A nonlinear PSE method for two-fluid shear flows with complex interfacial topology

A nonlinear stability method is developed for laminar two-fluid shear flows which undergo changes in the interface topology. The method is based on the nonlinear parabolized stability equations (PSE) and incorporates a scalar-based interface capturing (IC) scheme in order to track complex deformations of the fluid interface. In doing so, the formulation retains the flexibility and physical insight of instability-wave based methods, while providing hydrodynamic modeling capabilities similar to direct numerical calculations: the new formulation, referred to as the IC-PSE, can capture the nonlinear physical mechanisms responsible for generating large-scale, two-fluid structures, without incurring heavy computational costs. This approach is valid for spatially developing, laminar two-fluid shear flows which are convectively unstable, and can naturally account for the growth of finite amplitude interfacial waves, along with changes to the interfacial topology. We demonstrate the accuracy of the IC-PSE against direct Navier–Stokes calculations for two-fluid mixing layers with density and viscosity stratification. The comparisons show that the IC-PSE can predict the dynamics of the instability waves and capture the formation of Kelvin–Helmholtz vortex rolls and large scale liquid structures, at an order of magnitude less computational cost than direct calculations. The role of surface tension in the IC-PSE formulation is shown to be valid for flows in which Re/We ? 1, and the method accurately predicts the formation and non-linear evolution of flow structures in this limit. This is demonstrated for spatially developing mixing layers which lead to vortex roll-up and ligaments, prior to droplet formation. The pinch-off process itself is a high surface tension phenomenon and in not considered herein. The method also accurately captures the effect of interfacial waves on the mean flow, and the topology changes during the non-linear evolution of the two-fluid structures.     

Nonlinear electrohydrodynamic phenomena and droplet generation in charged jets of conducting liquid

Phenomena occurring at the tip of a charged conducting jet are analyzed in detail using numerical methods developed for axially symmetric flows. Universal mechanisms (independent of the method for producing the jet) for droplet formation with different ratios of the Laplace and electrical pressures on the lateral surface are identified. An explanatory analysis is given for all of the nonlinear stages of the classical Rayleigh instability of a charged conducting drop, beginning with the formation of a jet at the surface of the drop and culminating in the generation of a developed jet of secondary droplets. Zh. Tekh. Fiz. 69, 1–9 (November 1999)     

Dynamical instability of charged self-gravitating stars in modified gravity

This paper explores the instability limits for the stellar objects in the background of a particular modified gravity theory. In order to accomplish the instability conditions, a spherically symmetric anisotropic charged fluid influenced by the modified gravity is taken under consideration. The modified field equations and the equations of motion are accomplished in background of the Gauss–Bonnet gravity. These equations are perturbed to constitute the collapse equation. The Newtonian and post-Newtonian limits are imposed and found that the dynamical instability of the fluid is explained by the adiabatic index which consists on analytical value depending on static profile of material variables.     

Nonlinear frequency mixing in a resonant cavity: Numerical simulations in a bubbly liquid

The study of nonlinear frequency mixing for acoustic standing waves in a resonator cavity is presented. Two high frequencies are mixed in a highly nonlinear bubbly liquid filled cavity that is resonant at the difference frequency. The analysis is carried out through numerical experiments, and both linear and nonlinear regimes are compared. The results show highly efficient generation of the difference frequency at high excitation amplitude. The large acoustic nonlinearity of the bubbly liquid that is responsible for the strong difference-frequency resonance also induces significant enhancement of the parametric frequency mixing effect to generate second harmonic of the difference frequency.     

Coarsening in an interfacial equation without slope selection revisited: Analytical results

In this Letter, we re-examen a one-dimensional model of epitaxial growth that describes pyramidal structures characterized by the absence of a preferred slope [L. Golubovi?, Phys. Rev. Lett. 78 (1997) 90]. A similarity approach shows that the typical mound lateral size and the interfacial width growth with time like t1/2 and t1/4, respectively. This result was previously presented by Golubovi?. Our contribution provides a mathematical justification for the existence of similarity solutions which correspond to, or predict, the typical coarsening process.     

A Boussinesq system for two-way propagation of interfacial waves

The theory of internal waves between two layers of immiscible fluids is important both for its applications in oceanography and engineering, and as a source of interesting mathematical model equations that exhibit nonlinearity and dispersion. A Boussinesq system for two-way propagation of interfacial waves in a rigid lid configuration is derived. In most cases, the nonlinearity is quadratic. However, when the square of the depth ratio is close to the density ratio, the coefficients of the quadratic nonlinearities become small and cubic nonlinearities must be considered. The propagation as well as the collision of solitary waves and/or fronts is studied numerically.     

液体表面低频声波的非线性声光效应

实现了液体表面上低频声波的光衍射,得到了稳定的、具有高阶衍射的高反衬衍射图样.理论上首次考虑到表面声波中的高次谐波,得到了相应的非线性条件下衍射强度分布的解析表达式,并将这种非线性理论与实验结果进行对比.对比结果表明,非线性理论与实验结果有更高的吻合程度.     

SH ultrasonic guided waves for the evaluation of interfacial adhesion

Shear-Horizontally (SH) polarized, ultrasonic, guided wave modes are considered in order to infer changes in the adhesive properties at several interfaces located within an adhesive bond joining two metallic plates. Specific aluminium lap-joint samples were produced, with different adhesive properties at up to four interfaces when a glass–epoxy film is inserted into the adhesive bond. EMAT transducers were used to generate and detect the fundamental SH₀ mode. This is launched from one plate and detected at the other plate, past the lap joint. Signals are picked up for different propagation paths along each sample, in order to check measurement reproducibility as well as the uniformity of the adhesively bonded zones. Signals measured for four samples are then compared, showing very good sensitivity of the SH₀ mode to changes in the interfacial adhesive properties. In addition, a Finite Element-based model is used to simulate the experimental measurements. The model includes adhesive viscoelasticity, as well as spatial distributions of shear springs (with shear stiffness K_T) at both metal–adhesive interfaces, and also at the adhesive–film interfaces when these are present. This model is solved in the frequency domain, but temporal excitation and inverse FFT procedure are implemented in order to simulate the measured time traces. Values of the interfacial adhesive parameters, K_T, are determined by an optimization process so that best fit is obtained between both sets of measured and numerically predicted waveforms. Such agreement was also possible by adjusting the shear modulus of the adhesive component. This work suggests a promising use of SH-like guided modes for quantifying shear properties at adhesive interfaces, and shows that such waves can be used for inferring adhesive and cohesive properties of bonds separately. Finally, the paper considers improvements that could be made to the process, and its potential for testing the interfacial adhesion of adhesively bonded composite components.     

Nonlinear guided waves in plates: A numerical perspective

Harmonic generation from non-cumulative fundamental symmetric (_S0$S_0$) and antisymmetric (_A0$A_0$) modes in plate is studied from a numerical standpoint. The contribution to harmonic generation from material nonlinearity is shown to be larger than that from geometric nonlinearity. Also, increasing the magnitude of the higher order elastic constants increases the amplitude of second harmonics. Second harmonic generation from non-phase-matched modes illustrates that group velocity matching is not a necessary condition for harmonic generation. Additionally, harmonic generation from primary mode is continuous and once generated, higher harmonics propagate independently. Lastly, the phenomenon of mode-interaction to generate sum and difference frequencies is demonstrated.     

Nonlinear interaction of a Gaussian EM beam with an electrostatic upper hybrid wave: Stimulated Raman scattering

Summary In this paper we have studied the nonlinear interaction of a Gaussian electromagnetic beam with an electrostatic upper hybrid wave in a collisionless magnetized plasma. On account of the interaction of the incident Gaussian electromagnetic beam with the plasma, a time-independent component of the ponderomotive force becomes finite and leads to the modification in the background density. This results in the excitation of the upper hybrid mode of the plasma. The excited electrostatic wave leads to the enhanced Raman backscattering. An expression for the scattered power is derived and the effect of the external static magnetic field on the enhancement of the density perturbation and scattered power is discussed. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Nonlinear propagation of relativistically intense electromagnetic waves in a collisionless plasma

We discuss the nonlinear propagation of relativistically intense electromagnetic waves into collisionless plasmas with special emphasis on one dimensional plane wave solutions of the propagating, standing and modulated types. These solutions exhibit a rich variety of phenomena associated with relativistic electron mass variation and coupling between transverse electromagnetic and longitudinal fields. They have important applications to problems of laser propagation, self-focusing in overdense plasmas, particle and photon acceleration and to electromagnetic radiation around pulsars.     

Surface-driven instability and enhanced relaxation in the dynamics of a nonequilibrium interface

We determine the stability of a nonequilibrium interface between two coexisting solid phases in the presence of a weak external field. Starting at the coarsegrained (Cahn-Hilliard) level, we use the method of matched asymptotics to derive the macroscopic interfacial dynamics. We then show that the external field leads to an instability due to flux along the interface, in contrast with the more common Mullins-Sekerka type instability, which involves fluxes normal to the interface. We also find that the external field produces an important modification of the Gibbs-Thomson relation. With these results, we perform the linear stability analysis for an approximately flat interface. If the field is tangent to the interface, the modification of the Gibbs-Thomson relation is important and the interface is stabilized. If the field is normal to the interface, the surface flux is important, and the effect can be stabilizing or destabilizing, but the orientational dependence is opposite what would be obtained if the Mullins-Sekerka instability dominates. Numerical simulations are performed to study the effect of the surface current and are in agreement with our analytical results.     

Coherent structures in presence of dust charge fluctuations

This paper shows the formation of nonlinear coherent structures in a dusty plasma in presence of dust charge fluctuations. Using the typical plasma parameters the potential of the nonlinear coherent structures is derived.     

Instability of bound states of a nonlinear Schrödinger equation with a Dirac potential

We study analytically and numerically the stability of the standing waves for a nonlinear Schrödinger equation with a point defect and a power type nonlinearity. A major difficulty is to compute the number of negative eigenvalues of the linearized operator around the standing waves. This is overcome by a perturbation method and continuation arguments. Among others, in the case of a repulsive defect, we show that the standing-wave solution is stable in and unstable in under subcritical nonlinearity. Further we investigate the nature of instability: under critical or supercritical nonlinear interaction, we prove the instability by blowup in the repulsive case by showing a virial theorem and using a minimization method involving two constraints. In the subcritical radial case, unstable bound states cannot collapse, but rather narrow down until they reach the stable regime (a finite-width instability). In the nonradial repulsive case, all bound states are unstable, and the instability is manifested by a lateral drift away from the defect, sometimes in combination with a finite-width instability or a blowup instability.     

Equilibrium shape and hysteresis behavior of liquid jets in transverse electric fields

The stability of a liquid jet subject to a transverse electric field is investigated in the framework of electrohydrostatic theory. It is shown that depending on the magnitude of permittivity ratio of the involved fluids S = ε_i/ε_o (inner to outer) compared to a critical permittivity ratio S_cr ≈ 27.45 the jet exhibits distinct behaviors; for S < S_cr the jet is stable and elongates indefinitely as the electric field is increased, while for S > S_cr it shows hysteresis behavior and becomes unstable beyond a critical electric capillary number Ca_cr. The results suggest that the jets are generally more stable than liquid drops.     

Dynamics of a single peak of the Rosensweig instability in a magnetic fluid

To describe the dynamics of a single peak of the Rosensweig instability a model is proposed which approximates the peak by a half-ellipsoid atop a layer of magnetic fluid. The resulting nonlinear equation for the height of the peak leads to the correct subcritical character of the bifurcation for static induction. For a time-dependent induction the effects of inertia and damping are incorporated. The results of the model show qualitative agreement with the experimental findings, as in the appearance of period doubling, trebling, and higher multiples of the driving period. Furthermore, a quantitative agreement is also found for the parameter ranges of frequency and induction in which these phenomena occur.     

Nonlinear analysis of the gradient drift instability

An analytical study of the gradient drift instability in the equatorial electrojet of wavelengths in the order of one kilometer is presented. Different mechanisms, linear, non-local and turbulent, are found in the literature to explain the predominance of the 1 km wavelength in the electrojet. In the present work a simplified model is proposed in which the nonlinear evolution of three coupled modes is followed. By considering that one of the modes attains the stationary state, the evolution of the other two is obtained, and it is found that they follow equations of the Lotka–Volterra type. A stable stationary nonlinear solution for these equations is also found, and the conditions under which periodic solutions are possible are analyzed.     

Nonlinear ion-acoustic waves in magnetized plasmas in presence of energetic electrons and positively charged dust

A theoretical investigation has been carried out for exploring different features of ion-acoustic solitary and shock waves in a three-component magnetized plasma containing a mixture of thermal and nonthermal (energetic) inertialess electrons, warm inertial ions, and positively charged stationary dust particles. The standard Korteweg-de Vries (Burgers) equation has been derived by employing the reductive perturbation method, and its solitary (shock) wave solution has been derived and examined analytically as well as numerically. The latter exhibits characteristic properties (amplitude, width, speed, and polarity) of the ion-acoustic solitary and shock waves. It has been shown that the ion-acoustic solitary and shock waves are significantly modified by different plasma parameters (viz. parameter measuring the ratio of dust charge density to ion charge density, parameter measuring the fraction of energetic electrons, parameter measuring ion or electron temperature, and the external magnetic field). The present investigation may help in understanding the physics of various nonlinear phenomena formed in many space plasma systems, (viz. earth's mesosphere, solar wind, and cometary tails) and laboratory devices (laboratory experiments of Samarian et al., Phys. rev. E. 64 , 056407 [2001] and of Fortov et al., New J. Physics 5 , 102 [2003]).     

Effect of surface-tension relaxation on the spectrum of motions of a liquid with charged free surface

The spectrum of capillary-relaxational motions of a charged free liquid surface is analyzed. The analysis takes into account the effect of surface-tension relaxation and the existence of two relaxation times due to different physical mechanisms. Each relaxation mechanism is associated with certain liquid wave motions. Motions due to different relaxation processes interact with each other and with capillary-gravity waves through nonlinear mechanisms.     

Application of Davidenko''s Method to a Lossy Nonlinear Waveguide

Davidenko's method is implemented for determining the complex propagation constants (Modal index and attenuation coefficient) of nonlinear TE waves guided by an asymmetrical lossy nonlinear dielectric wave-guide. The waveguide structure has a generalized nonlinear substrate with a permittivity of the form | E |and an absorbing cover making the propagation constant to be complex. Davidenko's method shows to be a fast and accurate analysis in finding the complex propagation constants. The effects of initial condition parameter on the propagation characteristics are investigated, analyzed and discussed.