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1.
We present a new development in the asymmetric continuum theory with the shear oscillations (twist motions) and independent spin; these motions (displacement velocities and spin) can be shifted in phase to describe the independent rebound processes. Our approach provides an extension of the asymmetric continuum theory by including the microfragmentation processes with a double transport which may appear in an advanced fracture process under very high load. The related nonlinear equations, leading to soliton solutions, are derived.  相似文献   

2.
A first-order perturbation theory for seismic isochrons is presented in a model independent form. Two ray concepts are fundamental in this theory, the isochron ray and the velocity ray, for which I obtain first-order approximations to position vectors and slowness vectors. Furthermore, isochron points are connected to a shot and receiver by conventional ray fields. Based on independent perturbation of the shot and receiver ray I obtain first-order approximations to velocity rays. The theory is applicable for 3D inhomogeneous anisotropic media, given that the shot and receiver rays, as well as their perturbations, can be generated with such model generality. The theory has applications in sensitivity analysis of prestack depth migration and in velocity model updating. Numerical examples of isochron and velocity rays are shown for a 2D homogeneous VTI model. The general impression is that the first-order approximation is, with some exceptions, sufficiently accurate for practical applications using an anisotropic velocity model.  相似文献   

3.
Abstract

Some new measurements are presented of the axisymmetric heat transport in a differentially heated rotating fluid annulus. Both rigid and free upper surface cases are studied, for Prandtl numbers of 7 and 45, from low to high rotation rates. The rigid lid case is extended to high rotation rates by suppressing the baroclinic waves, that would normally develop at some intermediate rotation rate, with the use of sloping endwalls.

A parameter P is defined as the square of the ratio of the (non-rotating) thermal sidewall layer thickness to the Ekman layer thickness. For small P the heat transport remains unaffected by the rotation, but as P increases to order unity the Ekman layer becomes thin enough to inhibit the radial mass transport, and hence the heat flux. No explicit Prandtl number dependence is observed. Also this scaling allows the identification of the region in which the azimuthal velocity reaches its maximum. Direct comparisons are drawn with previous experimental and numerical results, which show what can be interpreted as an inhibiting effect of increasing curvature on the heat transport.  相似文献   

4.
Abstract

The flow properties of an homogeneous fluid which is bounded by two concentric spheres and two meridional planes which intersect along a diameter of the spheres are investigated. The spheres rotate about this diameter with slightly different angular velocities. As in the axisymmetric case studied by Proudman (1956) and Stewartson (1966) the viscous terms in the equations of motion are important only in boundary layers on the spheres and on the cylinder C which circumscribes the inner sphere and which has generators parallel to the axis of rotation, provided the Ekman number E is small. In the inviscid region the velocities are independent of the coordinate measuring distance along the axis of rotation and are much weaker, by a factor 0(E ½), than the velocities in the Ekman layer on the driving surface (outer sphere). (It is assumed that the reference frame is fixed in the slower rotating inner sphere.) If the separation of the spheres is small compared to their radii then the asymmetric circulation inside C is characterized by an intense jet along the western wall. Loss of fluid from this jet sustains the eastward and northward flow in the inviscid interior where motion is driven by the suction of the Ekman layer on the outer sphere. (Geophysical conventions have been adopted.) Outside C an intense current is present on the eastern, not western, wall while motion in the inviscid region is westward, and away from the axis of rotation. Though there is no transport across C in the inviscid region, the meridional transport of the Ekman layer on the outer sphere is continuous across C and increases, through suction, as the equator is approached until it drains into an eastward flowing equatorial current of width 0(E 1/7). The eastern boundary current outside C and shear layers on C carry this fluid to the intersection of C and the western wall where it feeds the western boundary current inside C.

The relation between this study and the experiments of Baker and Robinson (1970) is discussed.  相似文献   

5.
Stratified flow in pyroclastic surges   总被引：1，自引：0，他引：1  
Stratified flow theory is applied to pyroclatic surges in an effort to gain insight into transport dynamics during explosive eruptions. Particle transport is assumed to be by turbulent suspension, and calculations contained herein show that this is likely for many cases including the 18 May 1980 blast at mount St. Helens. The discussion centers on the Rouse number (Pn), which represents a ratio of particle settling velocity to scale of turbulence; the Brunt-Väisälä frequency (N), which is the maximum possible frequency of internal waves; the Froude number (Fr), representing the ratio of inertial forces to gravitational forces; and the Richardson number (Ri), a ratio of buoyant restoring forces to turbulent mixing forces. The velocity or flow power dependence of bed-form wavelength in surge deposits is related to a velocity dependence of wavelength of internal waves in the turbulent surge. This produces a decrease in dune wavelength with increasing distance from vent. Migration direction of bed forms is related toFr as it is defined for a continuously stratified flow. Proximal to distal facies variations in surge deposits reflect increasingPn andRi as the flows move away from their sources. This produces the progression from sandwave to massive to planar facies with increasing distance from vent. Where the long axis of topography is at low angles to the flow direction, massive facies in topographic lows may from concurrently with sandwave facies on highs, due to the higher particle concentration in the lows. Where long axis of topography is at high angles to flow direction, denser lower parts of the surge may be dammed or blocked. Blocked material tends to form massive flows that may move down slope independent of the overriding surge. A model incorporating turbulent transport, stratified flow, and time evolution of pyroclastic surges is proposed for deposits which have been attributed to both pyroclastic flow and pyroclastic surge transport by various workers. During the initial high energy (waxing) phase of the eruptive event,Pn is sufficiently low that only coarse, but poorly sorted, material is deposited to form relatively coarse bottom layers. As the event wanes, remaining finer material is deposited through a thin bed load to produce overlying bedded and cross-bedded veneer deposits. Throughout most of the event, blocking occurs to produce relatively thick and massive deposits in valley bottoms.  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.
A dynamo driven by motions unaffected by viscous forces is termed magnetostrophic. Although such a model might describe magnetic field generation in Earth’s core well, a magnetostrophic dynamo has not yet been found even though Taylor [Proc. R. Soc. Lond. A 1963, 274, 274–283] devised an apparently viable method of finding one. His method for determining the fluid velocity from the magnetic field and the energy source involved only the evaluation of integrals along lines parallel to the Earth’s axis of rotation and the solution of a second-order ordinary differential equation. It is demonstrated below that an approximate solution of this equation for a broad family of magnetic fields is immediate. Furthermore inertia, which was neglected in Taylor’s theory, is restored here, so that the modified theory includes torsional waves, whose existence in the Earth’s core has been inferred from observations of the length of day. Their theory is reconsidered.  相似文献   

8.

Linear and nonlinear dynamo action is investigated for square patterns in nonrotating and weakly rotating Boussinesq Rayleigh-Bénard convection in a plane horizontal layer. The square-pattern solutions may or may not be symmetric to up-down reflections. Vertically symmetric solutions correspond to checkerboard patterns. They do not possess a net kinetic helicity and are found to be incapable of kinematic dynamo action at least up to magnetic Reynolds numbers of , 12 000. There also exist vertically asymmetric squares, characterized by rising (descending) motion in the centers and descending (rising) motion near the boundaries, among them such that possess full horizontal square symmetry and others lacking also this symmetry. The flows lacking both the vertical and horizontal symmetries possess kinetic helicity and show kinematic dynamo action even without rotation. The generated magnetic fields are concentrated in vertically oriented filamentary structures. Without rotation these dynamos are, however, always only kinematic, not nonlinear dynamos since the back-reaction of the magnetic field then forces the solution into the basin of attraction of a roll pattern incapable of dynamo action. But with rotation added parameter regions are found where stationary asymmetric squares are also nonlinear dynamos. These nonlinear dynamos are characterized by a subtle balance between the Coriolis and Lorentz forces. In some parameter regions also nonlinear dynamos with flows in the form of oscillating squares or stationary modulated rolls are found.  相似文献   

9.
Abstract

The steady second-order motion induced by a first-order wave motion in a homogeneous, viscous and rotating fluid is examined. If the wave motion produces a steady Ekman layer suction by non-linear interactions, this suction must induce a steady component of interior, relative vorticity parallel to the axis of rotation in order to conserve mass. A boundary value problem for the determination of the induced, steady interior mass transport velocity is presented. The mass transport induced by a Kelvin wave is examined as an illustration and possible application of the theory.  相似文献   

10.
Diagnosing vertical motion in the Equatorial Atlantic   总被引：2，自引：0，他引：2  
Estimating the vertical velocity (w) in the oceanic upper-layers is a key issue for understanding the cold tongue development in the Eastern Equatorial Atlantic. In this methodological paper, we develop an expanded and general formulation of the vertical velocity equation based on the primitive equation (PE) system, in order to gain new insight into the physical processes responsible for the Equatorial and Angola upwellings. This approach is more accurate for describing the real ocean than simpler considerations based on just the wind-driven patterns of surface layer divergence. The w-sources/forcings are derived from the PE w-equation and diagnosed from a realistic ocean simulation of the Equatorial Atlantic. Sources of w are numerous and express the high complexity of terms related to the turbulent momentum flux, to the circulation and to the mass fields, some of them depending explicitly on w and others not. The equatorial upwelling is found to be mainly induced by the (i) the zonal turbulent momentum flux, (ii) the curl of turbulent momentum flux and (iii) the imbalance between the circulation and the pressure fields. The Angola upwelling in the eastern part of the basin is controlled by strong curl of turbulent momentum flux. A strong cross-regulation is evidenced between the w-forcings independent of w and dependent on w, which suggests an equatorial balanced-dynamics. The w-forcing depending on w represents the negative feedback of the ocean to the w-forcing independent of w: in the equatorial band, this adjustment is led by non-linear processes and by vortex stretching outside.  相似文献   

11.
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12.
《水文科学杂志》2013,58(6):1286-1299
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13.
The results of the laboratory and numerical experiments in circular rotating trays with thin layers of a conductive fluid under the MHD generation of small-scale velocity fields are presented. The configurations of constant magnets for MHD generation were determined based on the numerical calculations with shallow water equations. Both the laboratory and numerical experiments with rotating trays demonstrate the emergence of nonaxisymmetric structures and large-scale near-circular vortices caused by the energy transfer from the system of the externally generated small-scale vortices to the large-scale velocity fields under the action of the Coriolis force. The near-circular vortex has areas with differential rotation when the angular velocity of rotation decreases with the radius. The single large-scale vortices and wide jet flows arise in the regimes of subrotation and superrotation relative to the external rotation depending on its angular velocity. The emergence of the flow structures with the azimuthal wave number m = 2 is demonstrated, and their probable relation to the anomalies of the geomagnetic field observed on the Earth’s surface is considered.  相似文献   

14.
Alluvial gullies are often formed in dispersible sodic soils along steep banks of incised river channels. Field data collected by Shellberg et al. (Earth Surface Processes and Landforms 38: 1765–1778, 2013) from a gully outlet in northern Australia showed little hysteresis between water discharge and fine (<63 µm) and coarse (>63 µm) suspended sediment, indicating transport‐limited rather than source‐limited conditions. The major source of the fine (silt/clay) component was the sodic soils of upstream gully scarps, and the coarser (sand) component was sourced locally from channel bed material. In this companion paper at the same study site, a new method was developed for combining the settling velocity characteristics of these two sediment source components to estimate the average settling velocity of the total suspended sediment. This was compared to the analysis of limited sediment samples collected during flood conditions. These settling velocity data were used in the steady‐state transport limit theory of Hairsine and Rose (Water Resources Research 28: 237–243, 245–250, 1992) that successfully predicted field data of concentrations and loads at a cross‐section, regardless of the complexity of transport‐limited upstream sources (sheet erosion, scalds, rills, gullies, mass failure, bank and bed erosion, other disturbed areas). The analysis required calibration of a key model parameter, the fraction of total stream power (F ≈ 0.025) that is effective in re‐entraining sediment. Practical recommendations are provided for the prediction of sediment loads from other alluvial gullies in the region with similar hydrogeomorphic conditions, using average stream power efficiency factors for suspended silt/clay (Fw ≈ 0.016) and sand (Fs ≈ 0.038) respectively, but with no requirement for field data on sediment concentrations. Only basic field data on settling velocity characteristics from soil samples, channel geometry measurements, estimates of water velocity and discharge, and associated error margins are needed for transport limit theory predictions of concentration and load. This theory is simpler than that required in source‐limited situations. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

15.
Flow and transport in channels with submerged vegetation   总被引：3，自引：0，他引：3  
This paper reviews recent work on flow and transport in channels with submerged vegetation, including discussions of turbulence structure, mean velocity profiles, and dispersion. For submerged canopies of sufficient density, the dominant characteristic of the flow is the generation of a shear-layer at the top of the canopy. The shear-layer generates coherent vortices by Kelvin-Helmholtz (KH) instability. These vortices control the vertical exchange of mass and momentum, influencing both the mean velocity profile, as well as the turbulent diffusivity. For flexible canopies, the passage of the KH vortices generates a progressive wave along the canopy interface, termed monami. The KH vortices formed at the top of the canopy penetrate a distance δ e into the canopy. This penetration scale segregates the canopy into an upper layer of rapid transport and a lower layer of slow transport. Flushing of the upper canopy is enhanced by the energetic shear-scale vortices. In the lower layer turbulence is limited to length-scales set by the stem geometry, and the resulting transport is significantly slower than that of the upper layer.  相似文献   

16.
Aeolian sand transport is a complicated process that is affected by many factors (e.g. wind velocity, sand particle size, surface microtopography). Under different experimental conditions, erosion processes will therefore produce different results. In this study, we conducted a series of wind tunnel experiments across a range of wind velocities capable of entraining sand particles (8.0, 10.0, 12.0, and 14.0 m s-1) to study the dynamic changes of the shear velocity, aerodynamic roughness length, and sand transport. We found that the shear velocity and aerodynamic roughness length are not constant; rather, they change dynamically over time, and the rules that describe their changes depend on the free-stream air velocity. For wind tunnel experiments without feeding sand into the airflow, the sand bed elevation decreases with increasing erosion time, and this change significantly affected the values of shear velocity and aerodynamic roughness length. A Gaussian distribution function described the relationships between the sand transport rate (qT) and the duration of wind erosion (T). It is therefore necessary for modelers to consider both deflation of the bed and the time scale used when calculating sand transport or erosion rates. © 2018 John Wiley & Sons, Ltd.  相似文献   

17.
Abstract

we report the results of experiments on the spin-up of two layers of immiscible fluid with a free upper surface in a rotating cylinder over a wide range of internal Froude numbers. Observations of the evolution of the velocity field by particle tracking indicates that spin-up of the azimuthal velocity in the upper layer take much longer than in a homogeneous fluid. Initially, spin-up occurs at a rate comparable to that of homogeneous fluid but, at high internal Froude number, a second phase follows in which the remaining lative motion decays much more slowly. Quantitative comparison of these measurements to the theory of Pedlosky (1967) shows good agreement.

Visualization of the interface displacement during spin-up detected the presence of transient azimuthal variations in the interface elevation over a wide range of Froude (F), Ekman (E), and Rossby (ε) number. nalysis of the occurrence of the asymmetric variations using the parameter space (Q, F), where Q = E 1/2/ε, suggested by the baroclinic instability theory and experiments of Hart (1972), showed that the flow was stable for Q > 0.06 with no discernable dependence on F. This result, together with the prediction of Pedlosky's theory that radial gradient of potential vorticity in the two layers have opposite signs, suggests at the baroclinic instability mechanism was responsible for the asymmetries. The location and timing of these instabilities may account for the discrepancies between the observations and the Pedlosky (1967) theory.  相似文献   

18.
Unsteady bedload transport was measured in two c. 5 m wide anabranches of a gravel‐bed braided stream draining the Haut Glacier d'Arolla, Switzerland, during the 1998 and 1999 melt seasons. Bedload was directly sampled using 152 mm square Helley–Smith type samplers deployed from a portable measuring bridge, and independent transport rate estimates for the coarser size fractions were obtained from the dispersion of magnetically tagged tracer pebbles. Bedload transport time series show pulsing behaviour under both marginal (1998) and partial (1999) transport regimes. There are generally weak correlations between transport rates and shear stresses determined from velocity data recorded at the measuring bridge. Characteristic parameters of the bedload grain‐size distributions (D50, D84) are weakly correlated with transport rates. Analysis of full bedload grain‐size distributions reveals greater structure, with a tendency for transport to become less size selective at higher transport rates. The bedload time series show autoregressive behaviour but are dif?cult to distinguish by this method. State–space plots, and associated measures of time‐series separation, reveal the structure of the time series more clearly. The measured pulses have distinctly different time‐series characteristics from those modelled using a one‐dimensional sediment routing model in which bed shear stress and grain size are varied randomly. These results suggest a mechanism of pulse generation based on irregular low‐amplitude bedforms, that may be generated in‐channel or may represent the advection of material supplied by bank erosion events. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

19.
Previous studies of plate dynamics suggest that, at consuming plate boundaries, driving forces (negative buoyancy) acting on the slab are counterbalanced by viscous forces, proportional to the consumption velocity and resisting the downgoing motion into the mantle. New observations on the geometry of subduction zones may help test this equilibrium theory. A condition for local equilibrium of the driving and resistive forces is that the consumption velocity (V⊥) remains constant along a given trench. From this condition, a geometrical property of the shape of trenches and island arcs on the sphere is inferred: the consuming margin of two plates should follow segments of helices about the axis of rotation of their relative motion. A comparison of the shape of island arcs and trenches with helices supports this inference.  相似文献   

20.
A test is proposed for Bagnold's postulate that the normal weight stress due to moving ‘bedload’ is balanced by a solid transmitted stress due to the rate of change of momentum produced by grain impacts on unit area of the stationary bed. The test involves derivation of an expression for normal momentum transfer due to saltating grains at moderate transport stages when grain-to-grain collisions and partial suspension during saltation may be ignored. A dimensionless number, Φ, (a grain Froude Number) is derived, given by ū2/g where ū is the mean grain forward velocity, g is the gravitational acceleration and L? is the length of a single saltation ‘jump’. Equilibrium demands that Φ be unity during bedload transport involving saltating grains if Bagnold's postulate is correct. Experimental data shows Φ < 1, the discrepancy between theory and experiment being due to the existence of lift forces acting upon bedload grains. Bagnold's postulate is correct for concentrated dispersions of grains, as in grain flows, when fluid lift forces may be neglected due to high particle concentration.  相似文献   

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