共查询到20条相似文献，搜索用时 31 毫秒
1.
O. M. Podvigina 《地球物理与天体物理流体动力学》2013,107(4):409-433
Investigation of magnetic field generation by convective flows is carried out for three values of kinematic Prandtl number: P = 0.3, 1 and 6.8. We consider Rayleigh–Bénard convection in Boussinesq approximation assuming stress-free boundary conditions on horizontal boundaries and periodicity with the same period in the x and y directions. Convective attractors are modelled for increasing Rayleigh numbers for each value of the kinematic Prandtl number. Linear and non-linear dynamo action of these attractors is studied for magnetic Prandtl numbers P m ≤ 100. Flows, which can act as magnetic dynamos, have been found for all the three considered values of P, if the Rayleigh number R is large enough. The minimal R, for which of magnetic field generation occurs, increases with P. The minimum (over R) of critical Pm for magnetic field generation in the kinematic regime is admitted for P = 0.3. Thus, our study indicates that smaller values of P are beneficial for magnetic field generation. 相似文献
2.
R. Hide 《地球物理与天体物理流体动力学》2013,107(1):171-176
Abstract A method has recently been proposed for finding the radius rc of the electrically-conducting fluid core of a planet of outer radius rs from observations of the magnetic field B in the accessible region near or well above the surface of the planet (Hide, 1978). The method is based on the supposition that when the magnetic field is produced by hydromagnetic dynamo action in the core, implying that the magnetic Reynolds number R there is large, (a) fluctuations in B can occur everywhere on the comparatively short advective time-scale τ A associated with fluid motions in the core and so can fluctuations in the quantity N, defined for any closed surface S as the total number of intersection of magnetic lines of force with S, provided that S lies well outside the core, but (b) at the surface of the core, where lines of magnetic force emerge from their region of origin, concomitant fluctuations in N are negligibly small, of the order of τ A/τO where τ O (= RτA ) is the Ohmic decay time of the core. A proof of this supposition follows directly from the general expression derived in the present paper showing that when S is a material surface the time rate of change of N is equal to minus twice the line integral of the current density divided by the electrical conductivity around all the lines on S where the magnetic field is tangential to S. This expression (which Palmer in an accompanying paper rederives and extends to the relativistic case using the mathematical formalism of Cartan’s exterior calculus) also provides a direct demonstration of the well-known result that although high electrical conductivity, sufficient to make R ? 1, is a necessary condition for hydromagnetic dynamo action, such action is impossible in a perfect conductor, when R→ ∞. 相似文献
3.
—?From a data set of 150 digital records of T phases from 71 sources obtained on seismometers of the Polynesian Seismic Network, we define a discriminant separating earthquake and explosion sources, which uses the maximum amplitude of recorded ground velocity, measured on its envelope, e Max (in μm/s), and the duration of the phase measured at 1/3 of maximum amplitude, τ1/3 (in seconds). Earthquake sources and man-made explosions are effectively separated in a log-log space by the straight line ¶¶log10 e Max = 4.9 log10τ1/3 - 4.1 .¶¶Other criteria in both the time and frequency domains fail to reliably separate the populations of the various kinds of events. The application of this technique to analog records of large-scale man-made explosions carried out in the 1960s confirms that it provides an adequate discriminant over 3.5 orders of magnitude of ground velocity. 相似文献
4.
By modelling the observed distribution of210Pb and210Po in surface waters of the Pacific, residence times relative to particulate removal are determined. For the center of the North Pacific gyre these are τPo = 0.6years andτPb = 1.7years. The surface ocean τPb is determined by particulate transport rather than plankton settling. The fact that it is about two orders of magnitude smaller than τPb for the deep ocean implies a sharp change in the adsorptive quality of particles during descent through the water column. 相似文献
5.
Abstract The problem of the removal of the degeneracy of the patterns of convective motion in a spherically symmetric fluid shell by the effects of rotation is considered. It is shown that the axisymmetric solution is preferred in sufficiently thick shells where the minimum Rayleigh number corresponds to degree l = 1 of the spherical harmonics. In all cases with l > 1 the solution described by sectional spherical harmonics Yl l (θ,φ) is preferred. 相似文献
6.
Shawn M. Chartrand A. Mark Jellinek Marwan A. Hassan Carles Ferrer-Boix 《地球表面变化过程与地形》2019,44(15):3020-3041
A river at equilibrium is described by a statistically-stationary mean bed elevation profile that arises in response to steady supplies of relief, water and sediment. Outside of the profile shape, how is the equilibrium state of a river most reliably identified and rigorously defined? Motivated by a proposed link between equilibrium and physical processes, we use scaling theory to develop the dimensionless channel response number ξ=KUb/Up. ξ is a metric for the local disequilibrium state of gravel-bed mountain streams, which reflects a balance between the rate of topographic adjustment Ub, and the rate of bed sediment texture adjustment Up. The coefficient K can take one of two forms depending on choice of length scale for topographic adjustment. We hypothesize that equilibrium occurs where and when ξ≈O(1), and consequently, disequilibrium is the more general state captured by conditions of ξ≉O(1). The rates Ub and Up are controlled by the mechanics of sediment deposition and entrainment at the local scale of the channel width. The extent to which either process regulates disequilibrium depends on the bed strength, which is set by the time-varying grain size distribution and packing. We use flume experiments to understand ξ and find that in the limit ξ>>1, the time-varying response of an experimental channel depends sensitively on the spatially-averaged bed shear stress ratio τ/τref. When τ/τref≈1.5, Ub was the dominant control on disequilibrium. However, when τ/τref≈2.0, Up contributed more significantly to disequilibrium. These results suggest that after an upstream supply perturbation, the equilibrium timescale is governed by Up, which we show is consistent with expectations from linear damping theory. Our experimental test of ξ is promising, but inconclusive with respect to our hypothesis. This uncertainty can be readily addressed with numerical or additional physical experiments. © 2019 John Wiley & Sons, Ltd. 相似文献
7.
The mobility conditions of bedload transport in an alpine high‐gradient step–pool stream (Rio Cordon) are analysed. Since 1986, a device system at the downstream end section of the stream has been operating in order to monitor the water discharge, suspended sediment and bedload transport. Sediment distribution of bedload transported by various floods has been analysed, and equal‐mobility evidence is recognized only for the high‐magnitude flows ever recorded (RI > 50 years). The thresholds for size‐selective and equal‐mobility transport conditions are identified and quantified by using both data provided by the fractional transport rate and by length displacements of marked particles. Size‐selective bedload transport seems to dominate when the critical shear stress of the size fractions τci considered is exceeded, whereas the equal‐mobility condition is approached as levels of excess shear stress become higher (τeqi = 1·45τci). Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
8.
EXPERIMENTAL COMPARISON BETWEEN SPECTRAL RATIO AND RISE TIME TECHNIQUES FOR ATTENUATION MEASUREMENT*
Two techniques for the measurement of attenuation–spectral ratio and rise time techniques–were tested and compared in the laboratory. The spectral ratio technique proved to be reliable and easy to implement for intermediate values (5 < Q < 50) of attenuation. For low (Q > 50) and high attenuations, the spectral ratio technique is inaccurate. Calculating the rise time on simulated signals, we found a relation between rise time τ and the ratio travel-time to quality factor T/Q which could be approximated in intervals by the linear relation τ=τ+C*T/Q. The constants τ and C depend on the absolute value of T/Q and on the initial source signal. The rise time technique, performed on the first quarter period of the signal, enables high attenuations (Q < 5) to be measured. The determination of the relation between τ and T/Q is possible if one knows the initial source. We theoretically approximate this relation through a simulation using a realistic propagation model. With laboratory measurements made on Fontainebleau sandstone, we show that the rise time technique using the theoretical relation τ=τ(T/Q) gives comparable values of Q to those obtained from the spectral ratio technique. In borehole seismics, where it is often difficult to remove undesired signals, the rise time technique applied with the right (τ, T/Q) relation is the best method to use. 相似文献
9.
Abstract An exceptional case to the model-independent theory of Knobloch (1995) is presented, by investigating a rotating cylindrical annulus of height H and side wall radii r o and r i, with non-slip, perfectly thermally conducting side walls and thermally insulating stress-free ends. Radial heating permits the possibility of either two- or three-dimensional convective solutions being the preferred mode. An analytical solution is obtained for the two-dimensional case and a numerical solution for the three-dimensional solution, which is also applied to the two-dimensional solution. It is shown that both two- and three-dimensional solutions can be realized depending on the aspect ratio, γ = H/d, where d = r o-r i is the thickness of the annulus, the radii ratio λ = r i/r o and the rotation rate of the model. For γ = O(1) and λ = 0.4, the preferred convective solution is three-dimensional when the Taylor number, T < 102 and two-dimensional for T > 102. For small aspect ratios, γ ? 1, the preferred mode is two-dimensional for all rotation rates. 相似文献
10.
Abstract In a rapidly rotating, electrically conducting fluid we investigate the thermal stability of the fluid in the presence of an imposed toroidal magnetic field and an imposed toroidal differential rotation. We choose a magnetic field profile that is stable. The familiar role of differential rotation is a stabilising one. We wish to examine the less well known destabilising effect that it can have. In a plane layer model (for which we are restricted to Roberts number q = 0) with differential rotation, U = sΩ(z)1 ?, no choice of Ω(z) led to a destabilising effect. However, in a cylindrical geometry (for which our model permits all values of q) we found that differential rotations U = sΩ(s)1 ? which include a substantial proportion of negative gradient (dΩ/ds ≤ 0) give a destabilising effect which is largest when the magnetic Reynolds number R m = O(10); the critical Rayleigh number, Ra c, is about 7% smaller at minimum than at Rm = 0 for q = 106. We also find that as q is reduced, the destabilising effect is diminished and at q = 10?6, which may be more appropriate to the Earth's core, the effect causes a dip in the critical Rayleigh number of only about 0.001%. This suggests that we see no dip in the plane layer results because of the q = 0 condition. In the above results, the Elsasser number A = 1 but the effect of differential rotation is also dependent on A. Earlier work has shown a smooth transition from thermal to differential rotation driven instability at high A [A = O(100)]. We find, at intermediate A [A = O(10)], a dip in the Rac vs. Rm curve similar to the A = 1 case. However, it has Rac ≤ 0 at its minimum and unlike the results for high A, larger values of Rm result in a restabilisation. 相似文献
11.
R. S. Sidhu 《Pure and Applied Geophysics》1970,80(1):48-70
Summary The frequency equation of Rayleigh waves propagating over the free surface of an isotropic, perfectly elastic, heterogeneous semi-infinite medium with material properties varying as =
0
e
az
, =
0
e
az
, =
0
e
az
(a>0) has been obtained. Solution of the frequency equation in closed form is obtained in two cases (i) =0, (ii) =, and the Rayleigh wave dispersion curves for phase and group velocities drawn. In both the cases the medium yields single Rayleigh modes which cannot propagate below certain cut-off frequencies. It is found that in case (i), <c<c
0 and 0.87500 <c
g
<c
0, and in case (ii), 1.03082 <c<c
1 and 0.90850 <c
g
<c
1, wherec andc
g
denote phase nad group velocities respectively, is the constant shear wave velocity of the mediumc
0 andc
1 are the corresponding Rayleigh wave velocities of the homogeneous medium of the same Poisson's ratio. The motion of the surface particles is found to be retrograde elliptical as in the homogeneous case, but the ratic of the major and minor axes now becomes frequency dependent and is plotted against frequency. In both the cases (i) and (ii), the ratio starts at a lower value at the cut-off frequency and approaches the corresponding value of the homogeneous medium at high frequencies. 相似文献
12.
Whether in the mantle or in magma chambers, convective flows are characterized by large variations of viscosity. We study the influence of the viscosity structure on the development of convective instabilities in a viscous fluid which is cooled from above. The upper and lower boundaries of the fluid are stress-free. A viscosity dependence with depth of the form ν0 + ν1 exp(?γ.z) is assumed. After the temperature of the top boundary is lowered, velocity and temperature perturbations are followed numerically until convective breakdown occurs. Viscosity contrasts of up to 107 and Rayleigh numbers of up to 108 are studied.For intermediate viscosity contrasts (around 103), convective breakdown is characterized by the almost simultaneous appearance of two modes of instability. One involves the whole fluid layer, has a large horizontal wavelength (several times the layer depth) and exhibits plate-like behaviour. The other mode has a much smaller wavelength and develops below a rigid lid. The “whole layer” mode dominates for small viscosity contrasts but is suppressed by viscous dissipation at large viscosity contrasts.For the “rigid lid” mode, we emphasize that it is the form of the viscosity variation which determines the instability. For steep viscosity profiles, convective flow does not penetrate deeply in the viscous region and only weak convection develops. We propose a simple method to define the rigid lid thickness. We are thus able to compute the true depth extent and the effective driving temperature difference of convective flow. Because viscosity contrasts in the convecting region do not exceed 100, simple scaling arguments are sufficient to describe the instability. The critical wavelength is proportional to the thickness of the thermal boundary layer below the rigid lid. Convection occurs when a Rayleigh number defined locally exceeds a critical value of 160–200. Finally, we show that a local Rayleigh number can be computed at any depth in the fluid and that convection develops below depth zr (the rigid lid thickness) such that this number is maximum.The simple similarity laws are applied to the upper mantle beneath oceans and yield estimates of 5 × 1015?5 × 1016 m2 s?1 for viscosity in the thermal boundary layer below the plate. 相似文献
13.
14.
N. A. Silant'ev 《地球物理与天体物理流体动力学》2013,107(2-4):183-197
Abstract The exact numerical and approximate analytical solutions of the simplest nonlinear integral equation with second order nonlinearity for the averaged Green function are presented. It is assumed that the turbulence is stationary, homogeneous, isotropic and incompressible. Numerous examples of turbulent spectra are considered (peak-like spectrum, spectra of Kolmogorov's type with different forms of “pumping” regions, stepwise spectra etc.). Special emphasis is given to investigating the case of so called “frozen” turbulence when the parameter ξ =u 0τ/R→∞ where uτ0,R 0 are characteristic velocity, lifetime and space scale of turbulent pulsations, respectively. It is shown that these solutions allow us to calculate the turbulent diffusivities accurately for arbitrary spectra with any values of the parameter ξ. The results take into account the possible helicity of turbulence concerned only with scalar passive fields (number density and temperature). 相似文献
15.
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
16.
Excess stress parameters, critical shear stress (τc) and erodibility coefficient (kd), for degrading channels in the loess areas of the midwestern USA are presented based on in situ jet‐testing measurements. Critical shear stress and kd are used to define the erosion resistance of the streambed. The jet‐testing apparatus applies hydraulic stresses to the bed and the resulting scour due to the impinging jet is related to the excess stress parameters. Streams tested were primarily silt‐bedded in texture with low densities, which is typical of loess soils. Results indicate that there is a wide variation in the erosion resistance of streambeds, spanning six orders of magnitude for τc and four orders of magnitude for kd. Erosion resistance was observed to vary within a streambed, from streambed to streambed, and from region to region. An example of the diversity of materials within a river system is the Yalobusha River Basin in Mississippi. The median value of τc for the two primary bed materials, Naheola and Porters Creek Clay Formations, was 1·31 and 256 Pa, respectively. Streambeds composed of the Naheola Formation are readily eroded over the entire range of shear stresses, whereas only the deepest flows generate boundary stresses great enough to erode streambeds composed of the Porters Creek Clay Formation. Therefore, assessing material resistance and location is essential in classifying and modelling streambed erosion processes of these streams. 相似文献
17.
Unstable density‐driven groundwater flow and solute transport (i.e., free convection) leads to spatiotemporal variations in pressure. Specific storage (So) indicates the capability of a confined aquifer to release or store groundwater associated with a pressure change. Although So is known to dampen pressure propagation, So has been implicitly assumed to have a negligible impact on the unstable free convective process in prior studies. This work explores the effect of So on both the classic onset criterion and the fingering process using numerical models. Results show that the classic onset criterion is applicable when So is smaller than 10–1 m–1. Results also demonstrate that So does not play a significant role in the free convective fingering process unless it is greater than 10–3 m–1. For most practical purposes in hydrogeology (large Rayleigh number and small So), the implicit assumption of small or zero So is appropriate. 相似文献
18.
Following up our recent study of an indirect procedure for the practical determination of the maximum frequency-effect, defined as fe = 1 ? pρ∞/ρdc with ρ∞ the resistivity at infinite frequency, we show at first how, through the Laplace transform theory, ρ∞ can be related to stationary field vectors in the simple form of Ohm's law. Then applying the equation of continuity for stationary currents with a suitable set of boundary conditions, we derive the integral expression of the apparent resistivity at infinite frequency ρ∞,a in the case of a horizontally layered earth. Finally, from the definition of the maximum apparent frequency-effect, analytical expressions of feα are obtained for both Schlumberger and dipole arrays placed on the surface of the multi-layered earth section in the most general situation of vertical changes in induced polarization together with dc resistivity variations not at the same interfaces. Direct interpretation procedures are suggested for obtaining the layering parameters directly from the analysis of the sounding curves. 相似文献
19.
Abstract Nonlinear interactions of deviatoric stress components and the velocity field occur in all dynamic flows where convected elasticity is accounted for. By incorporating a linear Maxwellian constitutive relation (Oldroyd ‘B’ type) into a finite-amplitude convection model we quantify the magnitude of some of the effects of these nonlinear interactions. For viscoelastic flows the relevant nondimensional parameter is the ratio of viscoelastic constitutive relaxation time constant, λ1, to the basic flow process time. The Rayleigh number, Ra, and the nondimensional ratio of λ1 to thermal conduction time, τc, are part of the parameter space investigated. However, shorter basic flow time scales than that for thermal equilibration are of interest since most viscoelastic fluids have relatively small values of λ1 The ratio of λ1 to buoyant time [bcirc], or λ1/[bcirc], is, therefore, a pertinent parameter. Using both lithospheric and aesthenospheric values for λ1, the ratio appropriate to mantle convection is roughly bounded by O(1)[bcirc]>λ1/[bcirc]>O(10?6). Employing these bounds and computing low Rayleigh number time-dependent convective flows in a two-dimensional box, it is demonstrated that viscoelasticity has a negligible influence on quasi-steady heat transport even for λ1/[bcirc]～O(1) For any time-dependent behavior with time scales as short, or shorter than, the buoyant time, [bcirc], viscoelasticity might be important to the local exchange of mechanical energy. The recoverable strain energy in the descending portion of the lithosphere is comparable to the local viscous dissipation. The magnitude of this recoverable component of shear is proportional to λ1/[bcirc]. 相似文献
20.
Little Kickapoo Creek (LKC), a low‐gradient stream, mobilizes its streambed–fundamentally altering its near‐surface hyporheic zone–more frequently than do higher‐gradient mountain and karst streams. LKC streambed mobility was assessed through streambed surveys, sediment sampling, and theoretical calculations comparing basal shear stress (τb) with critical shear stress (τc). Baseflow τb is capable of entraining a d50 particle; bankfull flow could entrain a 51·2 mm particle. No particle that large occurs in the top 30 cm of the substrate, suggesting that the top 30 cm of the substrate is mobilized and redistributed during bankfull events. Bankfull events occur on average every 7·6 months; flows capable of entraining d50 and d85 particles occur on average every 0·85 and 2·1 months, respectively. Streambed surveys verify streambed mobility at conditions below bankfull. While higher gradient streams have higher potential energy than LKC, they achieve streambed‐mobilization thresholds less frequently. Heterogeneous sediment redistribution creates an environment where substrate hydraulic conductivity (K) varies over four orders of magnitude. The frequency and magnitude of the substrate entrainment has implications on hyporheic zone function in fluid, solute and thermal transport models, interpretations of hyporheic zone stability, and understanding of LKC's aquatic ecosystem. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献