Effect of the shear flow in the generation and self-organization of internal gravity wave structures in the dissipative ionosphere

A linear mechanism for the generation and amplification of internal gravity waves and their further nonlinear dynamics in the stably stratified dissipative ionosphere in the presence of an inhomogeneous zonal wind (shear flow) is studied. For shear flows, the operators of linear problems are non-self-conjugate and the corresponding eigenfunctions are nonorthogonal. Therefore, the canonical modal approach is poorly applicable to study such motions. In this case, the so-called nonmodal mathematical analysis is more adequate. Dynamic equations and equations for the energy transport of internal gravity perturbations in the ionosphere with shear flows are derived on the basis of the nonmodal approach. Exact analytic solutions of linear and nonlinear equations are found. The growth rate of the shear instability of internal gravity waves is determined. It is revealed that perturbations grow in time according to a power law, rather than exponentially. The frequency and wavenumber of the generated internal gravity modes depend on time; hence, a wide spectrum of wave perturbations caused by linear effects (rather than nonlinear turbulent ones) forms in the ionosphere with shear flows. The efficiency of the linear mechanism for the amplification of internal gravity waves during their interaction with the inhomogeneous zonal wind is analyzed. A criterion for the development of the shear instability of such waves in the ionospheric plasma is obtained. It is shown that, in the presence of shear instability, internal gravity waves extract the shear flow energy in the initial (linear) stage of their evolution, due to which their amplitude and, accordingly, energy increase substantially (by an order of magnitude). As the amplitude increases, the mechanism of nonlinear self-localization comes into play and the process terminates with the self-organization of strongly localized solitary nonlinear internal gravity vortex structures. As a result, a new degree of freedom of the system and a new way of the evolution of perturbations in a medium with a shear flow appear. Inductive and viscous dampings limit the lifetime of vortex internal gravity structures in the ionosphere; nevertheless, their lifetime is long enough for them to strongly affect the dynamic properties of the medium. It is revealed on the basis of the analytic solution of a set of time-independent nonlinear dynamic equations that, depending on the velocity profile of the shear flow, the nonlinear internal gravity structures can take the form of a purely monopole vortex, a dipole cyclone-anticyclone pair, a transverse vortex chain, or a longitudinal vortex path against the background of the inhomogeneous zonal wind. The accumulation of such vortices in the ionosphere can result in a strongly turbulent state.     

Self-organization of large-scale ULF electromagnetic wave structures in their interaction with nonuniform zonal winds in the ionospheric E region

A study is made of the generation and subsequent linear and nonlinear evolution of ultralow-frequency planetary electromagnetic waves in the E region of a dissipative ionosphere in the presence of a nonuniform zonal wind (a sheared flow). Hall currents flowing in the E region and such permanent global factors as the spatial nonuniformity of the geomagnetic field and of the normal component of the Earth’s angular velocity give rise to fast and slow planetary-scale electromagnetic waves. The efficiency of the linear amplification of planetary electromagnetic waves in their interaction with a nonuniform zonal wind is analyzed. When there are sheared flows, the operators of linear problems are non-self-conjugate and the corresponding eigenfunctions are nonorthogonal, so the canonical modal approach is poorly suited for studying such motions and it is necessary to utilize the so-called nonmodal mathematical analysis. It is shown that, in the linear evolutionary stage, planetary electromagnetic waves efficiently extract energy from the sheared flow, thereby substantially increasing their amplitude and, accordingly, energy. The criterion for instability of a sheared flow in an ionospheric medium is derived. As the shear instability develops and the perturbation amplitude grows, a nonlinear self-localization mechanism comes into play and the process ends with the self-organization of nonlinear, highly localized, solitary vortex structures. The system thus acquires a new degree of freedom, thereby providing a new way for the perturbation to evolve in a medium with a sheared flow. Depending on the shape of the sheared flow velocity profile, nonlinear structures can be either purely monopole vortices or vortex streets against the background of the zonal wind. The accumulation of such vortices can lead to a strongly turbulent state in an ionospheric medium.     

Generation of infrasonic waves by low-frequency dust acoustic perturbations in the Earth’s lower ionosphere

It is shown that, during Perseid, Geminid, Orionid, and Leonid meteor showers, the excitation of low-frequency dust acoustic perturbations by modulational instability in the Earth’s ionosphere can lead to the generation of infrasonic waves. The processes accompanying the propagation of these waves are considered, and the possibility of observing the waves from the Earth’s surface is discussed, as well as the possible onset of acoustic gravitational vortex structures in the region of dust acoustic perturbations. The generation of such structures during Perseid, Geminid, Orionid, and Leonid meteor showers can show up as an increase in the intensity of green nightglow by an amount on the order of 10% and can be attributed to the formation of nonlinear (vortex) structures at altitudes of 110–120 km.     

Synoptic-scale nonlinear stationary magnetized Rossby waves in the ionospheric E-layer

Magnetized Rossby waves are produced by a dynamo electric field and represent the ionospheric generalization of tropospheric Rossby waves in a rotating atmosphere with a spatially inhomogeneous geomagnetic field. They are described by the modified Charney-Obukhov equation with a Poisson-bracket convective nonlinearity. This type of equation has solutions in the form of synoptic-scale nonlinear solitary dipole vortex structures of 1000–3000 km in diameter. With the use of equivalence conditions, various stationary nonlinear solutions are obtained and investigated analytically. The basic characteristics of stationary vortex structures for magnetized Rossby waves are investigated. Published in Russian in Fizika Plazmy, 2006, Vol. 32, No. 12, pp. 1079–1091. The text was submitted by the authors in English.     

Emission of alfvén waves from a nonuniform MHD waveguide

The efficiency of the wave energy loss from a nonuniform MHD waveguide due to the conversion of the trapped magnetosonic waveguide modes into runaway Alfvén waves is estimated theoretically. It is shown that, if the waveguide parameters experience a jumplike change along the waveguide axis, the interaction between the waveguide modes and Alfvén waves occurs precisely at this “jump.” This effect is incorporated into the boundary conditions. A set of coupled integral equations with a singular kernel is derived in order to determine the transmission and reflection coefficients for the waveguide modes. The poles in the kernels of the integral operators correspond to the surface waves. When the jump in the waveguide parameters is small, analytic expressions for the frequency dependence of the transformation coefficients are obtained by using a model profile of the Alfvén velocity along the magnetic field. For the jump characterized by the small parameter value ε=0.3, the wave-amplitude transformation coefficient can amount to 5–10%. Under the phase synchronization condition (when the phase velocities of the waveguide modes on both sides of the jump are the same), the wave-energy transformation coefficient is much higher: it increases from a fraction of one percent to tens of percent. The transformation of fast magnetosonic waves into Alfvén waves is resonant in character, which ensures the frequency and wavelength filteringof the emitted Alfvén perturbations.     

Nonlinear Wave Structures and Plasma−Dust Effects in the Earth’s Atmosphere

The interaction of charged dust grains with nonlinear vortical structures in the Earth’s atmosphere is analyzed. Certain aspects of the atmosphere?ionosphere interaction, in particular, mechanisms for the appearance of dust grains at ionospheric altitudes, are discussed. It is shown that, at certain altitudes, there are regions in the wavenumber space in which conditions leading to the excitation of acoustic?gravity waves are satisfied. The interaction of nonlinear acoustic?gravity waves with dust grains of meteoric origin at ionospheric altitudes, which leads to the mixing and redistribution of dust grains over the region where vortices exist, is investigated. The possibility of formation of vertical and horizontal dust flows in dusty ionospheric plasma as a result of modulational instability is analyzed. The dynamics of dust grains in dust devils frequently arising in the atmosphere above well-heated surfaces is modeled. The vortical structure of such a dust devil is characterized by a reduced pressure in the center, which facilitates the lifting of small dust grains from the surface. The formulated model is used to calculate the trajectories of dust grains in dust devils with allowance for the influence of the electric field generated in the vortex by colliding dust grains. The calculations show that dust devils play an important role in the transport of dust grains.     

Theory of longitudinal plasma waves with allowance for ion motion

A study is made of the propagation of steady-state large-amplitude longitudinal plasma waves in a cold collisionless plasma with allowance for both electron and ion motion. Conditions for the existence of periodic potential waves are determined. The electric field, potential, frequency, and wavelength are obtained as functions of the wave phase velocity and ion-to-electron mass ratio. Taking into account the ion motion results in the nonmonotonic dependence of the frequency of the waves with the maximum possible amplitudes on the wave phase velocity. Specifically, at low phase velocities, the frequency is equal to the electron plasma frequency for linear waves. As the phase velocity increases, the frequency first decreases insignificantly, reaches its minimum value, and then increases. As the phase velocity increases further, the frequency continues to increase and, at relativistic phase velocities, again becomes equal to the plasma frequency. Finally, as the phase velocity approaches the speed of light, the frequency increases without bound.     

Channeling of high-power radio waves under conditions of strong anomalous absorption in the presence of an averaged electron heating source

Strong anomalous absorption of a high-power radio wave by small-scale plasma inhomogeneities in the Earth’s ionosphere can lead to the formation of self-consistent channels (solitons) in which the wave propagates along the magnetic field, but has a soliton-like intensity distribution across the field. The structure of a cylindrical soliton as a function of the wave intensity at the soliton axis is analyzed. Averaged density perturbations leading to wave focusing were calculated using the model proposed earlier by Vas’kov and Gurevich (Geomagn. Aéron. 16, 1112 (1976)), in which an averaged electron heating source was used. It is shown that, under conditions of strong electron recombination, the radii of individual solitons do not exceed 650 m.     

Nonlinear dynamics of Kelvin-Helmholtz instability in a finite-width plasma flow

The nonlinear stage of Kelvin-Helmholtz (KH) instability in a finite-width plane-parallel plasma flow is analyzed. The analysis is performed by means of two-dimensional numerical simulations with the use of ideal magnetohydrodynamic equations describing isothermal plasma flows propagating along the magnetic field. The influence of the magnetic field strength, the plasma temperature, and the ratio of the flow width to the width of the transition layer on the formation of vortex layers and large-scale flow perturbations is investigated. It is shown that, if the wavelength of periodic perturbations is shorter than the flow width, the symmetric and antisymmetric modes develop in a qualitatively similar manner. For waves with wavelengths longer than the flow width, the development of such modes is very different due to the mutual influence of the flow boundaries. Analysis of the development of instability at different values of the Alfvén Mach number M _A shows that long-lived vortices with a characteristic scale length on the order of the flow width appear in a weak magnetic field for both symmetric and antisymmetric modes; however, the vortex geometries for these modes are different. In a strong magnetic field, M _A ～ 5, the phase of vortex decay for both types of modes occurs faster than in a weak field; however, in the case of an antisymmetric mode, large-scale perturbations of the flow boundary are retained for a longer time. Analysis of the evolution of the initial disturbance produced by an ensemble of random small perturbations (noise) at different plasma temperatures shows that, for a flow width comparable with the width of the transition region, the development of KH instability is always antisymmetric in character and leads to well-developed large-scale perturbations of the flow as a whole. For a cold plasma with C _S < 0.5U (where C _S is the speed of sound and U is the flow velocity), in contrast to hot plasma with C _S > 0.5U, the development of KH instability leads to the growth of the antisymmetric mode even if the flow width is much larger than the width of the transition region.     

Unsteady flow field around a human hand and propulsive force in swimming

Much effort has been undertaken for the estimation of propulsive force of swimmers in the front crawl. Estimation is typically based on steady flow theory: the so-called quasi-steady analysis. Flow fields around a swimmer, however, are extremely unsteady because the change direction of hand produces unsteady vortex motions. To evaluate the force correctly, it is necessary to know the unsteady properties determined from the vortex dynamics because that unsteadiness is known to make the force greater. Unsteady flow measurements were made for this study using a sophisticated technique called particle image velocimetry (PIV) in several horizontal planes for subjects swimming in a flume. Using that method, a 100 time-sequential flow fields are obtainable simultaneously. Each flow field was calculated from two particle images using the cross-correlation method. The intensity of vortices and their locations were identified. A strong vortex was generated near the hand and then shed by directional change of the hand in the transition phase from in-sweep to out-sweep. When the vortex was shed, a new vortex rotating in the opposite direction around the hand was created. The pair of vortices induced the velocity component in the direction opposite to the swimming. Results of this study show that the momentum change attributable to the increase in this velocity component is the origin of thrust force by the hand.     

Planetary waves in rotating ionosphere

The problem of propagation of ultralong planetary waves in the Earth’s upper atmosphere is considered. A new exact solution to the MHD equations for the ionosphere is obtained in spherical coordinates with allowance for the geomagnetic field and Earth’s rotation. A general dispersion relation is derived for planetary waves in the ionospheric E and F regions, and the characteristic features of their propagation in a weakly ionized ionospheric plasma are discussed.     

Generation of auroral kilometric radiation by a finite-size source in a dipole magnetic field

Generation, amplification, and propagation of auroral kilometric radiation in a narrow three-dimensional plasma cavity in which a weakly relativistic electron beam propagates is studied in the geometrical optics approximation. It is shown that the waves that start with a group velocity directed earthward and have optimal relation between the wave vector components determining the linear growth rate and the wave residence time inside the amplification region undergo the largest amplification. Taking into account the longitudinal velocity of fast electrons results in the shift of the instability domain toward wave vectors directed to the Earth and leads to a change in the dispersion relation, due to which favorable conditions are created for the generation of waves with frequencies above the cutoff frequency for the cold background plasma at the wave generation altitude. The amplification factor for these waves is lower than for waves that have the same wave vectors but are excited by the electron beams with lower velocities along the magnetic field. For waves excited at frequencies below the cutoff frequency of the background plasma at the generation altitude, the amplification factor increases with increasing longitudinal electron velocity, because these waves reside for a longer time in the amplification region.     

The effects of abrupt topography on plankton dynamics

Plankton population dynamics in the upper layer of the ocean depends on upwelling processes that bring nutrients from deeper waters. In turn, these depend on the structure of the vertical velocity field. In coastal areas and in oceanic regions characterized by the presence of strong submarine topographic features, the variable bottom topography induces significant effects on vertical velocities and upwelling/downwelling patterns. As a consequence, large plankton and fish abundances are frequently observed above seamounts, canyons and steep continental shelves. In this work, the dynamics of an NPZ (nutrient-phytoplankton-zooplankton) system is numerically studied by coupling the ecosystem model with a quasi two-dimensional (2D) fluid model with topography. At variance with classical 2D approaches, this formulation allows for an explicit expression of the vertical motions produced when fluid columns are squeezed and stretched as they experience changes of depth. Thus, input or output of nutrients at the surface are associated with fluid motion over the bottom topography. We examine the dynamics of a cyclonic vortex over two basic topographies: a steep escarpment and a submarine mountain. We show that plankton abundance over the escarpment is modulated by the passing of topographic Rossby waves, generated by the vortex-topography interaction. In such configuration, advection effects driven by the flow over the escarpment are of limited relevance for the dynamics of biological fields. By contrast, we find that the flow resulting from the interaction of a vortex with a seamount is sufficiently strong and persistent to allow for a remarkable increase of nutrients, and a corresponding enhancement of phytoplankton and zooplankton concentrations. Over the seamount, advection effects associated with trapped flow perturbations around the summit play an essential role.     

The effects of abrupt topography on plankton dynamics

Plankton population dynamics in the upper layer of the ocean depends on upwelling processes that bring nutrients from deeper waters. In turn, these depend on the structure of the vertical velocity field. In coastal areas and in oceanic regions characterized by the presence of strong submarine topographic features, the variable bottom topography induces significant effects on vertical velocities and upwelling/downwelling patterns. As a consequence, large plankton and fish abundances are frequently observed above seamounts, canyons and steep continental shelves. In this work, the dynamics of an NPZ (nutrient-phytoplankton-zooplankton) system is numerically studied by coupling the ecosystem model with a quasi two-dimensional (2D) fluid model with topography. At variance with classical 2D approaches, this formulation allows for an explicit expression of the vertical motions produced when fluid columns are squeezed and stretched as they experience changes of depth. Thus, input or output of nutrients at the surface are associated with fluid motion over the bottom topography. We examine the dynamics of a cyclonic vortex over two basic topographies: a steep escarpment and a submarine mountain. We show that plankton abundance over the escarpment is modulated by the passing of topographic Rossby waves, generated by the vortex-topography interaction. In such configuration, advection effects driven by the flow over the escarpment are of limited relevance for the dynamics of biological fields. By contrast, we find that the flow resulting from the interaction of a vortex with a seamount is sufficiently strong and persistent to allow for a remarkable increase of nutrients, and a corresponding enhancement of phytoplankton and zooplankton concentrations. Over the seamount, advection effects associated with trapped flow perturbations around the summit play an essential role.     

Propagated disturbances of transverse potential gradient in intracellular fibrils as the source of motive forces for longitudinal transport in cells

Summary It is proposed as a working hypothesis that conformational changes propagated like waves along intracellular fibrils (tubules, microtubules, microfilaments) have an electric component,i.e., there are waves of disturbance of electric potential in the fibrils. The paper considers the unavoidable consequences of the wave. The latter is accompanied by local electric field in the boundary layer of cytoplasmic fluid. Both positively and negatively charged particles may be attracted to the fibril in certain regions of the field and, being attracted, the particle may be under the action of longitudinal component of electric force. When the force is strong enough to move the particle with wave velocity, the particle will travel smoothly along the fibril, otherwise the movement will be saltatory or of agitation type. Net electroosmotic flow in one direction in the boundary layer of fluid may be expected when the waves are propagated in series. Turbulent motion of the fluid caused by the waves may provide the basis for activated diffusion. Asymmetry of the wave may account for polar transport of this sort. The electric field transmitted along the fibril across a sieve pore in phloem may facilitate electroosmotically the flow through the pore. Quantitative requirements of the hypothesis that electric field generated by the waves may account for different aspects of longitudinal transport in cells are apparently met.     

Excitation of inertial Alfvén waves via modulational interaction with lower hybrid waves

The concept of modulational instability, which results from the coupling of waves modes of very different time and space scales, was introduced to plasma physics through an elegant paper by Vedenov and Rudakov in 1964 [1]. Our paper is devoted to the theory of modulational instability resulting from the interaction of lower hybrid waves and slow density perturbations associated with inertial Alfvén waves. The nonlinear set of equations describing the modulational coupling of these two types of waves is constructed. The lower hybrid wave trajectories are analyzed within predefined density structures and it is shown that these waves can be trapped in the vicinity of the density extremum. The density modulations, originally being associated with inertial Alfvén waves, deepen due to the trapping of lower hybrid waves; this leads to modulational instability. A dispersion relation describing the modulational instability is constructed and analyzed. The threshold intensity of the lower hybrid waves for the onset of instability is obtained and it is shown that instability can serve as an efficient mechanism for the excitation of inertial Alfvén waves in the auroral ionosphere.     

Nonlinear dynamics of drift structures in a magnetized dissipative plasma

A study is made of the nonlinear dynamics of solitary vortex structures in an inhomogeneous magnetized dissipative plasma. A nonlinear transport equation for long-wavelength drift wave structures is derived with allowance for the nonuniformity of the plasma density and temperature equilibria, as well as the magnetic and collisional viscosity of the medium and its friction. The dynamic equation describes two types of nonlinearity: scalar (due to the temperature inhomogeneity) and vector (due to the convectively polarized motion of the particles of the medium). The equation is fourth order in the spatial derivatives, in contrast to the second-order Hasegawa-Mima equations. An analytic steady solution to the nonlinear equation is obtained that describes a new type of solitary dipole vortex. The nonlinear dynamic equation is integrated numerically. A new algorithm and a new finite difference scheme for solving the equation are proposed, and it is proved that the solution so obtained is unique. The equation is used to investigate how the initially steady dipole vortex constructed here behaves unsteadily under the action of the factors just mentioned. Numerical simulations revealed that the role of the vector nonlinearity is twofold: it helps the dispersion or the scalar nonlinearity (depending on their magnitude) to ensure the mutual equilibrium and, thereby, promote self-organization of the vortical structures. It is shown that dispersion breaks the initial dipole vortex into a set of tightly packed, smaller scale, less intense monopole vortices-alternating cyclones and anticyclones. When the dispersion of the evolving initial dipole vortex is weak, the scalar nonlinearity symmetrically breaks a cyclone-anticyclone pair into a cyclone and an anticyclone, which are independent of one another and have essentially the same intensity, shape, and size. The stronger the dispersion, the more anisotropic the process whereby the structures break: the anticyclone is more intense and localized, while the cyclone is less intense and has a larger size. In the course of further evolution, the cyclone persists for a relatively longer time, while the anticyclone breaks into small-scale vortices and dissipation hastens this process. It is found that the relaxation of the vortex by viscous dissipation differs in character from that by the frictional force. The time scale on which the vortex is damped depends strongly on its typical size: larger scale vortices are longer lived structures. It is shown that, as the instability develops, the initial vortex is amplified and the lifetime of the dipole pair components-cyclone and anticyclone-becomes longer. As time elapses, small-scale noise is generated in the system, and the spatial structure of the perturbation potential becomes irregular. The pattern of interaction of solitary vortex structures among themselves and with the medium shows that they can take part in strong drift turbulence and anomalous transport of heat and matter in an inhomogeneous magnetized plasma.     

Langmuir wave in weakly inhomogeneous relativistic plasma

The evolution of a Langmuir wave in a weakly inhomogeneous relativistic plasma with a positive density gradient is considered. It is shown that, at relativistic phase velocities, the wave evolution even at the tail of the electron distribution, where it is close to linear in the nonrelativistic case, results in the wave transformation into a hybrid of two waves with different spatial periods. Nonlinear dispersion relations for different stages of the wave evolution are derived.     

Broadening of the frequency spectrum of waves forming a low-pressure helicon discharge

It is found experimentally that the spectrum of waves forming a low-pressure RF discharge in a strong magnetic field broadens toward lower frequencies. Such an asymmetric broadening is explained by the scattering of the pump wave by the electron flows escaping from the discharge. A similar effect can take place during the formation of the spectrum of artificial RF radiation in the Earth??s ionosphere.     

Effect of Long-Wavelength Magnetic Field Disturbances on the Generation of Auroral Kilometric Radiation

The effect of long-wavelength magnetic field disturbances typical of the Earth’s auroral region on the generation of auroral kilometric radiation in a narrow three-dimensional plasma cavity in which a weakly relativistic electron flow propagates against the background of cold low-density plasma is analyzed. The dynamics of the propagation and amplification of fluctuation waves with initial group velocities directed toward the higher magnetic field is considered in the geometrical optics approximation. Analysis of wave trajectories shows that the wave amplification coefficients depend on the magnetic field gradient in the reflection region. If the wave reflection point lies in the region where the gradient of the disturbed magnetic field is less than that of the undisturbed dipole field, then the wave amplification coefficients exceed those of waves propagating in the undisturbed field, and vice versa. Thus, the shape of the spectrum of generated waves changes in the presence of long-wavelength disturbances of the dipole magnetic field in such a way that segments with different curvatures can form in the spectrum.