Electrostatic stability of the liquid layer surface on a hard wettable cylindrical substrate

The wave motion in a cylindrical layer of an ideal conducting liquid on a hard rod kept at a constant electrical potential is calculated accurate to the first order of smallness in dimensional perturbation of the free surface. The instability of the free surface is also considered. A dispersion relation is derived. It is shown that the range of instability waves depends on only the electric field strength near the free surface and the instability increments of capillary waves decrease as the layer gets thinner. The influence of the hard rod becomes tangible only when its radius becomes comparable to the thickness of the liquid layer.     

Nonlinear analysis of interaction between finite-amplitude capillary waves in a layered inhomogeneous liquid

The nonlinear capillary wave motion in a two-layer liquid with a free surface is analytically investigated accurate to the second order of smallness in ratio of the wave amplitude to the layer thickness. The layers differ in physicochemical properties. A capillary analogue to the “dead water” effect is observed in the system in both linear and quadratic approximations. In the absence of an electric charge at the interfaces, internal nonlinear resonance interaction between capillary waves is also absent regardless of the place of their origination. When there is a charge at the interlayer boundary, capillary waves resonantly interact with each other.     

Thickness of a boundary layer attributed to the wave motion on the charged free surface of a viscous liquid

It is shown that the analytical estimator for the boundary layer thickness that contains the wave frequency in the denominator and is proposed for approximate calculation of the wave motion on the free surface of a viscous liquid cannot be formally applied to the wave motion on the uniformly charged liquid surface. The fact is that, when the surface charge density attains a value critical in terms for the Tonks-Frenkel instability, the wave frequency tends to zero. From the analysis of liquid motions near the electric charge critical density, a technique is proposed for calculating the thickness of a boundary layer attributed to flows of various kinds. It is found that the thickness of the boundary layer due to aperiodic flows with amplitudes exponentially growing with time (such flows take place at the stage of instability against the surface charge) does not exceed a few tenths of the wavelength, whereas the thickness of the boundary layer due to exponentially decaying liquid flows is roughly equal to the wavelength.     

Nonlinear calculation of the electric field strength on the surface of a melting hailstone in a thundercloud

The contribution of aerodynamic pressure acting on the surface of a water layer to a total electric field near the free surface of the layer is considered. The layer covers a charged melting hailstone moving parallel to the external electrostatic field vector. An asymptotic analytical expression for the electric field strength near a water-covered hailstone is derived in an approximation that is quadratic in the amplitude of capillary oscillations of a charged conducting liquid layer on the surface of the hailstone. It is found that the motion of the hailstone in ambient air influences the total electric field near the hailstone only slightly but noticeably enhances energy exchange between neighboring oscillation modes. An air flow about the hailstone is shown to have an appreciable effect on the possibility of nonlinear resonance energy exchange between initially excited modes and modes due to the nonlinear interaction.     

On the possibility of corona initiation at the surface of a liquid layer nonlinearly oscillating on the surface of a charged hailstone placed in a uniform electrostatic field

An expression for the electric field strength near a watered hailstone is derived in an approximation quadratic in the amplitude of capillary oscillations of a charged conducting liquid layer covering the hailstone. As the number of the mode governing the initial deformation of the equilibrium spherical free surface of the liquid layer increases and its thickness decreases, the electric field strength in the neighborhood of the capillary wave crests rises. Even in the case of small charges and low electric fields, the electric field near the hailstone is high enough to initiate a corona.     

On the possibility of initiating a corona discharge at the crests of nonlinear waves on the surface of a charged thin layer of a viscous conducting liquid

An analytic expression for the electrostatic field strength at the free surface of a thin layer of a uniformly charged viscous incompressible liquid is obtained in second-order asymptotic calculations in the amplitude of a periodic capillary-gravity wave propagating over the liquid surface. It is shown that a corona discharge at the crests of the waves can be initiated at subcritical values of the field strength (in the sense of possible realization of the Tonks-Frenkel instability). The electrostatic field strength at the crests of nonlinear waves increases with the wavenumber and the wave amplitude.     

Experimental observation of motion of edge dislocations in Ge/Ge<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Si<Subscript>1–<Emphasis Type="Italic">x</Emphasis></Subscript>/Si(001) (<Emphasis Type="Italic">x</Emphasis> = 0.2–0.6) heterostructures

The rotating magnetohydrodynamic flows of a thin layer of astrophysical and space plasmas with a free surface in a vertical external magnetic field are considered in the shallow water approximation. The presence of a vertical external magnetic field changes significantly the dynamics of wave processes in an astrophysical plasma, in contrast to a neutral fluid and a plasma layer in an external toroidal magnetic field. There are three-wave nonlinear interactions in the case under consideration. Using the asymptotic method of multiscale expansions, we have derived nonlinear equations for the interaction of wave packets: three magneto- Poincare waves, three magnetostrophic waves, two magneto-Poincare and one magnetostrophic waves, and two magnetostrophic and one magneto-Poincare waves. The existence of decay instabilities and parametric amplification is predicted. We show that a magneto-Poincare wave decays into two magneto-Poincare waves, a magnetostrophic wave decays into two magnetostrophic waves, a magneto-Poincare wave decays into one magneto-Poincare and one magnetostrophic waves, and a magnetostrophic wave decays into one magnetostrophic and one magneto-Poincare waves. There are the following parametric amplification mechanisms: the parametric amplification of magneto-Poincare waves, the parametric amplification of magnetostrophic waves, the amplification of a magneto-Poincare wave in the field of a magnetostrophic wave, and the amplification of a magnetostrophic wave in the field of a magneto-Poincare wave. The instability growth rates and parametric amplification factors have been found for the corresponding processes.     

Rossby waves in the magnetic fluid dynamics of a rotating plasma in the shallow-water approximation

We have studied rotating magnetohydrodynamic flows of a thin layer of astrophysical plasma with a free boundary in the β-plane. Nonlinear interactions of the Rossby waves have been analyzed in the shallow-water approximation based on the averaging of the initial equations of the magnetic fluid dynamics of the plasma over the depth. The shallow-water magnetohydrodynamic equations have been generalized to the case of a plasma layer in an external vertical magnetic field. We have considered two types of the flow, viz., the flow in an external vertical magnetic field and the flow in the presence of a horizontal magnetic field. Qualitative analysis of the dispersion curves shows the presence of three-wave nonlinear interactions of the magnetic Rossby waves in both cases. In the particular case of zero external magnetic field, the wave dynamics in the layer of a plasma is analogous to the wave dynamics in a neutral fluid. The asymptotic method of multiscale expansions has been used for deriving the nonlinear equations of interaction in an external vertical magnetic field for slowly varying amplitudes, which describe three-wave interactions in a vertical external magnetic field as well as three-wave interactions of waves in a horizontal magnetic field. It is shown that decay instabilities and parametric wave amplification mechanisms exist in each case under investigation. The instability increments and the parametric gain coefficients have been determined for the relevant processes.     

Sheared poloidal flow driven by mode conversion in tokamak plasmas

A two-dimensional integral full-wave model is used to calculate poloidal forces driven by mode conversion in tokamak plasmas. In the presence of a poloidal magnetic field, mode conversion near the ion-ion hybrid resonance is dominated by a transition from the fast magnetosonic wave to the slow ion cyclotron wave. The poloidal field generates strong variations in the parallel wave spectrum that cause wave damping in a narrow layer near the mode conversion surface. The resulting poloidal forces in this layer drive sheared poloidal flows comparable to those in direct launch ion Bernstein wave experiments.     

Nonlinear degenerate resonance interaction of waves on a charged liquid surface

The physics of nonlinear degenerate resonance energy exchange between waves on the flat free charged surface of a conducting liquid is analytically (asymptotically) studied up to the second order of smallness. A set of differential equations for the evolution of the amplitudes of nonlinearly resonantly interacting waves is derived. It turns out that nonlinear computations (taking into account the dependence of the wave frequency on the finite amplitude) yield an infinite number of degenerate resonances, although computations based on frequencies found in the linear theory give a finite number of resonances. In nonlinear computations, the positions of the degenerate resonances depend on the surface charge density (or on the external electric field normal to the free surface of the liquid) in contrast to the results of linear computations (based on frequencies found in the linear theory). It is found that as the wavenumber of an exact degenerate resonance is approached (that is, in the vicinity of this number), the direction of energy transfer changes sign: now the energy is transferred from a shorter wave to a longer one and not the reverse.     

Nonlinear periodic waves on the charged surface of a finite-thickness ideal liquid layer

In the fourth order of smallness in the amplitude of a periodic capillary-gravitational wave travelling over the uniformly charged free surface of an ideal incompressible conducting liquid of a finite depth, analytical expressions for the evolution of the nonlinear wave, velocity field potential of the liquid, electrostatic field potential above the liquid, and nonlinear frequency correction that is quadratic in a small parameter are derived. It is found that the dependence of the amplitude of the nonlinear correction to the frequency on the charge density on the free liquid surface and on the thickness of the liquid layer changes qualitatively when the layer gets thinner. In thin liquid layers, the resonant wavenumber depends on the surface charge density, while in thick layers, this dependence is absent.     

Acoustic flows in a fluid layer on a vibrating substrate

The field of radiation forces in a fluid layer on a solid substrate is calculated. This field is formed during propagation of surface capillary wave along a free surface. The wave is excited by substrate vibrations as a result of instability development. The structure of acoustic flows is studied. Their effect on small-size particles and the possibilities of generating ordered structures from these particles are discussed.     

On the initiation of a corona discharge near the surface of a nonlinearly oscillating liquid layer on the surface of a charged hailstone

An expression is derived for the electric field strength near a wet hailstone in an approximation quadratic in the oscillation amplitude of a charged liquid layer on its surface. It is found that the electric field strength in a small neighborhood of the capillary wave crests grows with the number of a mode governing the initial deformation of the equilibrium (spherical) shape of the liquid layer. Even if the charge is small (when the Rayleigh parameter of the hailstone equals one-hundredth of the value critical for stability against the self-charge), the electric field near the hailstone is high enough for initiating a corona discharge in its vicinity.     

Influence of charge relaxation on the capillary disintegration of a jet of a viscous dielectric liquid placed in an electrostatic field collinear with the axis of the jet

A dispersion relation is derived for capillary waves with an arbitrary symmetry on the surface of a charged jet of a finite-conductivity viscous liquid placed in an electric field collinear with the axis of the jet. Analytical calculations are carried out in an approximation that is linear in dimensionless wave amplitude. In the case of axisymmetric waves, the instability of which causes disintegration of the jet into drops, the finiteness of the potential equalization rate has a noticeable effect only for jets of poorly conducting liquids. The charge relaxation shows up in that “purely relaxation” periodic and aperiodic liquid flows arise. When the conductivity of the liquid declines, the instability growth rates for unstable waves increase and their spectrum extends toward short waves. A charge present on the surface of the jet enhances its instability. An increase in the charge surface diffusion coefficient variously influences the capillary and relaxation branches of the solution: the damping ratio increases in the former case and decreases in the latter. As the diffusion coefficient rises, relaxation flows may become unstable.     

Field distribution of a light wave near a magnetic defect in one-dimensional photonic crystals

The field distribution of a light wave near a magnetic defect in a one-dimensional photonic crystal is analyzed. It is shown that, by properly varying the magnetic defect thickness or the parameters of the photonic crystal surrounding the defect, one can create a situation where the electric field of a light wave will be localized predominantly inside the magnetic layer or, conversely, in the immediate vicinity of the layer surface. This opens up possibilities for optimizing the Q factor of a magnetic microcavity in the presence of dissipation in the magnetic layer and, hence, for enhancing the linear and nonlinear magneto-optical effects. The possibility of separating the contributions from the surface and volume of the magnetic material to the nonlinear magnetooptical properties by properly varying the field distribution over the defect thickness is discussed.     

Flow pattern due to capillary-gravitational waves in a charged layer of a viscous conducting liquid on a solid support

Analytical solutions for the time evolution of a capillary-gravitational wave in a charged layer of a viscous conducting liquid on a solid support are found. It is shown that the velocity field eddy component of the wave-induced liquid flow arises not only near the free surface of the liquid, but also at the solid bottom. The ratio between the amplitudes of these eddy components depends on the relationship between the thickness of the layer and the wavelength. If the wavelength far exceeds the thickness, the eddy flow amplitude near the bottom exceeds that near the free surface and the eddy flow occupies the whole volume of the liquid.     

Formation of singularities on the surface of a liquid metal in a strong electric field

The nonlinear dynamics of the free surface of an ideal conducting liquid in a strong external electric field is studied. It is established that the equations of motion for such a liquid can be solved in the approximation in which the surface deviates from a plane by small angles. This makes it possible to show that on an initially smooth surface for almost any initial conditions points with an infinite curvature corresponding to branch points of the root type can form in a finite time. Zh. éksp. Teor. Fiz. 114, 2043–2054 (December 1998)     

Effect of heat transfer on the penetration of an electromagnetic pulse into a plasma layer and the inverse skin effect

Penetration of a heating pulse into a plasma layer was studied using the system of coupled nonlinear equations for electric field, electron, and ion temperatures. Numerical calculations of field structure and temperature evolution are performed both in the absence and in the presence of heat transfer. It is established that heat transfer leads to a more rapid penetration of the field near the illuminated surface of the layer and impairs penetration in regions of the layer far from this surface. We found that heat transfer promotes the creation of more favourable conditions for manifestation of the inverse skin effect.     

Nonlinear interactions of surface waves with incident radiation at a narrow inhomogeneous plasma layer

The amplitudes of the waves radiating at combination frequencies from the plasma boundary due to nonlinear interaction of surface waves with radiation incident on a narrow inhomogeneous plasma layer, are determined. The method used allows for the discontinuity at the plasma boundary of the tangential components of the electric field of the wave at the combination frequencies.     

Nonlinear oscillations of a charged jet of a conducting liquid under multimode initial deformation of its surface

The subject of consideration is a uniformly charged jet of an ideal incompressible conducting liquid moving with a constant velocity along the symmetry axis of an undisturbed cylindrical surface. An evolutionary expression for the jet shape is derived accurate to the second order of smallness in oscillation amplitude for the case when the initial deformation of the equilibrium surface is a superposition of a finite number of both axisymmetric and nonaxisymmetric modes. The flow velocity field in the jet and the electric field distribution near it are determined. The positions of internal nonlinear secondary combined three-mode resonances are found, which are typical of nonlinear corrections to the analytical expressions for the jet shape, flow velocity field potentials, and electrostatic field in the vicinity of the jet.