Kelvin waves cascade in superfluid turbulence

We study numerically the interaction of four initial superfluid vortex rings in the absence of any dissipation or friction. We find evidence for a cascade of Kelvin waves generated by individual vortex reconnection events which transfers energy to higher and higher wave numbers k. After the vortex reconnections occur, the energy spectrum scales as k(-1) and the curvature spectrum becomes flat. These effects highlight the importance of Kelvin waves and reconnections in the transfer of energy within a turbulent vortex tangle.     

Wave-induced fluid flow in random porous media: attenuation and dispersion of elastic waves

A detailed analysis of the relationship between elastic waves in inhomogeneous, porous media and the effect of wave-induced fluid flow is presented. Based on the results of the poroelastic first-order statistical smoothing approximation applied to Biot's equations of poroelasticity, a model for elastic wave attenuation and dispersion due to wave-induced fluid flow in 3-D randomly inhomogeneous poroelastic media is developed. Attenuation and dispersion depend on linear combinations of the spatial correlations of the fluctuating poroelastic parameters. The observed frequency dependence is typical for a relaxation phenomenon. Further, the analytic properties of attenuation and dispersion are analyzed. It is shown that the low-frequency asymptote of the attenuation coefficient of a plane compressional wave is proportional to the square of frequency. At high frequencies the attenuation coefficient becomes proportional to the square root of frequency. A comparison with the 1-D theory shows that attenuation is of the same order but slightly larger in 3-D random media. Several modeling choices of the approach including the effect of cross correlations between fluid and solid phase properties are demonstrated. The potential application of the results to real porous materials is discussed.     

Rotational intermittency and turbulence induced lift experienced by large particles in a turbulent flow

The motion of a large, neutrally buoyant, particle freely advected by a turbulent flow is determined experimentally. We demonstrate that both the translational and angular accelerations exhibit very wide probability distributions, a manifestation of intermittency. The orientation of the angular velocity with respect to the trajectory, as well as the translational acceleration conditioned on the spinning velocity, provides evidence of a lift force acting on the particle.     

Faraday waves, streaming flow, and relaxation oscillations in nearly circular containers

Faraday waves near onset in an elliptical container are described by a third-order system of ordinary differential equations with characteristic slow-fast structure. These equations describe the interaction of standing waves with a weakly damped streaming flow driven by Reynolds stresses in boundary layers at the free surface and the rigid walls, and capture the proliferation with decreasing damping of periodic and nonperiodic relaxation oscillations observed near onset in previous simulations. These structures are the result of slow drift through symmetry-related Hopf bifurcations.     

Violation of the coherence of radio waves induced by a cascade shower in the lunar regolith

It has been shown that small fluctuations of the refractive index of the lunar regolith owing to, e.g., a nonuniform density distribution, give rise to the loss of the coherence of a Cherenkov radio pulse induced by a cascade shower from an ultrahigh-energy particle and to a strong decrease in the spectral density of the radio signal. This can be one of the causes of why no events from ultrahigh-energy cosmic particles on the surface of the moon have been detected.     

Nonlinear nature of kinetic undamped waves induced by electrostatic turbulence in stimulated Raman backscattering

The influence of low-frequency waves of kinetic nature induced by electron trapping in backward Stimulated Raman Scattering (SRS) is investigated. Semi-lagrangian Vlasov-Maxwell simulations are carried out not only for periodic boundary conditions but also in the case of an open plasma with parabolic shape, in optical mixing. We provide a numerical example of generation of KEEN (kinetic electrostatic electron nonlinear) waves nonlinearly induced from the SRS through a mechanism we first here elucidate. In particular we identify a process of backward scattering of the SRS probe light from the so generated KEEN waves, which may provide a mechanism for the possible experimental observation and measurement of such nonlinear structures.     

Microscale fluid flow induced by thermoviscous expansion along a traveling wave

The thermal expansion of a fluid combined with a temperature-dependent viscosity introduces nonlinearities in the Navier-Stokes equations unrelated to the convective momentum current. The couplings generate the possibility for net fluid flow at the microscale controlled by external heating. This novel thermomechanical effect is investigated for a thin fluid chamber by a numerical solution of the Navier-Stokes equations and analytically by a perturbation expansion. A demonstration experiment confirms the basic mechanism and quantitatively validates our theoretical analysis.     

Amplitude equation and pattern selection in Faraday waves

A nonlinear theory of pattern selection in parametric surface waves (Faraday waves) is presented that is not restricted to small viscous dissipation. By using a multiple scale asymptotic expansion near threshold, a standing wave amplitude equation is derived from the governing equations. The amplitude equation is of gradient form, and the coefficients of the associated Lyapunov function are computed for regular patterns of various symmetries as a function of a viscous damping parameter gamma. For gamma approximately 1, the selected wave pattern comprises a single standing wave (stripe pattern). For gamma<1, patterns of square symmetry are obtained in the capillary regime (large frequencies). At lower frequencies (the mixed gravity-capillary regime), a sequence of sixfold (hexagonal), eightfold, ...patterns are predicted. For even lower frequencies (gravity waves) a stripe pattern is again selected. Our predictions of the stability regions of the various patterns are in quantitative agreement with recent experiments conducted in large aspect ratio systems.     

Spin waves on chains of YIG particles: dispersion relations,Faraday rotation,and power transmission

We calculate the dispersion relations for spin waves on a periodic chain of spherical or cylindrical Yttrium Iron Garnet (YIG) particles. We use the quasistatic approximation, appropriate when kd ? 1, where k is the wave number and d the interparticle spacing. In this regime, because of the magnetic dipole-dipole interaction between the localized magnetic excitations on neighboring particles, dispersive spin waves can propagate along the chain. The waves are analogous to plasmonic waves generated by electric dipole-dipole interactions between plasmons on neighboring metallic particles. The spin waves can be longitudinal (L), transverse (T), or elliptically polarized. We find that a linearly polarized spin wave undergoes a Faraday rotation as it propagates along the chain. The amount of Faraday rotation can be tuned by varying the off-diagonal component of the permeability tensor. We also discuss the possibility of wireless power transmission along the chain using these coupled spin waves.     

The sensitive detection of NO by Faraday modulation spectroscopy with a quantum cascade laser

A spectrometer based on a quantum cascade laser and capable of operating at particular wavelengths in the mid-infrared with very high sensitivity for the detection of open-shell molecules has been developed. It exploits magnetic field modulation in the Faraday rotation configuration. The signals for nitric oxide (NO) that may be observed with this instrument have been studied and their dependence on the J and Ω quantum numbers investigated with a simulation program. It is shown that the Q(3/2) transition of NO in the ²Π_3/2 component at 1875.8 cm^?1 would provide the greatest sensitivity for detection. The experimental observation of the R(21/2) transition of the Ω = 1/2 component gives a detection limit of 41 ppb of NO in air at a pressure of 25 mbar. Detection of NO through the Q(3/2) transition would provide a detection limit of 4 ppb at this pressure.     

Heteroclinic dynamics in a model of Faraday waves in a square container

We study periodic orbits associated with heteroclinic bifurcations in a model of the Faraday system for containers with square cross-section and single-frequency forcing. These periodic orbits correspond to quasiperiodic surface waves in the physical system. The heteroclinic bifurcations are related to a continuum of heteroclinic connections in the integrable Hamiltonian limit, some of which persist in the presence of small damping. The dynamics in the neighborhood of one of the heteroclinic bifurcations are examined in detail using approximate Poincaré maps, with predictions that agree with numerical computations. The results suggest a great richness of possible dynamics of Faraday waves even in simple geometries and with single-frequency forcing.     

On the notion of a rotating fluid force induced by swirling flow

The Bently/Muszynska (B/M) model shows that oil whirl and oil whip are both self-sustained vibrations associated with two unstable modes of a rotor–fluid system. The model includes a rotating fluid damping and inertia force. In certain configurations, the rotating damping force overcomes the frictional internal damping of the rotor and pushes the rotor into a stable limit cycle of circular orbiting. Such a notion of a rotating fluid force is based on bulk-flow models of fluid-filled clearances that could be approximated as narrow since the tangential velocity of the fluid then translates to one angular velocity at a certain radial distance defined by an average radius. This paper scrutinizes the assumption of a rotating fluid inertia force and pinpoints the additional inertial effects of the swirling flow as the gap width increases. These effects are clarified by deriving the equation of motion of a body with a mass subjected to motion-induced fluid forces of a confined swirling flow. We show that the inertial effects of the swirling flow counteract the destabilizing effect of the rotating damping force. However, if the body mass is larger than the displaced fluid mass, instability follows. The frequency of the unstable mode is unchanged by the additional inertial effects and is always equal to the frequency of the damping that induces the instability.     

On nonanalytic solitary waves formed by a nonlinear dispersion

We study the prototypical, genuinely nonlinear, K(m, n) equation, u_t ± a(u^m)_x + (uⁿ)_xxx = 0, a = const, which exhibits a number of remarkable dispersive effects. In particular, the distinguished subclass wherein m = n + 2 is transformed into a new, purely dispersive equation free of convection. In addition to compactons, the K(m, n) can support both kinks and solitons with an infinite slope(s), periodic waves and dark solitons with cusp(s) all being manifestations of nonlinear dispersion in action. For n < 0 the enhanced dispersion at the tail may generate algebraically decaying patterns.     

湍流大气中反射光束的扩展

本文基于推广的惠更斯-菲涅耳原理,利用“平方近似”假设,导得湍流大气中被反射激光束扩展的表达式,并对反射光束的扩展特性作了讨论。证实了平面镜反射光束的扩展存在放大效应,角反射器反射光束的扩展存在自补偿效应。理论公式还表明,利用长波长激光及使用较大的发射、反射孔径,可以减小反射光束的扩展。     

Double atmospheric gravity wave frequency oscillations of sporadic E formed in a horizontal shear flow

The new theory of sporadic E density oscillation with double atmospheric gravity wave (AGW) frequency in two-dimensional case taking into account ions ambipolar diffusion is presented. It is found that densities of multi-layered sporadic E, formed under the influence of atmospheric vortical perturbation (with vertical wavelength λz≠0) evolving in the horizontal shear flow (shear wave), can oscillate with up to double Brunt-Väisälä frequency under the action of short-period AGW, in which shear wave is transformed. The formation of multi-layered sporadic E (inside regions with vertical thickness about λz/2) and its density changes in every half AGW period close to ions convergence region occur by combined action of ion-neutral collision and Lorentz forcing and can cause additional accumulation of ions responsible for sporadic E density oscillation with double AGW frequency.     

Observation of the nonlinear dispersion relation and spatial statistics of wave turbulence on the surface of a fluid

We report experiments on gravity-capillary wave turbulence on the surface of a fluid. The wave amplitudes are measured simultaneously in time and space by using an optical method. The full space-time power spectrum shows that the wave energy is localized on several branches in the wave-vector-frequency space. The number of branches depends on the power injected within the waves. The measurement of the nonlinear dispersion relation is found to be well described by a law suggesting that the energy transfer mechanisms involved in wave turbulence are restricted not only to purely resonant interaction between nonlinear waves. The power-law scaling of the spatial spectrum and the probability distribution of the wave amplitudes at a given wave number are also measured and compared to the theoretical predictions.