Linear mechanism by which internal gravity waves are generated and intensified in the ionosphere when interacting with an inhomogeneous zonal wind: 2. Internal gravity wave generation and intensification during the linear evolution stage

The linear mechanism by which internal gravity waves (IGWs) are generated and subsequently intensified in a stably stratified dissipative ionosphere in the presence of an inhomogeneous zonal wind (shear flow) has been studied. In the case of shear flows, the operators of linear problems are nonself-adjoint and the corresponding eigenfunctions are nonorthogonal; a canonical approach can hardly be used to study such motions. It is more adequate to apply the so-called nonmodal calculation. Dynamic equations and equations of energy transfer of IGW disturbances in the ionosphere with a shear flow have been obtained based on a nonmodal approach. Exact analytical solutions for the constructed dynamic equations have been found. The growth rate of the IGW shear instability has been determined. It has been established that IGW disturbances are intensified in an algebraically power manner rather than exponentially in the course of time. The effectiveness of the linear mechanism by which IGWs are intensified when interacting with an inhomogeneous zonal wind is analyzed. It has been indicated that IGWs effectively obtain the shear flow energy during the linear evolution stage and substantially increase (by an order of magnitude) their amplitude and energy. The frequency and the wave vector of generated IGW modes depend on time; therefore, a wide spectrum of wavelike disturbances, depending on the linear, rather than nonlinear, turbulent effects, is formed in the ionosphere with a shear flow. Thereby, a new degree of freedom appears, and the turbulent state of atmospheric—ionospheric layers can be formed on IGW disturbances.     

Particle energy fluxes in an unstable plasma with vortex structures in an inhomogeneous geomagnetic field in the topside ionosphere

Plasma inhomogeneities extending along geomagnetic field lines in the ionosphere and magnetosphere can have a vortex structure. Electromagnetic waves can propagate in plasma inhomogeneities in the waveguide channel mode. It has been indicated that energy and particle fluxes related to the development of small-scale electrostatic turbulence in a magnetized plasma with an unstable electron component promotes an increase in plasma density gradients in the walls of waveguide channels and an enhancement in plasma vortices. At low L shells in the region of the geomagnetic equator, the development of plasma electrostatic instability and the damping of drifting plasma vortices in the inhomogeneous geomagnetic field in the topside ionosphere can be the main mechanism by which large-scale (∼1000 km) regions with a decreased plasma density are formed.     

Linear mechanism of generation and intencification of internal gravity waves in the ionosphere at their interaction with a nonuniform zonal wind: 1. Model of the medium and initial dynamic equations

The specific features of the generation and intensification of internal gravity wave structures in different atmospheric-ionospheric regions, caused by zonal local nonuniform winds (shear flows), are studied. The model of the medium has been explained and an initial closed system of equations has been obtained in order to study the linear and nonlinear dynamics of internal gravity waves (IGWs) when they interact with the geomagnetic field in a dissipative ionosphere (for the D, E, and F regions).     

The coupling instability of Rossby and topographic Rossby waves in the equatorial area

Before the 1980s, El Ni?o was believed as the sea surface warming along the coast of Peru in South America. As the positive anomaly strengths, the warm water expands westward along the equator to form large area of anomalous high sea surface temperature. Rasmusson and Carpenter (1982) summarized the de-velopment process of the sea surface warm water and the corresponding wind field[1] during ENSO cylce. However, this canonical El Ni?o was questioned by 1982-1983 warm episode and later dat…     

On the transformation of planetary waves of tropospheric origin into waves in radio wave absorption in the lower ionosphere

Summary Calculations are carried out of upward propagation of a tropospherically forced 10-day planetary wave into the upper middle atmosphere with the use of the COMMA-R model of the University of Cologne, of its transformation into a wave in electron density by means of the model of the Comenius University, and of its final transformation into a wave in radio wave absorption in the lower ionosphere applying the computer code of the Geophysical Institute. The calculations show that the absorption may be used for investigating the planetary wave activity, particularly of its long-term trends. The possibility of propagation of planetary waves from the winter hemisphere to the summer hemisphere is illustrated, which could contribute to explanation of the occurrence of travelling planetary waves in the mesosphere in summer.Dedicated to the Memory of Professor Karel P     

Self-organization of IGW structures in an inhomogeneous ionosphere: 2. Nonlinear vortex structures

The generation and further nonlinear dynamics of internal gravity wave (IGW) structures in a dissipative ionosphere in the presence of an inhomogeneous zonal wind (shear flow) have been studied. The effectiveness of the IGW amplification mechanism during the interaction with an inhomogeneous zonal wind is analyzed based on the corresponding model system of nonlinear dynamic equations constructed in (Aburjania et al., 2013). It has been indicated that IGWs effectively obtain the shear flow energy at the initial linear evolution stage and substantially (by an order of magnitude) increase their amplitude and, correspondingly, energy. The nonlinear self-localization mechanism starts operating with increasing amplitude, and the process terminates with the self-organization of nonlinear solitary strongly localized vortex structures. A new degree of system freedom and the disturbance evolution trend in a medium with a shear flow appear in such a way. Nonlinear IGW structures can be a purely monopoly vortex, a transverse vortex chain, and/or a longitudinal vortex path against the background of an inhomogeneous zonal wind, depending on the shear flow velocity profile. The accumulation of such vortices in the ionospheric medium can generate a strongly turbulent state.     

Self-organization of internal gravity wave structures in an inhomogeneous ionosphere: 1. Nonlinear model dynamic equations

A corresponding model system of nonlinear dynamic equations for the lower ionosphere has been constructed in order to study the generation and further nonlinear dynamics of internal gravity wave (IGW) structures in a dissipative ionosphere in the presence of a nonuniform zonal wind (shear flow). The criterion for the development of the IGW shear instability in the ionosphere has been obtained.     

A note on the general concept of wave breaking for Rossby and gravity waves

A recently proposed general definition of wave breaking is further discussed, in order to deal with some points on which misunderstanding appears to have arisen. As with surface and internal gravity waves, the classification of Rossby waves into breaking and not breaking is a generic classification based on dynamical considerations, and not a statement about any unique signature or automatically recognizable shape. Nor is it a statement about passive tracers uncorrelated with potential vorticity on isentropic surfaces. A strong motivation for the definition is that proofs of the nonacceleration theorem of wave, mean-flow interaction theory rely, explicitly or implicitly, on a hypothesis that the waves do not break in the sense envisaged.The general definition refers to the qualitative behaviour of a certain set of material contours, namely those, and only those, which would undulate reversibly, with small slopes, under the influence of the waves' restoring mechanism, in those circumstances for which linearized, nondissipative wave theory is a self-consistent approximation to nonlinear reality. The waves' restoring mechanism depends upon the basic-state vertical potential density gradient in the case of gravity waves, and upon the basic-state isentropic gradient of potential vorticity in the case of Rossby waves. In the usual linearized theory of planetary scale Rossby waves on a zonal shear flow, the relevant material contours lie along latitude circles when undisturbed.     

Evidence of global-scale waves with zonal wave number zero in the stratosphere

Coherency spectra derived from time series of stratospheric quantities indicate oscillations in the frequency range below 0.5 d^–1 which are correlated on a global scale. Satellite observations of total ozone and stratospheric radiance (BUV and SIRS, Nimbus4, April–November 1970) have been used to derive phase relationships of such oscillations. As an example, an oscillation of total ozone with a period of 7.5 d and zonal wave number zero is analyzed in detail. The basic assumption is made and tested, that the oscillation reflects stratospheric planetary waves as obtained from Laplace's tidal equations. The observed latitudinal phase shifts for the total ozone oscillation are in good agreement with theoretical predictions. It is concluded from the observations of ozone and radiance that mainly divergence effects related to global-scale waves are responsible for the 7.5 d oscillations of total ozone at high and middle latitudes and at the equator whereas in the latitude range 10°S–20°S predominantly temperature effects are important. Meridional wind amplitudes of some 10 cm/s are sufficient to explain the high and mid-latitude ozone oscillations. At low latitudes vertical wind amplitudes of about 0.2 mm/s corresponding to height changes of the ozone layer of roughly ±20 m are obtained.     

Dynamics of equilibrium upset and electromagnetic energy transformation in the geomagnetotail: A theory and simulation using particles. 1. Evolution of configurations in an MHD approximation

The process of equilibrium disruption in the system with a current sheet (CS) under the conditions of small magnetic field component normal to CS, which is induced by an external disturbance, has been theoretically studied within the scope of MHD. In the geomagnetotail, this disturbance can be caused by a tearing instability developing in the more distant tail section, or by a ballooning instability in the tail nearest section, or by a rapid reconfiguration at the magnetopause during the disturbance passage in the solar wind. Locally, in a limited CS section, a longitudinal momentum balance is rapidly (on the Alfvén time scale) upset when a fast MHD disturbance, the form of which depends on the presence of CS, passes along the tail. The nonequilibrium temperature, which subsequently evolves through splitting of CS into several current structures, originates on a substantially larger (due to the smallness of the normal field component) time scale. Such a reconfiguration SPONTANEOUSLY develops after the initial equilibrium upset under the action of an external (weak) disturbance. During an analysis within the scope of MHD, this reconfiguration can be described as the well-known process with two pairs of nonlinear waves propagating in both directions from the central sheet plane at constant velocities: these are fast rarefaction waves and the following slow “switching-off” shocks. However, the kinetic theory reveals substantially different relaxation channels. These channels are studied in the second and third work sections, where the kinetic numerical simulation of the problem is presented and the results of this simulation are analyzed.     

Electromagnetic waves in the auroral and subauroral regions of the topside ionosphere

The density and temperature of the plasma electron component and wave emission intensity in the topside ionosphere were measured by the INTERCOSMOS-19 satellite. In the subauroral ionosphere, a decrease in the plasma density correlates with an increase in the plasma electron component temperature. In this case, the additional increase in the electron component temperature was measured in regions with increased plasma density gradients during the substorm recovery phase. In a linear approximation, the electromagnetic wave growth increments are small on electron fluxes precipitating in the auroral zone. It has been indicated that Bernstein electromagnetic waves propagating in the subauroral topside ionosphere can intensify in regions with increased plasma density gradients on electron fluxes orthogonal to the geomagnetic field, which are formed when plasma is heated by decaying electrostatic oscillations of the plasma electron component. This can be one of the most important factors responsible for the intensification of auroral kilometric radiation.     

Simulation of irregular waves in an offshore wind farm with a spectral wave model

A numerical study of irregular waves in the Norwegian continental shelf wind farm (HAVSUL-II) was conducted using 3rd generation spectral wave models. The study was composed of two parts: the study of the effect of a single windmill monopile in the local incoming wave field using an empirical JONSWAP spectrum, and a wave hindcast study in the wind farm area using realistic incoming wave spectra obtained from large scale simulations for the 1991-1992 winter period. In the single windmill monopile study the SWAN wave model was used, while the hindcast study was conducted by successively nesting from a coarse grid using the WAM model up to a high-resolution (56 m) grid covering 26.2 km² of the HAVSUL-II windmill farm using the SWAN model. The effect of a single monopile on incident waves with realistic spectra was also studied. In the single windmill study the monopile was represented as a closed circular obstacle and in the hindcast study it was represented as a dry grid point. The results showed that the single windmill monopile creates a shadow zone in the down wave region with lower significant wave height (H_s) values and a slight increase of H_s in the up wave region. The effects of the windmill monopile on the wave field were found to be dependent on the directional distribution of the incoming wave spectrum and also on the wave diffraction and reflection. The hindcast study showed that the group of windmill monopiles may contribute to the reduction of the wave energy inside the offshore wind farm and that once the waves enter into the offshore wind farm they experience modifications due to the presence of the windmill monopiles, which cause a blocking of the wave energy propagation resulting in an altered distribution of the H_s field.     

A method for the study of the zonal kinetic energy balance in the atmosphere

Summary The atmospheric balance of the kinetic energy of the zonally averaged zonal motion is investigated from five years of daily data at 800 stations for the northern hemisphere. The basic equation for such energy is used, together with the simplifying assumption that the frictional destruction is due in the main to stresses acting across horizontal surfaces, being thus presumably related to the vertical shear of the mean zonal wind, although no further details are needed in the analysis. The five-year averages of various terms as well as their seasonal means appear to give reasonable results.The research reported in this paper was sponsored by the U.S. National Science Foundation under Grant No. GA-1310X.     

The energy and energy flux of planetary waves in an ocean of variable depth

Abstract

In a recent paper, Buchwald (1972a) has shown that besides the kinetic energy and gravitational potential energy usually associated with planetary waves in an ocean of uniform depth it is useful to define also a “spin energy”, associated with the rotation.

The present paper is basically an extension of Buchwald's result to a uniformly rotating β-plane ocean of variable depth. As in the previous work, energy conservation equations are derived and the separate energies shown to be independently conserved over the total volume of the ocean. The time-averaged energies are further shown to be propagated in the direction of the group velocity and to satisfy the equipartition rule.

Unlike Buchwald, however, we need not consider the boundary conditions in order to achieve these results. Furthermore, the use of a more realistic ocean configuration admits the possibility of a multiply connected region in the present of mean currents.

Finally, there is a physical explanation for the appearance of a spin energy in a rotating system.     

Dynamics of equilibrium upset and electromagnetic energy transformation in the geomagnetotail: A theory and simulation using particles. 3. Versions of formation of thin current sheets

The final part of the study is devoted to the process of rapid reconfiguration of the geomagnetotail after the upset of the equilibrium, i.e., to substorm activation. Such a version of spontaneous formation of nonlinear kinetic small-scale structures at the site occupied by an initial current sheet (CS), which results in the formation of a specific equilibrium current structure with strong ion anisotropy (forced kinetic current sheet, FKCS), has been revealed in the course of numerical simulation. This reconfiguration “channel” is realized when the relative value of the magnetic field component normal to CS is smaller than a certain critical value. In this case the disturbance intensity is SPONTANEOUSLY settled at a certain final level at the late stages. The obtained results are compared with the previous study of the system evolution under the action of the external trigger. The physical causes and specific features of different CS evolution regimes are considered. The studied plasma mechanisms are responsible for the effects of rapid energy transformation—magnetic field “annihilation”—that took place in the geomagnetotail.     

Spatial distribution of the field-aligned current density in the polar ionosphere and the contribution of magnetosound waves

The regular appearance of the chain of oppositely directed field-aligned current (FAC) pairs near the noon-midnight meridian during three considered substorms has been described. The FAC pairs (FACs flowing into the ionosphere in the morning and flowing out of this region in the evening and vice versa) are observed in each of three Iijima and Potemra zones. The FAC direction in the fixed LT sector periodically varies along the chain. The scenario, according to which each FAC pair (seven pairs) is identified with a hump or trough of one of the waves propagating from the Earth and toward the Earth in different magnetospheric domains, has been described. The estimated wave velocities differ from ∼100 to >1000 km/s depending on the propagation region but everywhere agree with the corresponding velocities of magnetosound waves (MSWs). The hypothesis is proposed, according to which these MSWs are excited by plasma ejection during current disruption and reconnection near the dayside magnetopause and in the near/middle regions of the nightside tail.     

Numerical simulation of the electric field and zonal current in the Earth’s ionosphere: The dynamo field and equatorial electrojet

The work is devoted to the numerical simulation of the dynamo electric field and its effects in the Earth’s ionosphere within the scope of the thermosphere-ionosphere-protonosphere global self-consistent model developed at WD IZMIRAN. The new electric field calculation block, which was used to obtain results of the self-consistent calculations of the electric field potential generated by the dynamo effect of the thermospheric winds (the dynamo field) and the equatorial electrojet for March 22, 1987, is briefly described in this work. A comparison of the obtained results with the experimental data showed a satisfactory agreement. Moreover, the proposed model was used to calculate the diurnal variations in the ionospheric parameters for Jicamarca equatorial station under the same conditions with the help of the new block of the electric field. The results of these calculations are also presented and discussed in this work. It has been indicated that the new model satisfactorily describes the specific features of electric field distribution at the geomagnetic equator and the well-known phenomenon of equatorial electrojet.     

Internal gravity waves in atmospheres with realistic dissipation and temperature part I. Mathematical development and propagation of waves into the thermosphere

Abstract

In this, the first part of a three part study, we develop a model for the theoretical analysis of 3‐dimensional internal gravity waves in atmospheres with arbitrary distributions of basic temperature, molecular weight, viscosity and conductivity (both eddy and molecular), Newtonian cooling, anisotropic hydromagnetic (ion) drag, and thermal excitation. Attention is given to the physical bases for our models, and a detailed outline is given of the numerical method used to solve the resulting system of equations.

As an application of the above development, we study the ability of five particular gravity waves (chosen for their observed importance in the neighborhood of 90–100 km—four of the waves are simulated tidal modes) to propagate from 90 km into the thermosphere. We choose to define the thermosphere as that portion of the atmosphere above the turbopause (ca. 110 km). Among the most significant results to emerge are the following: (i) the effects of molecular viscosity and conductivity appear to be more significant than the effects of hydromagnetic drag, and (ii) while most waves considered are significantly attenuated somewhere between 90 Ian and the thermosphere, the main semidiurnal tidal mode is not. In fact, semidiurnal temperature oscillations of only a few degrees amplitude at 90 km can give rise to oscillations of over a hundred degrees amplitude in the exosphere.