Equatorial Motions Research Articles

Slow persistent mixing in the abyss

Knowledge about deep-ocean turbulent mixing and flow circulation above abyssal hilly plains is important to quantify processes for the modelling of resuspension and dispersal of sediments in areas where turbulence sources are expected to be relatively weak. Turbulence may disperse sediments from artificial deep-sea mining activities over large distances. To quantify turbulent mixing above the deep-ocean floor around 4000 m depth, high-resolution moored temperature sensor observations have been obtained from the near-equatorial southeast Pacific (7{\deg}S, 88{\deg}W). Models demonstrate low activity of equatorial flow dynamics, internal tides and surface near-inertial motions in the area. The present observations demonstrate a Conservative Temperature difference of about 0.012{\deg}C between 7 and 406 meter above the bottom (hereafter, mab, for short), which is a quarter of the adiabatic lapse rate. The very weakly stratified waters with buoyancy periods between about six hours and one day allow for slowly varying mixing. The calculated turbulence dissipation rate values are half to one order of magnitude larger than those from open-ocean turbulent exchange well away from bottom topography and surface boundaries. In the deep, turbulent overturns extend up to 100 m tall, in the ocean-interior, and also reach the lowest sensor. The overturns are governed by internal-wave-shear and -convection. The turbulence inertial subrange is observed to extend into the internal wave frequency band. The associated mixing is not related to bottom friction processes but to internal wave breaking and near-inertial shear. The mixing facilitates long (hours to day) and high (exceeding 100 mab) dispersal of suspended sediments.

The Theoretical Basis of the Possible Application of a Kovalevsky Gyroscope as Three-Component Angular-Velocity Meter

Two schemes of the three-component angular-velocity meter based on the Kovalevsky gyroscope are described: on the electrostatic and mechanical spring suspensions. The gyroscopic degrees of freedom are restricted on the observation coordinates, and there is a rapid rotation around its principal axis. A mathematical model of the device motion along three translational coordinates and two angular coordinates is presented. The formulas for determining the two components of the mobile-object angular velocities lying in the equatorial plane are derived by using the signals in the channels of the radial interaxial correction as well as the algorithm of calculation with the help of an onboard controller of the angular-velocity component of rotation around the object axis, which practically coincides with the principal one. The algorithm includes the coordinates of the relative translational equatorial motions of the rotor and their first and second time derivatives. The algorithms of their determination with the interference filtering based on the Leuenberger observing identification device are given.

Possible new poor open clusters according to the data from the 2MASS survey

Thirteen candidates for poor open star clusters have been found in the II quadrant of the Milky Way. We determined the equatorial coordinates, color excesses, distance moduli, angular sizes, ages, and average proper motions of the candidates.

Comment on “The importance of auroral features in the search for substorm onset process” by Syun-Ichi Akasofu, A. T. Y. Lui, and C.-I. Meng

Comment on “The importance of auroral features in the search for substorm onset process” by Syun-Ichi Akasofu, A. T. Y. Lui, and C.-I. Meng

Symplectic coordinates on [formula omitted] for perturbed Keplerian problems: Application to the dynamics of a generalised Størmer problem

In order to analyse the dynamics of a given Hamiltonian system in the space defined as the Cartesian product of two spheres, we propose to combine Delaunay coordinates with Poincaré-like coordinates. The coordinates are of local character and have to be selected accordingly with the type of motions one has to take into consideration, so we distinguish the following types: (i) rectilinear motions; (ii) circular and equatorial motions; (iii) circular non-equatorial motions; (iv) non-circular equatorial motions; and (v) non-circular and non-equatorial motions. We apply the theory to study the dynamics of the reduced flow of a generalised Størmer problem that is modelled as a perturbation of the Kepler problem. After using averaging and reduction theories, the corresponding flow is analysed on the manifold S 2 × S 2 , calculating the occurring equilibria and their stability. Finally, the flow of the original problem is reconstructed, concluding the existence of some families of periodic solutions and KAM tori.

A Nonlinear Perspective on the Dynamics of the MJO: Idealized Large-Eddy Simulations

AbstractThe 30–60-day intraseasonal atmospheric oscillation in the equatorial atmosphere, the Madden–Julian oscillation (MJO), is most visible in its signature of outgoing longwave radiation and associated convective centers. Diabatic processes related to tropical convection and two-way atmosphere–ocean interaction are hence generally believed to be crucial in explaining the origin of the MJO phenomenon. However, reliable deterministic forecasting of the MJO in global circulation models and understanding its mechanism remains unsatisfactory. Here a different approach is taken, where the hypothesis is tested that eastward-propagating MJO-like structures originate fundamentally as a result of nonlinear (dry) Rossby wave dynamics. A laboratory-scale numerical model is constructed, where the generation of solitary structures is excited and maintained via zonally propagating meanders of the meridional boundaries of a zonally periodic β plane. The large-eddy simulations capture details of the formation of solitary structures and of their impact on the convective organization. The horizontal structure and the propagation of anomalous streamfunction patterns, a diagnostic typically used in tracing the equatorial MJO, are similar to archetype solutions of the Korteweg–deVries equation, which extends the linear shallow water theory—commonly used to explain equatorial wave motions—to a weakly nonlinear regime for small Rossby numbers. Furthermore, the characteristics of the three-dimensional laboratory-scale numerical results compare well with observed features of the equatorial MJO and thus the study provides indirect evidence of the basic principles underlying the wave-driven eastward propagation of the MJO.

African Meridian B-Field Education and Research (AMBER) Array

The AMBER array contains four magnetometers and spans across the geomagnetic equator from L of 1 to an L of 1.4. In addition to filling the largest land-based gap in global magnetometer coverage, the AMBER array will address two fundamental areas of space physics: (1) the processes governing electrodynamics of the equatorial ionosphere as a function of latitude (or L-shell), local time, longitude, magnetic activity, and season, and (2) ULF pulsation strength and its connection with equatorial electrojet strength at low/mid-latitude regions. Satellite observations show unique equatorial ionospheric structures in the African sector, though these have not been confirmed by observation from the ground due to lack of ground-based instruments in the region. In order to have a complete global understanding of equatorial ionosphere motions, deployment of ground-based magnetometers in Africa is essential. One focus of IHY is the deployment of networks of small instruments, including the development of research infrastructure in developing nations through the United Nations Basic Space Science (UNBSS) Small Instrument Array. Therefore, AMBER magnetometer array in partnership with parallel US funded GPS receivers in Africa will allow us to understand the electrodynamics that governs equatorial ionosphere motions. While AMBER routinely observes the F region plasma drift mechanism (E × B drift), the GPS stations will monitor the structure of plasma at low/mid-latitudes in the African sectors. In addition to new scientific discoveries and advancing the space science research into Africa by establishing scientific collaborations between scientists in the developing and developed nations, the AMBER project also contributes to developing the basic science of heliophysics through cross-disciplinary studies of universal process. This includes the creation of sustainable research/training infrastructure within the developing nations (Africa).

Charged particle dynamics in the combined field of two rotating magnetic dipoles: A numerical investigation of the parametric effect on the equatorial motions

In this contribution we study some aspects of the dynamics of a charged particle in the field produced by two magnetic dipoles that rotate in circular orbits around their common center of mass under their mutual Newtonian attraction. More precisely, we numerically investigate the evolution of the regions of the particle motion on the equatorial plane of each dipole and we explore their parametric variation. We focus our investigation on those problem parameters that are related with the magnetic fields and the masses of the primaries. The obtained preliminary results show that for each particular set of the above parameters and for certain values of energy these regions are bounded, and therefore the motion of the particle is confined inside them.

A reduced model of the Madden–Julian oscillation

AbstractWe have extended our virtual laboratory for internal wave motions (Int. J. Numer. Meth. Fluids 2005; 47:1369–1374) to the case of rotating fluids on an equatorial β‐plane. A virtual wave‐maker is introduced via a time‐dependent coordinate transformation in the meridional direction, represented by two lateral boundary meanders. The technique is consistently incorporated into the numerical algorithm of the nonhydrostatic model EULAG. The modelling framework is applied in simulations of equatorial wave motions to enhance our understanding of the Madden–Julian oscillation (MJO). The simulation of a realistic MJO in global circulation and climate models is a continuing challenge—in part, due to the failure of existing theories to explain the ubiquitous modelling difficulties of the phenomenon. Virtual laboratory experiments appear ideal complementary tools to isolate and study particular geophysical flow structures. In these laboratory‐scale ‘climate’ simulations we observe eastward propagating low‐frequency horizontal structures consistent with Rossby solitary wave theory, representing a particular solution of the Korteweg–de Vries equation for the evolution of the wave amplitude under a given forcing. The latter extends the linear shallow water theory—commonly used to explain different modes of equatorial wave motions—to the weakly nonlinear regime. One important outcome of our simulations is the finding that these structures depend on strong stratification, and may be easily destroyed or weakened if substantial near‐surface perturbations and associated vertical motions exist. This could play a role in the failure to simulate a realistic MJO, but it may also provide an explanation why solitary waves are not as readily observed in oceans as they are in models and theory. Ultimately, our research aims at constructing a simplified dynamical apparatus to reproduce MJO‐like structures in a laboratory analogue, in the spirit of the Plumb–McEwan experiment for the quasi‐biennial oscillation and vis‐a‐vis its numerical equivalent. Copyright © 2007 John Wiley & Sons, Ltd.

Eastward and westward drift of the Earth's magnetic field for the last three millennia

We analyse the secular variation captured by the archaeomagnetic field model CALS7K.2 in an effort to determine episodes of eastward and westward motions of Earth's magnetic field at the core–mantle boundary (CMB) over the past 3000 yr. The direction, amplitude and geographical distribution of these motions are described. We find that the clearest azimuthal motions are observed at mid- to high latitudes in the Northern hemisphere, where both eastward and westward motions occur. These azimuthal motions correspond to displacements and distortions of the two main, quasi-stationary, high-latitude magnetic flux patches. Similar motions are not observed in the Southern hemisphere, although this may be a consequence of the poorer data coverage there. The globally averaged drift for the past 1000 yr has been westward since 1400 AD, but eastward between 1000 AD and 1400 AD. In the broad region of the CMB under Europe, the times of transition in the direction of the mean azimuthal motion coincide with the times at which “archaeomagnetic jerks” have been reported. Our results suggest that these are caused by a relatively rapid (<100 yr) change in the direction of the underlying azimuthal flow near the core surface. We find indications that equatorial westward motions of field features at the CMB, similar to those observed during historical times, may have been present for much of the past 3000 yr. When observed, these low-latitude motions are most prominent in the Atlantic hemisphere, which we interpret as a signature of core–mantle thermal coupling.

The Role of Gravity Waves in Slowly Varying in Time Tropospheric Motions near the Equator

A mathematical theory was recently developed on the relationship between the dominant and gravity wave components of the slowly varying in time solutions (solutions varying on the advective timescale) corresponding to midlatitude mesoscale motions forced by cooling and heating. Here it will be shown that slowly varying in time equatorial motions of any length scale satisfy the same balance between the vertical velocity and heating as in the midlatitude mesoscale case. Thus any equatorial gravity waves that are generated will have the same time- and depth scales and the same size of pressure perturbations as the corresponding dominant component, a horizontal length scale an order of magnitude larger than that of the heat source, and an order of magnitude smaller velocity than the corresponding dominant component. In particular, in the large-scale equatorial case, when the heating has a timescale O(1 day), horizontally propagating gravity waves with a timescale O(1 day) and a length scale O(10 000 km) can be generated. But in the large-scale equatorial case when the heating has a timescale O(10 days), balanced pressure oscillations with a timescale O(10 days) are generated. It is also shown that if a solution of the diabatic system describing equatorial flows (and hence equatorial observational data in the presence of heating) is written in terms of a series of the modes of the linear adiabatic system for those flows, then a major portion of the dominant solution is projected onto gravity wave modes, and this result can explain the confusion over the relative importance of equatorial gravity waves.

Exploring the effects of forcing quasi‐biennial oscillations in a two‐dimensional model

Analytic forcing of the stratospheric quasi‐biennial oscillation (QBO) is introduced into a two‐dimensional middle atmosphere model containing interactive radiation, dynamics, photochemistry and climatological aerosols. The “WISCAR” model integrates the temperature equation in time, but diagnoses the meridional stream function and zonal wind. An analytic forcing function for the QBO is derived from zonal wind observations and employed in three different ways: (1) as a “thermal nudge” in the temperature equation, or in the diagnostic meridional stream function equation as (2) additional heating or (3) equivalent wave driving. A different amplification factor for each method is required to achieve good agreement with the observed QBO in column ozone. This lends insight into the relationship among thermal perturbations, heating, and vertical motion. The vertical variation of QBO amplitude leads to a vertical dependence of the phase relationship among vertical motion, temperature, and zonal wind. Equatorial upward motions range from nearly zero to twice the time mean. Feedbacks in the model result in different extratropical responses for the two hemispheres and modulation of the equatorial semiannual oscillation. Chemical feedbacks and phase relationships are explored for the two ozone regimes: photochemical control above 30 km and advective control beneath. Confirming other studies, QBO vertical motions alter the distribution of odd nitrogen species above 30 km, which, together with the temperature dependence of reaction rates, combine to exert a strong control on ozone perturbations.

The Cold-Core Temperature Structure in a Tropical Easterly Wave

The purpose of this study is to identify what effects are responsible for the observed temperature field, in particular the lower-level cold core, in the trough region of a convectively active tropical easterly wave disturbance. GATE Phase III A/B- and B-scale data were used in the analysis, and the divergence equation, a first-order balance condition proposed by Cho and Jenkins applicable to slowly evolving or near-steady-state large-scale convectively active tropical circulation systems, and the standard nonlinear and linear balance equations were chosen as the framework in which to assimilate the observational data in order to understand the spatial anticorrelation between temperature changes and latent heating. It is shown that all three balance conditions reproduced the thermal structure of the easterly waves that passed over GATE during Phase III. Despite the differences in formulation and form, the simpler standard balance equations were as accurate as the first-order divergence equation in diagnosing the temperature field. The central result of the analysis is that the lower cold-core temperature anomaly observed in the near-trough region of easterly wave disturbances is not a direct consequence of the distribution of latent heat released by cumulus clouds, but reflects instead a balance of forces that dominate the momentum field and that the agreement between the observed and diagnosed temperature fields is dominated by the rotational component of the flow. This has possible implications for a first-order model of the interaction between cumulus-scale and large-scale equatorial wave motions, and for the distinction between developing and nondeveloping easterly waves in terms of the ambient vorticity field, which may aid future numerical investigations of tropical cyclogenesis

Effects of electrical coupling on equatorial ionospheric plasma motions: When is the F region a dominant driver in the low‐latitude dynamo?

Previous studies of the low‐latitude atmospheric dynamo have concluded that the E region dynamo is the principal source of electric fields during the day, with the F region dynamo being of significant importance in the postsunset period. By computing field line integrals of the Hall and Pedersen conductivities and wind‐driven currents from a sophisticated F region model, we find that the F region may provide a significant contribution to the dynamo electric field at all local times in a limited altitude and latitude region. Though the peak value of the Pedersen conductivity in the E region is larger than the peak value of the F region Pedersen conductivity, the field line integrated Pedersen conductivity of the F region can be significantly larger than the integrated Pedersen conductivity of the E region. This effect is most pronounced for low‐latitude flux tubes with apex altitudes slightly above the F peak. This is due to the unique geometry of the equatorial geomagnetic field in which the field line path length through the F region is much greater than the field line path length through the E region. This effect decreases with increasing latitude as the field lines become more vertical and the path lengths through the appropriate parts of E and F regions become more comparable. We examine the consequences of this effect upon the low‐latitude drifts derived from three dynamo circuit assumptions and compare the results to average drifts observed at Jicamarca, Peru.

Effect of low‐latitude western boundary gaps on the reflection of equatorial motions

The western tropical Pacific is thought to be an important zone for generating El Niño: reflections at the boundary make it a source region of equatorial Kelvin waves. Calculations of the effect of a gappy western boundary on the reflection process are carried out in the framework of the low‐frequency limit of the shallow‐water equations and thus are highly idealized. The method is also applied to a schematic version of the flow through the Indonesian seas from the western Pacific to the Indian Oceans. The results indicate some strong sensitivities to the location of the gap and to the structure of the incoming flows. In addition, the results can be quite different, depending on whether the zonal extend of the gap is assumed to be infinite or finite. (More precisely, the latter means that the extend of the gap is short compared with the zonal wavelength of the relevant free waves at that frequency.) In view of the complexity of the results for even such a simplified model, it will be very difficult to be confident of any modeling study of the Indonesian throughflow short of a highly resolved numerical calculation with a detailed representation of the geometry and bathymetry. Nonetheless, we offer tentative conclusions concerning the efficiency of the western Pacific boundary as a reflector. Our results suggest that the realistic boundary will not greatly alter expectations based on a simple solid boundary if the reflections important for El Niño are primarily in motion, represented by low‐order Rossby modes. This is also consistent with observational evidence indicating no anomalous throughflow during El Niño events.

Set-up of deep circulation in multi-level numerical models

The present study investigates the way an ocean filled with homogeneous warm water is cooled by prescribing cold water formation inside the ocean in the southern part of the southern hemisphere using multi-level numerical models. Cooling of the whole ocean starts with introduction of the cold water from the formation region into the deepest part of the ocean in the equatorial and eastern boundary regions by Kelvin wave-type density currents. The cold water along the eastern boundary extends westward as a Rossby wave-type density current setting up an interior poleward flow, and hits the western boundary to form a northward flowing boundary current in the northern hemisphere. Only then does the western boundary current cross the equator. Cooling of the rest of the ocean basin is accomplished by upwellings in the interior and also along the coasts. During this introduction the cold water is mixed with surrounding warm waters, and the thermocline, rather than forming just below the top level where heating is imposed, tends to spread down to deeper depths. Consequently the circulation at a steady state has a significant vertical structure such that the maximum upwelling in the interior occurs in the mid-depths, and only the deeper part of the deep ocean yields the Stommel and Arons circulation pattern. In the equatorial region higher vertical mode motions dominate, and a set of alternating zonal jets forms along the equator.

The Effect of Varying Stratification on Low-Frequency Equatorial Motions

Abstract A formalism is developed to examine the effect of zonally varying stratification on equatorial wave phenomena; an effect present in the real ocean but neglected from standard linear theory. The approach utilized involves the application of a matching condition to equatorial waves incident on a single zonal discontinuity in the density field of a shallow water system. Transmission and reflection coefficients are sought for the projection of an incoming wave onto the entire set of resultant vertical and horizontal wave modes of a general continuously stratified fluid. The limiting case of a meridional density front is extended, in a manner analogous to radiative transfer problems, to a series of discrete density intervals. These techniques are applied to specific choices of stratification ranging from a zonal jump discontinuity in the density field to density changes with zonal scales large with respect to the waves in question, i.e., a WKB limit. The results demonstrate that zonally varying strati...

Equatorial orbits in superposed dipole and uniform magnetic fields

In the present work we study the equatorial motions of charged par ticles that are performed within a field consisting of the superposition of a dipole field—that could represent the magnetic field of a planet — and of a uniform magnetic field normal to the dipole's equator. We use a non-dimensional coordinate system in which the velocity of the charged particle is unit. The model depends on two parameters: the constant of the generalized momentum and the parameter of the interplanetary magnetic field. It is proved that the motion is always bounded. The regions of the motion and the corresponding orbits are studied with respect to the constant of the generalized momentum. We also, investigate numerically conditional periodic and asymptotic orbits.

Equatorial Long Waves in Geostationary Satellite Observations and in a Multichannel Sea Surface Temperature Analysis

Geostationary satellite observations of a zonally oriented sea surface temperature front in the eastern equatorial Pacific were made between 1975 and 1981. Long waves appeared along the front mainly during the summer and fall, except during 1976, the year of an El Nino. The waves have averaged periods of 25 days and wavelengths of 1000 km. At the end of 1981, the long waves also were detected in a new sea surface temperature analysis based on multichannel infrared measurements from a polar-orbiting satellite. This quantitative analysis may improve the ability to resolve low-frequency equatorial wave motions from satellite observations.

Asymptotic eigensolutions of Laplace’s tidal equation

Asymptotic approximations to the eigenfunctions of Laplace’s tidal equation (Hough functions) are obtained for prescribed λ = σ /2 ω ( σ = angular frequency, ω = angular velocity of planet) and large values of Lamb’s parameter, β = 4 ω 2 a 2 / gh ( a is the planetary radius, and h the equivalent depth for a particular vertical structure), qua eigenvalue. Both positive and negative eigenvalues are considered. The results are validated by comparison with the extensive numerical results of Flattery (1967) and Longuet-Higgins (1968). They should be useful in atmospheric tidal studies, especially for a rapidly rotating planet, and may be useful for studies of equatorial motions in the oceans.