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1.
The influence of the interplanetary magnetic field (IMF) on the occurrence of sporadic E (Es)-layers in the southern polar cap ionosphere has been investigated. We statistically analysed ionogram and Doppler velocity observations made using a HF digital ionosonde located at Casey, Antarctica (66.3°S, 110.5°E; 81°S magnetic latitude) during the two summer campaign intervals 1 January to 18 February, and 1 November to 31 December 1997. The ionogram and Doppler velocity measurements were used to determine the Es-occurrence and electric field vectors (assuming E×B/B2 drift), respectively. Concurrent IMF data were obtained from measurements made on board the Wind spacecraft. First, the gross properties of the IMF dependence of Es-formation were obtained: the occurrence rate was higher for negative By and/or positive Bz, and lower for positive By and/or negative Bz. To reconcile these gross properties with the electric field theory of Es-layer formation, the detailed diurnal variation of both Es-occurrence and the ionospheric electric field were obtained for different orientations of the IMF. The main statistical results are that: (1) the By component mainly controls the occurrence of the midnight Es-layers through its influence on the corresponding South West electric field; and (2) the Bz component mainly controls the occurrence of the evening Es-layers. However, the change in the occurrence rate for evening Es-layers was not related to the strength of the associated North West and North East electric fields. The total occurrence of Es-layers depended more on By than on Bz, owing to the dominance of By-controlled midnight Es-layers in the occurrence distribution. Nevertheless, the dependence of Es-occurrence on Bz was important. We suggest that the increase in Es-occurrence for positive Bz might be explained by the intermittent production of lower F-region ionisation by polar showers and squalls, which also increase in frequency and intensity for positive Bz. The importance of metallic ion transport within the ionosphere is also considered.  相似文献   

2.
Abstract

Adiabatic, two-dimensional, steady-state finite-amplitude, hydrostatic gravity waves produced by flow over a ridge are considered. Nonlinear self advection steepens the wave until the streamlines attain a vertical slope at a critical height zc. The height zc , where this occurs, depends on the ridge crest height and adiabatic expansion of the atmosphere. Dissipation is introduced in order to balance nonlinear self advection, and to maintain a marginal state above zc. The approach is to assume that the wave is inviscid except in a thin layer, small compared to a vertical wavelength, where dissipation cannot be neglected. The solutions in each region are matched to obtain a continuous solution for the streamline displacement δ. Solutions are presented for different values of the nondimensional dissipation parameter β. Eddy viscosity coefficients and the thickness of the dissipative layer are expressed as functions of β, and their magnitudes are compared to other theoretical evaluations and to values inferred from radar measurements of the stratosphere.

The Fourier spectrum of the solution for z ≫ zc is shown to decay exponentially at large vertical wave numbers n. In comparison, a spectral decay law n ?-8/3 characterizes the marginal state of the wave at z = zc .  相似文献   

3.
This is the first of a two‐part paper exploring the coevolution of bedrock weathering and lateral flow in hillslopes using a simple low‐dimensional model based on hydraulic groundwater theory (also known as Dupuit or Boussinesq theory). Here, we examine the effect of lateral flow on the downward fluxes of water and solutes through perched groundwater at steady state. We derive analytical expressions describing the decline in the downward flux rate with depth. Using these, we obtain analytical expressions for water age in a number of cases. The results show that when the permeability field is homogeneous, the spatial structure of water age depends qualitatively on a single dimensionless number, Hi. This number captures the relative contributions to the lateral hydraulic potential gradient of the relief of the lower‐most impermeable boundary (which may be below the weathering front within permeable or incipiently weathered bedrock) and the water table. A “scaled lateral symmetry” exists when Hi is low: age varies primarily in the vertical dimension, and variations in the horizontal dimension x almost disappear when the vertical dimension z is expressed as a fraction z/H(x) of the laterally flowing system thickness H(x). Taking advantage of this symmetry, we show how the lateral dimension of the advection–diffusion‐reaction equation can be collapsed, yielding a 1‐D vertical equation in which the advective flux downward declines with depth. The equation holds even when the permeability field is not homogeneous, as long as the variations in permeability have the same scaled lateral symmetry structure. This new 1‐D approximation is used in the accompanying paper to extend chemical weathering models derived for 1‐D columns to hillslope domains.  相似文献   

4.
Inverse dynamo theory seeks to gain information about the motion of a liquid conductor from measurements of the magnetic field in the surrounding vacuum. We consider here a highly simplified model problem, namely a steady α2-dynamo in plane geometry with an α-field varying only in the z-direction normal to the conductor–vacuum interface. Based on perturbation theory about constant-α solutions, we find as many integral conditions on α(z) as modes are present in the vacuum field. This result is corroborated by the complete solution of a special case.  相似文献   

5.
The first part of this paper examines a special case of acoustical imaging in which the source and the receiver coincide. The benefits of weighting and muting are studied in detail by means of computer modeling. The test model consists of a single planar interface z=z1, abruptly terminated at x= o. The amplitude and phase responses are computed in the plane z=z0= o for two separations of neighboring stations, Δx=λ/10 and Δx=λ/2. Six different weighting factors are used in the test. However, in this source-receiver coincident case, three of the weighting factors produce identical responses, so that all six test factors may be represented by only four curves. It is found that when the spatial sampling at the aperture approaches the condition of critical sampling, i.e. Δx=λ/2, only the weighting factor which implicitly takes into account beam steering along the specular reflection path is acceptable. This factor alone keeps the amplitude and the phase curves undistorted until the difference 2 ·ΔR between two neighboring paths reaches approximately λ/2. If we set 2 ·ΔR=λ/2, we may construct a set of curves which we may call quite appropriately muting curves. These curves are physically interpretable only for station separation Δx > λ/4. The muting curves are symmetrical about the line x= 0 and their angular opening depends on spatial separation Δx, depth z, and wavelength λ (which may vary with depth). The second part of this paper suggests how the weighting factor with implicit beam steering can be applied to reconstruction of two and three-dimensional wavefields. Seismic migration of common depth point (CDP) stacked line data is also discussed. This is a hybrid case which presents certain theoretical difficulties. We shall also mention the velocity problem which is inherent to migration of CDP stacked data. The third and final part concerns implementation of the migration of CDP stacked data. When the spatial sampling is between λ/4 and λ/2, the migration process will benefit from beam steering and from muting. The benefits are more subtle when the separation of the traces is less than λ/4. However, in that case the cost of data collection is considerable and often prohibitive. In either case the migration of seismic data can be expedited by use of precalculated tables of migration velocities, ray path distances, and weights (including muting).  相似文献   

6.
Summary In this paper, the problem of a normal load moving over the surface of a layer of ice, lying on a rigid foundation, has been considered. FollowingHearmon, the ice is taken to be transversely isotropic. Two cases have been considered-in the first case, the rigid foundation is taken to be smooth, and in the second case, it is taken to be in welded contact with the layer of ice. Expressions have been obtained in both cases for the stresses at any point of the layer. From detailed numerical calculations, it has been found that the value of the normal stress at a point directly below the moving load falls of approximately as that of 1/z with increase in the depthz below the surface. On calculating the normal stress at the boundary between the layer of ice and the foundation, it is found that the normal stress falls off rapidly as we move away along the boundary from the point directly below the load.  相似文献   

7.
Homogeneous, nonrotating flow over a backward-facing rounded step is simulated using the 2D vertical version of two general circulation models, a z-coordinate model—the Massachusetts Institute of Technology general circulation model (MITgcm)—and a σ-coordinate model—the Bergen Ocean Model (BOM). The backward-facing step is a well-known testcase since it is geometrically simple but still embodies important flow characteristics such as separation point, reattachment length, and recirculation of the flow. The study compares the core of the two models and uses constant eddy viscosities and diffusivities. The Reynolds numbers ranges from 2·102 to 2·106. The results correspond with previously published results having a relatively stationary separation point and a fluctuating reattachment length due to downslope propagating eddies released from the reattachment zone for Reynolds numbers higher than or equal to 2 · 104. For Reynolds number within the laminar regime, the flow is stationary. The discrepancies between the models increase by enhancing Reynolds numbers. The σ-coordinate model experiences a reduction in eddy sizes with increasing resolution and Reynolds numbers in correspondence with published experiments, while the size of the eddies are independent of the Reynolds number using the MITgcm. Due to mixing generated by the staircase topography, the z-coordinate model gives a better convergence of the separation point and reattachment length compared with the BOM; however, this conclusion might change with the inclusion of a relevant turbulence scheme.  相似文献   

8.
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9.
Abstract

We consider the mixing of passive tracers and vorticity by temporally fluctuating large scale flows in two dimensions. In analyzing this problem, we employ modern developments stemming from properties of Hamiltonian chaos in the particle trajectories; these developments generally come under the heading “chaotic advection” or “Lagrangian turbulence.” A review of the salient properties of this kind of mixing, and the mathematics used to analyze it, is presented in the context of passive tracer mixing by a vacillating barotropic Rossby wave. We then take up the characterization of subtler aspects of the mixing. It is shown the chaotic advection produces very nonlocal mixing which cannot be represented by eddy diffusivity. Also, the power spectrum of the tracer field is found to be k ? l at shortwaves—precisely as for mixing by homogeneous, isotropic two dimensional turbulence,—even though the physics of the present case is very different. We have produced two independent arguments accounting for this behavior.

We then examine integrations of the unforced barotropic vorticity equation with initial conditions chosen to give a large scale streamline geometry similar to that analyzed in the passive case. It is found that vorticity mixing proceeds along lines similar to passive tracer mixing. Broad regions of homogenized vorticity ultimately surround the separatrices of the large scale streamline pattern, with vorticity gradients limited to nonchaotic regions (regions of tori) in the corresponding passive problem.

Vorticity in the chaotic zone takes the form of an arrangement of strands which become progressively finer in scale and progressively more densely packed; this process transfers enstrophy to small scales. Although the enstrophy cascade is entirely controlled by the large scale wave, the shortwave enstrophy spectrum ultimately takes on the classical k ? l form. If one accepts that the enstrophy cascade is indeed mediated by chaotic advection, this is the expected behavior. The extreme form of nonlocality (in wavenumber space) manifest in this example casts some doubt on the traditional picture of enstrophy cascade in the Atmosphere, which is based on homogeneous two dimensional turbulence theory. We advance the conjecture that these transfers are in large measure attributable to large scale, low frequency, planetary waves.

Upscale energy transfers amplifying the large scale wave do indeed occur in the course of the above-described process. However, the energy transfer is complete long before vorticity mixing has gotten very far, and therefore has little to do with chaotic advection. In this sense, the vorticity involved in the enstrophy cascade is “fossil vorticity,” which has already given up its energy to the large scale.

We conclude with some speculations concerning statistical mechanics of two dimensional flow, prompted by our finding that flows with identical initial energy and enstrophy can culminate in very different final states. We also outline prospects for further applications of chaotic mixing in atmospheric problems.  相似文献   

10.
Abstract

The nonlinear equations of motion are integrated numerically in time for a region of x‐y‐z space of volume 3h × h × h, where h turns out to be a height slightly above the level where the wind first attains the geostrophic flow direction. Only the ideal case is treated of a horizontal lower boundary, neutral stability, horizontal homogeneity of all dependent mean variables except the mean pressure, and statistically steady state. The resulting flow patterns are turbulent and the eddies transport required amounts of momentum vertically.

Topics which are investigated include the relative directions of stress, wind shear and wind; differences in Ekman wind spirals for the neutral numerical case and a stable atmospheric case; profiles of dimensionless turbulence statistics; effect of allowing the mean density to be either constant or to decrease with height; effect of the wind direction or latitude upon the turbulence intensities; and characteristic structure of the eddies in the planetary boundary layer.  相似文献   

11.
This paper presents more data on the properties of type-1 irregularities in the nighttime midlatitude E-region ionosphere. The measurements were made with a 50-MHz Doppler radar system operating in Crete, Greece. The type-1 echoes last from several seconds to a few minutes and are characterized by narrow Doppler spectra with peaks corresponding to wave phase velocities of 250–350 m/s. The average velocity of 285 m/s is about 20% lower than nominal E-region ion-acoustic speeds, probably because of the presence of heavy metallic ions in the sporadic-E-layers that appear to be associated with the mid-latitude plasma instabilities. Sometimes the type-1 echoes are combined with a broad spectrum of type-2 echoes; at other times they dominate the spectrum or may appear in the absence of any type-2 spectral component. We believe these echoes are due to the modified two-stream plasma instability driven by a polarization electric field that must be larger than 10 mV/m. This field is similar in nature to the equatorial electrojet polarization field and can arise when patchy nighttime sporadic-E-layers have the right geometry.  相似文献   

12.
Large-scale zonal flow driven across submarine topography establishes standing Rossby waves. In the presence of stratification, the wave pattern can be represented by barotropic and baroclinic Rossby waves of mixed planetary topographic nature, which are locked to the topography. In the balance of momentum, the wave pattern manifests itself as topographic formstress. This wave-induced formstress has the net effect of braking the flow and reducing the zonal transport. Locally, it may lead to acceleration, and the parts induced by the barotropic and baroclinic waves may have opposing effects. This flow regime occurs in the circumpolar flow around Antarctica. The different roles that the wave-induced formstress plays in homogeneous and stratified flows through a zonal channel are analyzed with the BARBI (BARotropic-Baroclinic-Interaction ocean model, Olbers and Eden, J Phys Oceanogr 33:2719–2737, 2003) model. It is used in complete form and in a low-order version to clarify the different regimes. It is shown that the barotropic formstress arises by topographic locking due to viscous friction and the baroclinic one due to eddy-induced density advection. For the sinusoidal topography used in this study, the transport obeys a law in which friction and wave-induced formstress act as additive resistances, and windstress, the effect of Ekman pumping on the density stratification, and the buoyancy forcing (diapycnal mixing of the stratified water column) of the potential energy stored in the stratification act as additive forcing functions. The dependence of the resistance on the system parameters (lateral viscosity ε, lateral diffusivity κ of eddy density advection, Rossby radius λ, and topography height δ) as well as the dependence of transport on the forcing functions are determined. While the current intensity in a channel with homogeneous density decreases from the viscous flat bottom case in an inverse quadratic law ~δ –2 with increasing topography height and always depends on ε, a stratified system runs into a saturated state in which the transport becomes independent of δ and ε and is determined by the density diffusivity κ rather than the viscosity: κ/λ 2 acts as a vertical eddy viscosity, and the transport is λ 2/κ times the applied forcing. Critical values for the topographic heights in these regimes are identified.  相似文献   

13.
Abstract

The process of wave steepening in Long's model of steady, two-dimensional stably stratified flow over orography is examined. Under conditions of the long-wave approximation, and constant values of the background static stability and basic flow, Long's equation is cast into the form of a nonlinear advection equation. Spectral properties of this latter equation, which could be useful for the interpretation of data analyses under mountain wave conditions, are presented. The principal features, that apply at the onset of convective instability (density constant with height), are:

i) a power spectrum for available potential energy that exhibits a minus eight-thirds decay, in terms of the vertical wavenumber k z -;

ii) a rate of energy transfer across the spectrum that is inversely proportional to the wavenumber for large k z -;

iii) an equipartition between the kinetic energy of the horizontal motion and the available potential energy, under the longwave approximation, although all the disturbance energy is kinetic at the point where convective instability is initiated. It is also shown that features i) and ii) apply to more general conditions that are appropriate to Long's model, not just the long-wave approximation. Application to fully turbulent flow or to conditions at the onset of shearing instability are not considered to be warranted, since the development only applies to conditions at the onset of convective instability.  相似文献   

14.
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15.
Estimates of the wind shear stress exerted on Earth's surface using the fully rough form of the law‐of‐the‐wall are a function of the aerodynamic roughness length, z0. Accurate prediction of aeolian sediment transport rates, therefore, often requires accurate estimates of z0. The value of z0 is determined by the surface roughness and the saltation intensity, both of which can be highly dynamic. Here we report field measurements of z0 values derived from velocity profiles measured over an evolving topography (i.e. sand ripples). The topography was measured by terrestrial laser scanning and the saltation intensity was measured using a disdrometer. By measuring the topographic evolution and saltation intensity simultaneously and using available formulae to estimate the topographic contribution to z0, we isolated the contribution of saltation intensity to z0 and document that this component dominates over the topographic component for all but the lowest shear velocities. Our measurements indicate that the increase in z0 during periods of saltation is approximately one to two orders of magnitude greater than the increase attributed to microtopography (i.e. evolving sand ripples). Our results also reveal differences in transport as a function of grain size. Each grain‐size fraction exhibited a different dependence on shear velocity, with the saltation intensity of fine particles (diameters ranging from 0.125 to 0.25 mm) saturating and eventually decreasing at high shear velocities, which we interpret to be the result of a limitation in the supply of fine particles from the bed at high shear velocities due to bed armoring. Our findings improve knowledge of the controls on the aerodynamic roughness length and the grain‐size dependence of aeolian sediment transport. The results should contribute to the development of improved sediment transport and dust emission models. © 2018 John Wiley & Sons, Ltd.  相似文献   

16.
Abstract

The onset of convection in a cylindrical fluid annulus is analyzed in the case when the cylindrical walls are rotating differentially, a temperature gradient in the radial direction is applied, and the centrifugal force dominates over gravity. The small gap approximation is used and no-slip conditions on the cylindrical walls are assumed. It is found that over a considerable range of the parameter space either convection rolls aligned with the axis of rotation or rolls in the perpendicular (azimuthal) direction are preferred. It is shown that by a suitable redefinition of parameters, results for finite amplitude Taylor vortices and for convection rolls in the presence of shear can be applied to the present problem. Weakly nonlinear results for transverse rolls in a Couette flow indicate the possibility of subcritical bifurcation for Prandtl numbers P less than 0.82. Heat and momentum transports are derived as functions of P and the problem of interaction between transverse and longitudinal rolls is considered. The relevance of the analysis for problems of convection in planetary and stellar atmospheres is briefly discussed.  相似文献   

17.
For the computation of the vertical component Hz of the magnetic field of a horizontal A.C. dipole lying on the earth's surface, a recurrence formula is presented for a horizontally stratified half space, to obtain the (n+ 1)-layer case from the w-layer case. By means of several computed diagrams for the two-layer case, Hz can be determined for different ratios of conductivity of the subsoil and that of the overburden. Thereby the distance from the dipole as well as the layer thickness h are expressed in terms of the wave length A of a plain wave in the overburden. Assuming a sufficiently large conductivity difference, the results show that evidence about the subsurface conditions can be obtained if the distance between the measuring coil and the dipole is of the order of A/3, and if the thickness h of the layer varies within the range A/100 < h < A/6. As an example for the 3-layer case, a nonconducting intermediate layer is assumed.  相似文献   

18.
Abstract

Recent work pertaining to estimating error and accuracies in geomagnetic field modeling is reviewed from a unified viewpoint and illustrated with examples. The formulation of a finite dimensional approximation to the underlying infinite dimensional problem is developed. Central to the formulation is an inner product and norm in the solution space through which a priori information can be brought to bear on the problem. Such information is crucial to estimation of the effects of higher degree fields at the Core-Mantle boundary (CMB) because the behavior of higher degree fields is masked in our measurements by the presence of the field from the Earth's crust. Contributions to the errors in predicting geophysical quantities based on the approximate model are separated into three categories: (1) the usual error from the measurement noise; (2) the error from unmodeled fields, i.e. from sources in the crust, ionosphere, etc.; and (3) the error from truncating to a finite dimensioned solution and prediction space. The combination of the first two is termed low degree error while the third is referred to as truncation error.

The error analysis problem consists of “characterizing” the difference δz = z—z, where z is some quantity depending on the magnetic field and z is the estimate of z resulting from our model. Two approaches are discussed. The method of Confidence Set Inference (CSI) seeks to find an upper bound for |z—?|. Statistical methods, i.e. Bayesian or Stochastic Estimation, seek to estimate E(δz2 ), where E is the expectation value. Estimation of both the truncation error and low degree error is discussed for both approaches. Expressions are found for an upper bound for |δz| and for E(δz2 ). Of particular interest is the computation of the radial field, B., at the CMB for which error estimates are made as examples of the methods. Estimated accuracies of the Gauss coefficients are given for the various methods. In general, the lowest error estimates result when the greatest amount of a priori information is available and, indeed, the estimates for truncation error are completely dependent upon the nature of the a priori information assumed. For the most conservative approach, the error in computing point values of Br at the CMB is unbounded and one must be content with, e.g., averages over some large area. The various assumptions about a priori information are reviewed. Work is needed to extend and develop this information. In particular, information regarding the truncated fields is needed to determine if the pessimistic bounds presently available are realistic or if there is a real physical basis for lower error estimates. Characterization of crustal fields for degree greater than 50 is needed as is more rigorous characterization of the external fields.  相似文献   

19.
Zusammenfassung Es werden einige Produkte aus zwei (höhenabhängigen) meteorologischen Parametern auf ihre Extreme im Vertikalverlauf untersucht (z-System). Die Lage der Extreme wird in Zusammenhang gebracht mit der Lage der Schichten extremer und verschwindender Meridionalgradienten vonp, T und der Windextremschichten.
Summary In the atmosphere there exist layers with vanishing values (H-layers in Figure 2) of the meridional gradients of pressure, temperature and density. Further: There are three cases with regard of the behaviour with altitude of wind and pressure gradientz-system). Case I: both decreasing with height; case II: wind increasing, pressure gradient decreasing with height; case III: both increasing with height. Then: There exist Null Layers (N 1 connected with wind maximum,N 2 with wind minimum) which reverse the large scale vertical motion of the air. In the vertical coordinate the three cases are separated by theH- and the Null Layers. In this paper the extremes of simple product functions are brought into connection with the above mentioned layers.

Deutscher Wetterdienst, 605 Offenbach a. M. — Die Durchführung dieser Untersuchung wurde unterstützt vom US Department of the Army, European Research Office, Frankfurt/Main unter Kontrakt Nr. DA-91-591-EUC-3237.  相似文献   

20.
Summary The object of this paper is to study the stresses produced in a porous liquid-saturated solid of the type considered byBiot [1]2) by a normal load moving along the surface of such a solid. Two cases have been considered. In the first case, the porous solid is taken to be semi-infinite, while in the second case we consider a layer of the liquid-saturated porous solid resting on a smooth rigid foundation. Expressions have been obtained for the stresses at any point in the medium due to a normal load moving along the free surface of the porous solid. Detailed numerical calculations have been carried out for liquid-saturated sandstone, using the data given byFatt [9] for such a medium. These calculations show that the normal stress zz in the solid falls off approximately as 1/z with increase in the depthz below the free surface, and that the stresses in the solid and in the liquid fall off rapidly as we move away from the point directly below the moving load.  相似文献   

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