to high wave numbers as convection fills in in high and middle latitudes, and as the longitudinal scale of equatorial convection grows. By R = 3 |MX 104, m = 8 is the peak convective mode. There is a clear minimum in the total kinetic energy at middle latitudes relative to low and high, well into the nonlinear regime, representing the continued dominance of equatorial and polar modes found in the linear case. The kinetic energy spectrum for m > 0 is maintained primarily by buoyancy work in each mode, but with substantial nonlinear transfer of kinetic energy from the peak modes to both lower and higher wave numbers.

For R = 1 to 2 |MX 104, the differential rotation takes the form of an equatorial acceleration, with angular velocity generally decreasing with latitude away from the equator (as on the sun) and decreasing inwards. By R = 4 |MX 104, this equatorial profile has completely reversed, with angular velocity increasing with depth and latitude. Also, a polar vortex which has positive rotation relative to the reference frame (no evidence of which has been seen on the sun) builds up as soon as polar modes become important. Meridional circulation is quite weak relative to differential rotation at R = 104, but grows relative to it as R is increased. This circulation takes the farm of a single cell of large latitudinal extent in equatorial regions, with upward flow near the equator, together with a series of narrower cells in high latitudes. It is maintained primarily by axisymmetric buoyancy forces. The differential rotation is maintained at all R primarily by Reynolds stresses, rather than meridional circulation. Angular momentum transport toward the equator for R = 1–2 |MX 104 maintains the equatorial acceleration while radially inward transport maintains the opposite profile at R = 4 |MX 104.

The total heat flux out the top of the convective shell always shows two peaks for the range of R studied, one at the equator and the other near the poles (no significant variation with latitude is seen on the sun), while heat flux in at the bottom shows only a polar peak at large R. The meridional circulation and convective cells transport heat toward the equator to maintain this difference.

The helicity of the convection plus the differential rotation produced by it suggest the system may be capable of driving a field reversing dynamo, but the toroidal field may migrate with lime in each cycle toward the poles and equator, rather than just toward the equator as apparently occurs on the sun.

We finally outline additions to the physics of the model to make it more realistic for solar application.  相似文献   

7.
Abstract

An inviscid, electrically conducting fluid is contained between two rigid horizontal planes and bounded laterally by two vertical walls. The fluid is permeated by a strong uniform horizontal magnetic field aligned with the side wall boundaries and the entire system rotates rapidly about a vertical axis. The ratio of the magnitudes of the Lorentz and Coriolis forces is characterized by the Elsasser number, A, and the ratio of the thermal and magnetic diffusivities, q. By heating the fluid from below and cooling from above the system becomes unstable to small perturbations when the adverse density gradient as measured by the Rayleigh number, R, is sufficiently large.

With the viscosity ignored the geostrophic velocity, U, which is aligned with the applied magnetic field, is independent of the coordinate parallel to the rotation axis but is an arbitrary function of the horizontal cross-stream coordinate. At the onset of instability the value of U taken ensures that Taylor's condition is met. Specifically the Lorentz force, which results from marginal convection must not cause any acceleration of the geostrophic flow. It is found that the critical Rayleigh number characterising the onset of instability is generally close to the corresponding value for the usual linear problem, in which Taylor's condition is ignored and U is chosen to vanish. Significant differences can occur when q is small owing to a complicated flow structure. There is a central interior region in which the local magnetic Reynolds number, Rm , based on U is small of order q and on exterior region in which Rm is of order unity.  相似文献   

8.
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9.
In wind‐driven rains, wind velocity and direction are expected to affect not only energy input of rains but also shallow ?ow hydraulics by changing roughness induced by raindrop impacts with an angle on ?ow and the unidirectional splashes in the wind direction. A wind‐tunnel study under wind‐driven rains was conducted to determine the effects of horizontal wind velocity and direction on sediment transport by the raindrop‐impacted shallow ?ow. Windless rains and the rains driven by horizontal wind velocities of 6 m s?1, 10 m s?1, and 14 m s?1 were applied to three agricultural soils packed into a 20 by 55 cm soil pan placed on both windward and leeward slopes of 7 per cent, 15 per cent, and 20 per cent. During each rainfall application, sediment and runoff samples were collected at 5‐min intervals at the bottom edge of the soil pan with wide‐mouth bottles and were determined gravimetrically. Based on the interrill erosion mechanics, kinetic energy ?ux (Ern) as a rainfall parameter and product of unit discharge and slope in the form of qbSco as a ?ow parameter were used to explain the interactions between impact and ?ow parameters and sediment transport (qs). The differential sediment transport rates occurred depending on the variation in raindrop trajectory and rain intensity with the wind velocity and direction. Flux of rain energy computed by combining the effects of wind on the velocity, frequency, and angle of raindrop impact reasonably explained the characteristics of wind‐driven rains and acceptably accounted for the differences in sediment delivery rates to the shallow ?ow transport (R2 ≥ 0·78). Further analysis of the Pearson correlation coef?cients between Ern and qSo and qs also showed that wind velocity and direction signi?cantly affected the hydraulics of the shallow ?ow. Ern had a smaller correlation coef?cient with the qs in windward slopes where not only reverse splashes but also reverse lateral raindrop stress with respect to the shallow ?ow direction occurred. However, Ern was as much effective as qSo in the sediment transport in the leeward slopes where advance splashes and advance lateral raindrop stress on the ?ow occurred. Copyright © 2004 John Wiley & Sons, Ltd.  相似文献   

10.
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   

11.
Summary A modified method of computing theS q -range in terms ofR x inH, D andZ has been suggested. Mean quiet-day daily rangesR x , have been computed for five Indian stations usingH, D andZ data for selected years. The seasonal and latitudinal variation ofR x (H), R x (Z) andR x (D) are discusses. Thee-season maximum inR x (H) andR x (Z) is attributed to the decrease in the distance between the foci during equinoxes; the electrojet and theS q -foci movement with seasons have little influence onS q (D). It is inferred that the electrojet current is independent of the worldwideS q current system and stands with its own return currents.The variation of lunar semi-diurnal tide inH[L 2 (H)] with the dip latitude in Indian region shows a secondary peak at 9° N dip latitude. This secondary peak in theL 2 (H) is termed as Lunar secondary electrojet, and it is suggested that this is possibly produced by magneto-acoustic oscillations due to the drift motion of the charged particles that produce the primary jet in a direct transverse to itself.  相似文献   

12.
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   

13.
Soil detachment in concentrated flow is due to the dislodging of soil particles from the soil matrix by surface runoff. Both aggregate stability and shear strength of the topsoil reflect the erosion resistance of soil to concentrated runoff, and are important input parameters in predicting soil detachment models. This study was conducted to develop a formula to predict soil detachment rate in concentrated flow by using the aggregate stability index (As), root density (Rd) and saturated soil strength (σs) in the subtropical Ultisols region of China. The detachment rates of undisturbed topsoil samples collected from eight cultivated soil plots were measured in a 3.8 m long, 0.2 m wide hydraulic flume under five different flow shear stresses (τ = 4.54, 9.38, 15.01, 17.49 and 22.54 Pa). The results indicated that the stability index (As) was well related with soil detachment rate, particularly for results obtained with high flow shear stress (22.54 Pa), and the stability index (As) has a good linear relationship with concentrated flow erodibility factors (Kc). There was a positive linear relationship between saturated soil strength (σs) and critical flow shear stress (τc) for different soils. A significant negative exponential relationship between erodibility factors (Kc) and root density (Rd) was detected. This study yielded two prediction equations that allowed comparison of their efficiency in assessing soil detachment rate in concentrated flow. The equation including the root density (Rd) may have a better correlation coefficient (R2 = 0.95). It was concluded that the formula based on the stability index (As), saturated soil strength (σs) and root density (Rd) has the potential to improve methodology for assessing soil detachment rate in concentrated flow for the subtropical Chinese Ultisols. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

14.
In the light of the single scattering model of coda originating from local earthquakes, and based on the aftershock coda registered respectively at the 4 short period stations installed near the foci shortly after theM7.6 Lancang andM7.2 Gengma earthquakes, this paper has tentatively calculated the rate of amplitude attenuation and theQ c-value of the coda in the Lancang and Gengma areas using a newly-founded synthetic determination method. Result of the study shows the rate of coda amplitude attenuation demonstrates remarkable regional differences respectively in the southern and northern areas. The southern area presents a faster attenuation (Q c=114), whereas the northern area shows a slower attenuation (Q c=231). The paper also discusses the reasons causing such differences. Result of the study also suggests a fairly good linear relation between the coda source factorA o(f) and the seismic moment and the magnitude. Using the earthquake scaling law, the following formulas can be derived: lgM 0=lgA 0(f)+17.6,M D=0.67lgA 0(f)+1.21 and logM 0=1.5M D+15.79. In addition, the rates of amplitude attenuationβ s andβ m are respectively calculated using the single scattering and multiple scattering models, and the ratioβ s/βm=1.20−1.50 is found for the results respectively from the two models. Finally, the mean free pathL of the S-wave scattering in the southern and northern areas are determined to be 54 km and 122 km respectively by the relations which can distinguish between the inherentQ i and scatteringQ s, testify to this areas having lowQ-values correspond to stronger scatterings. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 71–82, 1992. This study is partly supported by the Seismological Science Foundation of the State Seismological Bureau of China, and the present English version of the paper is translated from its Chinese original by Wenyi Xia, Seismological Bureau of Yunnan Province.  相似文献   

15.
Abstract

This paper demonstrates the appearance of tangential discontinuities in deformed force-free fields by direct integration of the field equation ? x B = αB. To keep the mathematics tractable the initial field is chosen to be a layer of linear force-free field Bx = + B 0cosqz, By = — B 0sinqz, Bz = 0, anchored at the distant cylindrical surface ? = (x 2 + y 2)1/2 = R and deformed by application of a local pressure maximum of scale l centered on the origin x = y = 0. In the limit of large R/l the deformed field remains linear, with α = q[1 + O(l 2/R 2)]. The field equations can be integrated over ? = R showing a discontinuity extending along the lines of force crossing the pessure maximum. On the other hand, examination of the continuous solutions to the field equations shows that specification of the normal component on the enclosing boundary ? = R completely determines the connectivity throughout the region, in a form unlike the straight across connections of the initial field. The field can escape this restriction only by developing internal discontinuities.

Casting the field equation in a form that the connectivity can be specified explicitly, reduces the field equation to the eikonal equation, describing the optical analogy, treated in papers II and III of this series. This demonstrates the ubiquitous nature of the tangential discontinuity in a force-free field subject to any local deformation.  相似文献   

16.
Abstract

Electromagnetic induction measurements (EM) were taken in a saline gypsiferous soil of the Saharan-climate Fatnassa oasis (Tunisia) to predict the electrical conductivity of saturated soil extract (ECe) and shallow groundwater properties (depth, Dgw, and electrical conductivity, ECgw) using various models. The soil profile was sampled at 0.2 m depth intervals to 1.2 m for physical and chemical analysis. The best input to predict the log-transformed soil salinity (lnECe) in surface (0–0.2 m) soil was the EMh/EMv ratio. For the 0–0.6 m soil depth interval, the performance of multiple linear regression (MLR) models to predict lnECe was weaker using data collected over various seasons and years (R a 2 = 0.66 and MSE = 0.083 dS m-1) as compared to those collected during the same period (R a 2 = 0.97, MSE = 0.007 dS m-1). For similar seasonal conditions, for the Dgw–EMv relationship, R 2 was 0.88 and the MSE was 0.02 m for Dgw prediction. For a validation subset, the R 2 was 0.85 and the MSE was 0.03 m. Soil salinity was predicted more accurately when groundwater properties were used instead of soil moisture with EM variables as input in the MLR.

Editor D. Koutsoyiannis; Associate editor K. Heal

Citation Bouksila, F., Persson, M., Bahri, A., and Berndtsson, R., 2012. Electromagnetic induction predictions of soil salinity and groundwater properties in a Tunisian Saharan oasis. Hydrological Sciences Journal, 57 (7), 1473–1486.  相似文献   

17.
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   

18.
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19.
On the basis of fault’s dynamic model of Knopoffet al. (1973), this paper has finally obtained a simple approximate formula to be able to estimate the recurrence time intervalT R of earthquake on strike-slip fault. Preliminary result holds thatμ andδ s — δ f have not much effect onT R . Leta is the ratio of the coseismic displacementD s to the total displacementD t in whole event course, i.e.,a =D s /D t , thena = 1/3 may represent the standard theoretical state in whichT R is independent onμ andδ s — δ f . At this time,T R is the arithmetic average ofs 0/v andkd/β, wheres 0 is the long-term preseismic accumulated slippage,v is fault’s average displacement rate,d is the fracture length on the fault of seismic focal region andβ is shear wave velocity. In addition,k =υ 0/aυ, whereυ 0 is the initial fracture velocity of actual structure at the coseismic instant. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 187–194, 1992. This paper is a part of contracted item of State Seismological Bureau — Tectonic Physical Study of Earthquake Recurrence Period and Characteristic Magnitude.  相似文献   

20.
. Kaste  P. J. Dillon 《水文研究》2003,17(12):2393-2407
In‐lake retention of inorganic nitrogen species (nitrate and ammonium) was estimated from mass balances in five acid‐sensitive lakes in southern Norway and eight in southern Ontario, Canada, to evaluate an empirical in‐lake N retention (RN) model. This model is included in the First‐order Acidity Balance (FAB) model, which currently is used for calculation of critical acid loads and exceedances in many countries. To estimate in‐lake RN, the FAB model uses a recommended mass transfer coefficient (SN) of 5 m year−1, which mainly is derived from NO3− mass balances in Canadian lakes. To date, the in‐lake RN model has not been evaluated for large parts of Europe. At the Norwegian study sites receiving the highest N deposition (>120 meq m−2 year−1) the net in‐lake retention of inorganic N (TIN) exceeded the corresponding terrestrial retention by a factor of 1·1–2·6. Despite differences in N loading and hydrology at the Norwegian and Canadian sites, both the mean mass transfer coefficients for NO3− (SNO3; 6·5 versus 5·6 m year−1) and TIN (STIN; 7·9 versus 7·0 m year−1) were of comparable magnitude. Both mean values and ranges of SNO3 suggest that the default SN value presently recommended for FAB model applications seems valid over a large range in N inputs and areal water loads (qs). However, owing to the relatively few data available for lakes with high qs values (15–150 m year−1), it is recommended that more lakes within this range be included in future studies to obtain a more precise prediction of in‐lake N retention over a wide qs gradient. Also, when considering that the FAB model treats all inorganic N leaching from a catchment as NO3−, it seems reasonable to use a default STIN value instead of just SNO3 when estimating in‐lake RN. In that case, the in‐lake RN presently calculated by the FAB model might be slightly underestimated. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

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