On the formation of a plasma pressure anisotropy in the dayside magnetosheath

We present a numerical solution for the momentum equation of the magnetosheath particles that describes the distribution of the pressure anisotropy of the magnetosheath plasma in the midday meridian plane. The pressure anisotropy is a maximum near the magnetopause subsolar point (p_⊥/p_\Vert\cong10). The pressure anisotropy is caused by two factors: particles with small pitch angles (V_\Vert>V_⊥) which travel along the magnetic field lines away from the equatorial plane of the magnetosheath; and particles, after crossing the bowshock, which reach the bulk velocity component directed along the magnetic field lines again, away from the magnetosheath equatorial plane. This velocity increases with increasing distance from the subsolar point of the bowshock, and does not permit particles with large pitch angles (V_⊥>V_\Vert) to move toward the equatorial plane.     

A study on three-dimensional structures of the ionospheric dynamo currents induced by the neutral winds simulated by the Kyushu-GCM

Three-dimensional structures of the ionospheric dynamo currents are examined using the neutral winds in a general circulation model of the middle atmosphere at Kyushu University. A quasi-three-dimensional ionospheric dynamo model is constructed assuming an infinite parallel conductivity in the ionosphere. This model is able to simulate both the equatorial electrojet and the global Sq current system successfully. The simulated results reveal that the equatorial electrojet is confined in quite narrow latitudes around the equator accompanied with meridional current circulations and satisfies a non-divergent structure mainly within the E region. A vertically stratified double layered structure is seen in the east–west current density near the focus latitude of the global Sq current system. It is shown that the stratified structure mainly consists of the east–west Hall current associated with the eastward wind of zonal wavenumbers 1 and 2 in the lower altitudes and the westward wind of zonal wavenumber 2 in the upper altitudes. The day-to-day variation of the neutral winds can significantly vary the induced ionospheric dynamo current system, which is recognized as changes of the focus latitude and/or the maximum value of the equatorial electrojet.     

Evidence and effects of a wave-driven nonlinear current in the equatorial electrojet

Ionospheric two-stream waves and gradientdrift waves nonlinearly drive a large-scale (D.C.) current in the E-region ionosphere. This current flows parallel to, and with a comparable magnitude to, the fundamental Pedersen current. Evidence for the existence and magnitude of wave-driven currents derives from a theoretical understanding of E-region waves, supported by a series of nonlinear 2D simulations of two-stream waves and by data collected by rocket instruments in the equatorial electrojet. Wave-driven currents will modify the large-scale dynamics of the equatorial electrojet during highly active periods. A simple model shows how a wave-driven current appreciably reduces the horizontally flowing electron current of the electrojet. This reduction may account for the observation that type-I radar echoes almost always have a Doppler velocity close to the acoustic speed, and also for the rocket observation that electrojet regions containing gradientdrift waves do not appear also to contain horizontally propagating two-stream waves. Additionally, a simple model of a gradient-drift instability shows that wavedriven currents can cause nonsinusoidal electric fields similar to those measured in situ.     

Some effects of a mean zonal thermocline gradient on planetary equatorial waves

Planetary equatorial waves are studied with the shallow water equations in the presence of a mean zonal thermocline gradient. The interactions between this gradient and waves are represented by three non-linear terms in the equations: one in the wind-forcing formulation in the x-momentum equation, and two for the advection of mass and divergence of the velocity field in the continuity equation. When the mean gradient is imposed but small, these three (linearized) terms will perturb the behavior of the equatorial waves. This paper gives a simple analytic treatment of this problem.The equatorial Kelvin mode is first solved with all three contributions, using a Wentzel-Kramers-Brillouin method. The Kelvin mode shows a spatial or/and temporal growth when the thermocline gradient is negative which is the usual situation in the equatorial Pacific ocean (deep thermocline in the west and shallow in the east). The more robust and efficient contribution comes from the advection term.The single effect of the advection of the mean zonal thermocline gradient is then studied for the Kelvin and planetary Rossby modes. The Kelvin mode remains unstable (damped), while the Rossby modes appear damped (unstable) for a negative (positive) thermocline gradient.     

The equatorial dynamics of a shallow,homogeneous ocean

Abstract

It is shown that the linear equatorial dynamics of a shallow ocean is characterized by two boundary layers of width γ^? L and γL (γ is the Ekman number of the flow, assumed small, and L is a horizontal dimension of the basin). In the γ^? layer stress in the bottom Ekman layer is comparable to that in the surface Ekman layer. In the γ layer vertical friction is important throughout the depth of the ocean. Should the Rossby number ? be so large as to invalidate a linear theory (? > γ^5/3), then inertial effects become important at a distance ?^2/5 L from the equator. The role played in the circulation of the basin by the non-linear equatorial current first studied by Charney (1960) is shown to be similar to that of the γ layer of the linear theory. Though lateral friction is unimportant in a linear model of the flow, shear layers at the equator are found to be a necessary feature of non-linear flow.     

Meridional equatorial electrojet current in the American sector

Huancayo is the only equatorial electrojet station where the daytime increase of horizontal geomagnetic field (H) is associated with a simultaneous increase of eastward geomagnetic field (Y). It is shown that during the counter electrojet period when H is negative, Y also becomes negative. Thus, the diurnal variation of Y at equatorial latitudes is suggested to be a constituent part of the equatorial electrojet current system. Solar flares are known to increase the H field at an equatorial station during normal electrojet conditions (nej). At Huancayo, situated north of the magnetic equator, the solar flare effect, during nej, consists of positive impulses in H and Y and negative impulse in Z field. During counter electrojet periods (cej), a solar flare produces a negative impulse in H and Y and a positive impulse in Z at Huancayo. It is concluded that both the zonal and meridional components of the equatorial electrojet in American longitudes, as in Indian longitudes, flows in the same, E region of the ionosphere.     

Morphological aspects of a new type of counter electrojet event

The study describes the time and space morphologies of a rather new type of counter electrojet event on the basis of data from the excellent chain of magnetic and ionospheric observatories along the Indo-Russian longitude sector. Abnormally large westward currents are observed during almost the whole of the daytime hours on a series of days. These events do not form any vortices in the current system and do not apparently seem to be associated with tidal effects or any solar magnetosphere events or geomagnetic disturbances. The existence of a westward electric field over the equatorial ionosphere has been confirmed by the absence of an equatorial type of sporadic E in the ionograms at Thumba precisely during the periods when H at Trivandrum minus H at Alibag is negative. The equatorial F region anomaly was also absent on the counter electrojet day. Such counter electrojet events during the northern winter months of low solar activity years are suggested to be the result of the modified wind system in the ionosphere associated with stratospheric warming events.     

Nonlinear dynamics of boussinesq convection in a deep rotating spherical shell-i

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.     

Diagnosing vertical motion in the Equatorial Atlantic

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.     

Equatorial electrojet as part of the global circuit: a case-study from the IEEY

Geomagnetic storm-time variations often occur coherently at high latitude and the day-side dip equator where they affect the normal eastward Sq field. This paper presents an analysis of ground magnetic field and ionospheric electrodynamic data related to the geomagnetic storm which occured on 27 May 1993 during the International Equatorial Electrojet Year (IEEY) experiment. This storm-signature analysis on the auroral, mid-latitude and equatorial ground field and ionospheric electrodynamic data leads to the identification of a sensitive response of the equatorial electrojet (EEJ) to large-scale auroral return current: this response consists in a change of the eastward electric field during the pre-sunrise hours (0400–0600 UT) coherently to the high-, mid-, and equatorial-latitude H decrease and the disappearance of the EEJ irregularities between the time-interval 0800–0950 UT. Subsequent to the change in hF during pre-sunrise hours, the observed foF2 increase revealed an enhancement of the equatorial ionization anomaly (EIA) caused by the high-latitude penetrating electric field. The strengthening of these irregularities attested by the Doppler frequency increase tracks the H component at the equator which undergoes a rapid increase around 0800 UT. The H variations observed at the equator are the sum of the following components: S_R, DP, DR, DCF and DT.     

Characteristics of VHF scintillations in the equatorial anomaly crest region in India

The characteristics of ionospheric scintillations at Rajkot in the equatorial anomaly crest region in India are described for the years 1987–1991 by monitoring the 244-MHz transmission from the satellite FLEETSAT. This period covers the ascending phase of solar cycle 22. Scintillations occur predominantly in the pre-midnight period during equinoxes and winter seasons and in the post-midnight period during summer season. During equinoxes and winter, scintillation occurrence increases with solar activity, whilst in summer it is found to decrease with solar activity. Statistically, scintillation occurrence is suppressed by magnetic activity. The characteristics observed during winter and equinoxes are similar to those seen at the equatorial station, Trivandrum. This, coupled with the nature of the post-sunset equatorial F-region drift and h‘F variations, supports the view that at the anomaly crest station, scintillations are of equatorial origin during equinox and winter, whilst in summer they may be of mid-latitude type. The variations in scintillation intensity (in dB) with season and solar activity are also reported.     

Magnetic Rossby waves in a stably stratified layer near the surface of the Earth's outer core

Abstract

The stratification profile of the Earth's magnetofluid outer core is unknown, but there have been suggestions that its upper part may be stably stratified. Braginsky (1984) suggested that the magnetic analog of Rossby (planetary) waves in this stable layer (the ‘H’ layer) may be responsible for a portion of the short-period secular variation. In this study, we adopt a thin shell model to examine the dynamics of the H layer. The stable stratification justifies the thin-layer approximations, which greatly simplify the analysis. The governing equations are then the Laplace's tidal equations modified by the Lorentz force terms, and the magnetic induction equation. We linearize the Lorentz force in the Laplace's tidal equations and the advection term in the magnetic induction equation, assuming a zeroth order dipole field as representative of the magnetic field near the insulating core-mantle boundary. An analytical β-plane solution shows that a magnetic field can release the equatorial trapping that non-magnetic Rossby waves exhibit. A numerical solution to the full spherical equations confirms that a sufficiently strong magnetic field can break the equatorial waveguide. Both solutions are highly dissipative, which is a consequence of our necessary neglect of the induction term in comparison with the advection and diffusion terms in the magnetic induction equation in the thin-layer limit. However, were one to relax the thin-layer approximations and allow a radial dependence of the solutions, one would find magnetic Rossby waves less damped (through the inclusion of the induction term). For the magnetic field strength appropriate for the H layer, the real parts of the eigenfrequencies do not change appreciably from their non-magnetic values. We estimate a phase velocity of the lowest modes that is rather rapid compared with the core fluid speed typically presumed from the secular variation.     

Thermospheric Meridional Wind Control on Equatorial Scintillations and the Role of the Evening F-Region Height Rise, E?×?B Drift Velocities and F2-Peak Density Gradients

The possible role, on L-band scintillation activity, played by the nighttime magnetic meridional component of the thermospheric horizontal neutral winds, the post-sunset F-layer base height, the electrical field pre-reversal enhancement (PRE) and the latitudinal gradients of the F2-layer peak density is analyzed, considering different cases of scintillation occurrence (and their latitudinal extent) during August and September 2002. The meridional winds were derived over low-latitudes from a modified form of the nonlinear time-dependent servo-model. A chain of two scintillation monitors and three digital ionosondes was operational in Brazil and used to collect, respectively, global positioning system signal amplitude scintillation and ionospheric height (h′F; hpF2) and frequency (foF2) parameters. From the overall behavior in the 2 months analyzed, the results suggest that high near sunset upward vertical plasma drifts are conducive for the generation of spread-F irregularities, whereas large poleward meridional winds tend to suppress the development of plasma bubble irregularities and the occurrence of their associated scintillations. Even when generated, a reduced fountain effect, due to weak electric field PRE, acts for the bubbles to be expanded less effectively to higher latitudes. The results also reveal that high F-layer base and peak heights (at equatorial and off-equatorial latitudes), and intense gradients in the F2-peak density between the dip equator and the equatorial anomaly crests, are favorable conditions for the generation of F-region irregularities and increased scintillation activity. Other distinct features of the controlling factors in the cases of occurrence and non-occurrence of equatorial scintillations are presented and discussed.     

Is the equatorial radius of the earth a primary constant,a derived constant,or a defining constant?

Summary The procedure of determining the equatorial radius of the Earth is briefly described and the problem whether the equatorial radius of the Earth is a primary constant, a derived constant, or a defining constant is discussed from various points of view. Contribution to the I. A. G. Special Commission SC3 Fundamental Constants (SCFC)     

Electromagnetic response of a buried cylindrical conductor for sheet and line current sources

A major problem in electromagnetic induction studies in regions of localized source fields, such as the auroral and equatorial electrojet regions, is the source effect. Using an analytical model, the electromagnetic response of a buried conducting cylinder to sheet current and line current excitations has been studied for the period rangeT=5 s to 24 h. The validity of the numerical results obtained from the analytical model are compared with the numerical results obtained from a finite difference model. The results show that for periods less than 30 min, there is no significant difference in the response of the cylinder to both source fields. However, significant differences are observed at longer periods. It was also observed that the equivalent height at which a uniform sheet current at 100 km above the earth's surface can be approximated by a line current varies as a function of the source period.     

On recent developments in E-region irregularity simulationsand a summary of related theory

Theoretical and simulation approaches to E-region irregularities (gradient drift and Farley-Buneman instabilities) are reviewed, and an account is given of some relevant observations. A new hybrid linear dispersion relation is also derived and presented. The most important problem that cannot be explained by more straightforward theories is the saturation of the phase velocity to the ion acoustic speed (C_s saturation). This phenomenon is well-known from equatorial electrojet radar observations. Recent particle simulations have yielded an interesting new explanation for the (C_s saturation, which has been named flow angle stabilization: the phase velocity is not actually (C_s saturated, but the flow angle distribution of the spatial power spectrum is highly asymmetric. The asymmetry is such that the most intense waves propagate at the k⋅E < 0 edge of the linearly unstable sector, and thus the phase velocity of the most intense waves is close to (C_s. Depending on the level of larger scale turbulence, the radar observes varying degrees of (C_s saturation. If the larger scale turbulence level is high (equatorial electrojet case), the local flow angle fluctuates, and there are always subregions within the scattering volume with local flow angles favorable for the detection of the most intense waves. Under these conditions, the spectra show (C_s saturation. If the larger scale turbulence level is lower, there will not always be enough mixing of the flow angle for even the most intense waves to be observed. In these cases, the mean Doppler shift will be proportional to the electric fied, i.e. it will obey the linear theory.     

Effect of equatorial ionization anomaly on the occurrence of spread-F

The unique geometry of the geomagnetic field lines over the equatorial ionosphere coupled with the E–W electric field causes the equatorial ionization anomaly (EIA) and equatorial spread-F (ESF). lonosonde data obtained at a chain of four stations covering equator to anomaly crest region (0.3 to 33 °N dip) in the Indian sector are used to study the role of EIA and the associated processes on the occurrence of ESF. The study period pertains to the equinoctial months (March, April, September and October) of 1991. The ratios of critical frequency of F-layer (f₀F₂) and electron densities at an altitude of 270 km between Ahmedabad (33 °N dip) and Waltair (20 °N dip) are found to shoot up in the afternoon hours on spread-F days showing strengthening of the EIA in the afternoon hours. The study confirms the earlier conclusions made by Raghava Rao et al. and Alex et al. that a well-developed EIA is one of the conditions conducive for the generation of ESF. This study also shows that the location of the crest is also important in addition to the strength of the anomaly.     

Unstable plasma irregular structures in the topside ionosphere and spread-<Emphasis Type="Italic">F</Emphasis>

The results of the Cosmos-900 satellite observ ations of plasma density inhomogeneities in the geomagnetic equator region and the longitudinal distributions of the equatorial spread-F, according to the Intercosmos-19 satellite data are presented. It is show n that the dependence of radiosignal propagation in the ionosphere on geophysical parameters is related to development of the electrostatic instability of the inhomo-geneous ionospheric plasma. The longitudinal dependence of the spread-F, can reflect the influence of the energetic sources, located outside the ionospheric layer that scatters a radio pulse, on the ionosphere. The manifestation of the longitudinal effect in the equatorial spread-F, in the Atlantic region can be explained by the influence of the cone instability on the plasma electrodynamics in the South Atlantic geomagnetic anomaly.     

Sudden post-midnight decrease in equatorial F-region electron densities associated with severe magnetic storms

A detailed analysis of the responses of the equatorial ionosphere to a large number of severe magnetic storms shows the rapid and remarkable collapse of F-region ionisation during post-midnight hours; this is at variance with the presently accepted general behaviour of the low-latitude ionosphere during magnetic storms. This paper discusses such responses as seen in the ionosonde data at Kodaikanal (Geomagn. Lat. 0.6 N). It is also observed that during magnetic storm periods the usual increase seen in the hF at Kodaikanal during sunset hours is considerably suppressed and these periods are also characterised by increased foF2 values. It is suggested that the primary process responsible for these dramatic pre- and post-midnight changes in foF2 during magnetic storms could be due to changes in the magnitude as well as in the direction of usual equatorial electric fields. During the post-midnight periods the change in electric-field direction from westward to eastward for a short period causes an upward E × B plasma drift resulting in increased hF and decreased electron densities in the equatorial region. In addition, it is also suggested that the enhanced storminduced meridional winds in the thermosphere, from the poles towards the equator, may also cause the decreases in electron density seen during post-midnight hours by spatially transporting the F-region ionisation southwards away from Kodaikanal. The paper also includes a discussion on the effects of such decreases in ionisation on low-latitude HF communications.     

Midday reversal of equatorial ionospheric electric field

A comparative study of the geomagnetic and ionospheric data at equatorial and low-latitude stations in India over the 20 year period 1956–1975 is described. The reversal of the electric field in the ionosphere over the magnetic equator during the midday hours indicated by the disappearance of the equatorial sporadic E region echoes on the ionograms is a rare phenomenon occurring on about 1% of time. Most of these events are associated with geomagnetically active periods. By comparing the simultaneous geomagnetic H field at Kodaikanal and at Alibag during the geomagnetic storms it is shown that ring current decreases are observed at both stations. However, an additional westward electric field is superimposed in the ionosphere during the main phase of the storm which can be strong enough to temporarily reverse the normally eastward electric field in the dayside ionosphere. It is suggested that these electric fields associated with the V × Bz electric fields originate at the magnetopause due to the interaction of the solar wind and the interplanetary magnetic field.