Two-stream-like mechanism of zonal-flow generation by Rossby waves in a shallow rotating fluid

It is shown that the small-scale Rossby waves in a shallow rotating fluid placed in a gravitational field can generate large-scale zonal flows by means of a two-stream-like mechanism. This mechanism is revealed under the conditions when the Lighthill instability criterion is not satisfied. The text was submitted by the authors in English.     

Analytical investigation of Rossby waves in atmospheric dynamics

The (2+1)-dimensional nonlinear inviscid barotropic nondivergent vorticity equation in a beta-plane is analyzed by using the classical Lie group approach. Using the group theory, some types of general exact Rossby wave solutions can be obtained whence a special Rossby wave solution is known. Especially, it is found that the only effect of the time-dependent background basic wind on the Rossby waves is the accumulate motion in the zonal direction. Some types of exact explicit similarity Rossby wave solutions with both nonconstant linear and nonlinear shears are also given.     

Nonlinear waves in a rotating plasma cylinder

Previous work on exact cylindrical surface waves in a nonneutral cold-electron plasma bounded by a dielectric is extended to include plasma rotation. A set of nonlinear rate equations describing the temporal behavior of the system is derived by first determining an appropriate spatial wave structure. Physically relevant periodic solutions are obtained     

On the resonance effect in a rotating magnetic fluid

Data for the low-frequency magnetic susceptibility of a rotating magnetic fluid measured in a permanent bias field are presented. It is found that the susceptibility of the medium resonantly grows when the rotation frequency coincides with the measuring field frequency. Reasons for and mechanisms behind this phenomenon are discussed.     

Generation of electromagnetic waves by a rotating plasma

Generation of electromagnetic waves by an annular shell of plasma rotating in crossed radial electrostatic and axial magnetic fields in a cylindrical resonator is investigated theoretically. Dispersion relations are obtained describing the interaction of the waves with the plasma. It is shown that generation of waves by a narrow plasma shell is possible due to a cyclotron resonance, Čerenkov resonance, or plasma resonance. Here we consider a Čerenkov resonance, where the velocities of the plasma components and the phase velocities of the waves are perpendicular to the constant magnetic field. The frequencies and growth rates of the waves are found under conditions of the above-mentioned resonances in a uniform and in a nonuniform plasma shell. Advantages and disadvantages of wave generation under various conditions are noted. Zh. Tekh. Fiz. 69, 16–21 (February 1999)     

Over-reflection of travelling internal waves in a rotating stratified fluid

Summary It has been known for many years that waves of different kind propagating in a fluid and incident on a mean flow localized shear layer can exhibit, in the linear theory, a reflection coefficient larger than unity. When this phenomenon takes place the wave is said to be over-reflected at the shear layer. In this paper the over-reflection of inertial-gravity waves in a stratified rotating fluid in horizontal sheared motion is studied by making use of the constancy of the net vertical energy flux associated with the wave field. It is found that over-reflection can take place if some physical conditions, explicitly evaluated, are locally satisfied in the fluid. Such conditions are discussed and a comparison is carried out with the same phenomenon in a nonrotating system.

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Riassunto Si sa da molti anni che la teoria lineare di onde di diversa natura, propagantesi in un fluido ed interagenti con uno strato localizzato di shear, prevede, in alcuni casi, un coefficiente di riflessione maggiore dell'unità. Questo fenomeno prende il nome di super riflessione. In questo articolo si studia la super riflessione delle onde gravito-inerziali in un fluido stratificato in moto orizzontale con la velocità dipendente dalla sola coordinata verticale. Lo studio è portato a termine servendosi della condizione di continuità e costanza del flusso netto verticale di energia associata al campo d'onda. Si trova che la super riflessione avviene se sono soddisfatte alcune condizioni fisiche che sono esplicitamente determinate: tali condizioni sono inoltre discusse in dettaglio ed i risultati sono confrontati con quelli, classici, relativi alla propagazione di onde interne nei fluidi stratificati in assenza di rotazione.

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Резюме В течение многих лет известно, что линейная теория волн различной природы, которые распространяются в жидкости и взаимодействуют с локализованным пограничным слоем, предсказывает, что в некоторых случаях коэффициенты отражения могут превьщать единицу. Зто явление носит название супер-отражения (сверх-отражение) на пограничном слое. В этой статье исследуется супер-отражение инерциальной гравитационной волны в стратифицированной вращающейся жидкости в случаэ горизонтального движения со скоростью, зависящей только от вертикальной координаты. При рассмотрении учитывается постоянство результирующей вертикальной энергии, связанной с полем волны. Получено, что сверх-отражение может иметь место, если локально в жидкости выполняются некоторые физические условия. Проводится обсуждение этих условий и полученные результаты сравниваются с классическими результатами по распространению внутренних волн в стратифицированной жидкости в отсутствии вращения.

     

Bifurcations of the shape of a magnetic fluid droplet in a rotating magnetic field

An analysis is made of the behavior of a magnetic droplet suspended in a liquid in a high-frequency uniform, rotating magnetic field. In weak fields the droplet is spheroidal while in strong fields it is disk-shaped. The observed change in the shape of the droplet as the amplitude of the field increases depends on the magnetic permeability μ of the liquid and takes place according to three scenarios: (a) for small μ the spheroidal droplet is continuously converted into a disk; (b) for intermediate μ there is a range of fields in which the droplet becomes a triaxial ellipsoid with its major axis lying in the plane of the field, and spheroid-triaxial ellipsoid-disk transitions take place as a result of a soft bifurcation; (c) at high μ both transitions are hard. Theoretical calculations are made of the stability curve for the various droplet shapes. It is predicted that a change in the types of droplet shape bifurcations will occur in strong fields. A comparison is made with the experimental data.     

Shock waves in a rotating non-Maxwellian viscous dusty plasma

A theoretical model is presented to study the characteristics of dust acoustic shock in a viscous, magnetized, rotating dusty plasma at both fast and slow time scales. By employing the reductive perturbation technique, the non-linear Zakharov–Kuznetsov–Burger (ZKB) equation is derived for both cases when the dust is inactive and dynamic (fast and slow time scales). Both electrons and ions are considered to follow the kappa/Cairns distribution. It is observed that in both cases, i.e. when dust is in the background and active, viscosity plays a key role in dissipation for the propagation of acoustic shock. Magnetic field and rotation are responsible for the dispersive term. Superthermality is found to affect significantly the formation of the shock wave along with viscous nature of plasma, whereas the dust charge affects the non-linear coefficient of the ZKB equation. The present investigation may be beneficial to the understanding of the rotating plasma, in particular the experiments being carried out.     

Thermal convection in a rotating layer of a magnetic fluid

We consider Brownian particles with the ability to take up energy from the environment, to store it in an internal depot, and to convert internal energy into kinetic energy of motion. Provided a supercritical supply of energy, these particles are able to move in a “high velocity” or active mode, which allows them to move also against the gradient of an external potential. We investigate the critical energetic conditions of this self-driven motion for the case of a linear potential and a ratchet potential. In the latter case, we are able to find two different critical conversion rates for the internal energy, which describe the onset of a directed net current into the two different directions. The results of computer simulations are confirmed by analytical expressions for the critical parameters and the average velocity of the net current. Further, we investigate the influence of the asymmetry of the ratchet potential on the net current and estimate a critical value for the asymmetry in order to obtain a positive or negative net current. Received 20 September 1999     

Photon dynamics in plasma waves

In this Letter the evolution of a single photon and collective effect of a photon system in background plasma waves are uniformly described in the framework of photon dynamics. In a small-amplitude plasma wave the modulation of photon dynamical behavior by the plasma wave can be treated as perturbation, and photon acceleration effect and photon Landau damping are investigated in linear theory. In an arbitrary-amplitude plasma wave, photon evolution trajectories in phase space are obtained by solving dynamical equations, and photon trapping effect and motion equations in the given plasma wave are also discussed.     

Dynamics of a nonmagnetic drop suspended in a magnetic fluid in a rotating magnetic field

The behavior of a nonmagnetic drop suspended in a magnetic fluid and subjected to the action of a rotating magnetic field is studied experimentally. The configurations of the drop in the form of prolate and oblate ellipsoids of revolution in the rotating field are investigated, and disintegration of the drop in the rotating field and the development of comb instability of its surface under certain conditions are observed.     

Excitation of magnetic field by Langumuir oscillations in a rotating plasma

Tadzhik State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 4, pp. 405–410, April, 1989.     

On the linearized shallow-water waves over a sloping bottom

Summary This paper presents an investigation concerning long waves on sloping beaches. On the other hand, an attempt is made to broaden the class of the realistic forms of bottom topography,h(x), with which an exact solution of the related eigenvalue problem is possible. Under the linearizing assumption, the investigation confirms thath ^−1/2 is a factor associated with the bottom topography which is involved in wave breaking along the shoreline (Green's law). Further, the bottom topography in the neighbourhood of the shoreline is approximated byh(x)=K ₀ x ^j. There-from it is deduced that all positive real values ofj are associated with the possible structure of the bottom profile. Consequently, each can be employed in the construction of possible wave forms. Finally, an attempt is made to obtain a closed form of solution associated with the governing linear differential equation whenh(x) is arbitrary. The comparison of the results with those obtained by using the refraction diagram suggests close agreement over the beach considered.

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Riassunto In questo lavoro si presenta una ricerca che riguarda onde lunghe su spiagge in pendenza. Inoltre si fa un tentativo di ampliare la classe delle forme realistiche della topografia del fondo,h(x), con cui è possibile una soluzione esatta del problema correlato dell'autovalore. Nell'ipotesi di linearizzazione la ricerca conferma cheh ^−1/2 è un fattore associato con la topografia del fondo che è implicata nella rottura dell'onda lungo la linea di costa (legge di Green). Inoltre, la topografia del fondo in prossimità della linea di costa si approssima conh(x)=K ₀ x ^j. Da questo si deduce che tutti i valori reali positivi dij sono associati con la struttura possibile del profilo del fondo. Di conseguenza, ognuno di questi può essere utilizzato nella costruzione di possibili forme d'onda. Infine, si tenta di ottenere una forma chiusa della soluzione associata con l'equazione principale lineare differenziale quandoh(x) è arbitrario. Il confronto dei risultati con quelli ottenuti usando diagrammi di rifrazione suggerisce un accordo stretto per tutta la spiaggia considerata.

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Резюме В этой работе исследуются длинные волны на наклонных берегах. С другой стороны делается попытка расширить класс реалистических форм топографии дна,h(x), для которых возможно точное решение проблемы собственных значений. Предполагая линеаризацию, исследование подтверждает, чтоh ^−1/2 представляет фактор, связанный с топографией дна, который входит в разрушение волн вдоль береговой линии. Топографиа дна в окрестности береговой линии аппроксимируется выражениемh(x)=K ₀ x ^j. Отсюда следует, что все положительные значенияj связаны с возможной структурой профиля дна. Следовательно, каждое значение может быть использовано при конструровании возможных волновых форм. В заключение, предпринимается попытка получить замкнутую форму решения, связанного с определяющим дифференциальным уравнением, когдаh(x) является произвольной функцией. Сравнение результатов с результатами, полученными, используя диаграмму рефракции, свидетельствует о согласии вдоль всего рассмотренного берега.