It is now apparent that the two principal models of turbulence (the ‘‘beta’’ and ‘‘lognormal’’ models) and the extremes of a continuous family of (stable, attractive, hence ‘‘universal’’) multifractals characterized by Levy indices α=0 and 2, respectively. Using a technique called double trace moment analysis, and turbulent velocity data, we empirically obtain α≊1.3±0.1: As has long been suspected, turbulence really is ‘‘in between’’ the β and lognormal models. This describes the entire hierarchy of singularities of the Navier-Stokes equations.

A method for conditioning electron beams is proposed to enhance gain in resonant electron-beam devices by introducing a correlation between betatron amplitude and energy. This correlation reduces the axial-velocity spread within the beam, and thereby eliminates an often severe constraint on beam emittance. Free-electron-laser performance with a conditioned beam is examined and analysis is performed of a conditioner consisting of a periodic arry of ‘‘FODO’’ channels and idealized microwave cavitites excited in the ${\mathrm{TM}}_{210}$ mode. Numerical examples are discussed.

We present a new scheme, the ion-ripple laser, for generating tunable coherent radiation ranging from microwaves to the ultraviolet. A relativistic electron beam obliquely propagating through an ion ripple excites electromagnetic radiation which is coupled to a negative-energy electrostatic wave via backward Raman scattering. The radiation peaks at a resonance frequency of ω∼2${\gamma }^2$${\mathrm{\kappa }}_{\mathit{i}\mathit{r}}$c cosθ. We derive the fluid theory dispersion relation for wave coupling and estimate the nonlinear saturation level. A 1 2/2 D PIC simulation code is used to verify the theory and scaling laws.

The dynamics of transverse particle oscillations in the Fermilab Tevatron, artificially made nonlinear, is studied by observing beam profiles over periods up to an hour. A ‘‘diffusive’’ model with amplitude-dependent diffusion coefficient gives a quantitatively accurate description of beam evolution. The evolution is influenced strongly by nonlinear resonance.

The nonlinear beam dynamics of transverse betatron oscillators were studied experimentally at the Indiana University Cyclotron Facility Cooler Ring. Particles were kicked onto resonance islands and the properties of these islands were studied. The island tune was determined with high precision by Fourier analyzing the spectrum containing the island oscillations. The island width was estimated based on a single-resonance model. The Hamiltonian of particle motion near a resonance condition was thus deduced.

Freely evolving two-dimensional turbulence is studied experimentally, in thin layers of electrolyte. The density of vortices, their mean sizes, and the average separation between them are measured during the decay phase. Power laws are observed, and the corresponding exponents are found in good agreement with a recent analysis of Carnevale et al.

We study the dynamics of Staffman-Taylor fingering in terms of topological defects of the flow field. The defects are created and/or annihilated at the interface. The route towards the single-finger steady state is characterized by a detailed mechanism for defect annihilation. For small viscosity contrast this mechanism is impeded, and creation of new defects leads the system away from a single-finger solution. Strong evidence for a drastic reduction of the basin of attraction of the Saffman-Taylor finger is presented.

We examine the kinematics of quantum vortex configurations in three-dimensional space for an ideal incompressible fluid. The permitted quantum configurations are shown to be surfaces of vorticity, characterized topologically not only by their knottedness, but also by additional global properties such as twists and holes. Our results, obtained by representing an infinite-dimensional group of diffeomorphisms, contradict conclusions reached by approximating the infinite-dimensional system with finitely many degrees of freedom.

The probability distribution of passive temperature fluctuations is experimentally studied in grid-generated wind tunnel turbulence. It is shown that exponential tails occur for a mean temperature gradient but do not in the absence of a mean gradient. The velocity probability distribution is Gaussian.

The effective thermal diffusivity ${\mathit{D}}^{\mathrm{*}}$ and the probability distribution of temperature fluctuations are measured in a stirred fluid across which a temperature gradient is maintained. A distinct mixing transition is observed for ${\mathit{D}}^{\mathrm{*}}$ as a function of Reynolds number R. Above the transitions, the distribution is strongly non-Gaussian and approaches an exponential exp(-‖δT‖/βξ), where β is the local temperature gradient and ξ the correlation length.

We investigate numerically the question of blowup in finite time for the ‘‘swirling flow’’ of the three-dimensional incompressible Euler equations. Using rotational symmetry, the Euler equations reduce to a two-dimensional problem which is numerically solved by finite differences. The elliptic equation relating vorticity to velocity is solved with the multigrid method. Calculations were performed with 896×640 mesh points.

The wavelet decomposition is used to generalize the multifractal formalism to singular signals. The singularity spectrum is directly determined from the scaling behavior of partition functions that are defined from the wavelet transform modulus maxima. Illustrations on fractal signals with a recursive structure, e.g., devil’s staircases, are shown. Applications to fully developed turbulence data and Brownian signals are reported.

New numerical evidence for a transition to hard turbulence in 2D Boussinesq convection is presented. These 2D simulations agree with some, but not all, experimental results for the scaling properties of 3D hard turbulence. The transition to 2D hard turbulence, as measured by a change in the Nusselt-Rayleigh scaling law, coincides with a gradual change in the velocity probability distribution from Gaussian to exponential form and with the development of a ‘‘well-mixed’’ central region.

We show that the photoacoustic pressure in one, two, and three dimensions can be found as mappings of the optical deposition of heat in space for short optical radiation pulses. In addition, we find the photoacoustic pressure to be proportional to the zeroth derivative in one dimension, the one-half derivative in two dimensions, and the first derivative in three dimensions of the optical radiation intensity for long pulses. Experiments with fluid layers, cylinders, and droplets give ultrasonic wave forms that are in general agreement with the theorems.

We report experimental and theoretical results for the absolute and convective instability boundaries in Taylor-Couette flow with imposed axial flow as a function of the axial Reynolds number. Experiment and theory agree quantitatively. In the downstream region of a large-aspect-ratio system, noise-sustained structures of traveling vortices exist in much of the convectively unstable regime. These structures have a nearly time-independent amplitude, but a noisy phase. The phase noise ceases abruptly upon crossing the absolute instability boundary.

Focusing of and imaging with atoms by means of a spherical Fresnel zone plate has been observed for the first time. An intense beam of metastable helium atoms with atomic de Broglie wavelength ${\lambda }_{\mathrm{dB}}$=0.5–2.5 Å is passed through either a single or a double slip with dimensions in the 10-μm range. This transverse intensity distribution is imaged by a Fresnel zone plate, 210 μm in diameter and with an innermost zone diameter of 18.76 μm. For ${\lambda }_{\mathrm{dB}}$=1.96 Å the focal length is 0.45 m. The imaging properties of the zone plate are presented and compared with numerical calculations.

A driven-oscillator model is developed to examine the orbital-velocity harmonics of off-axis electrons in combined helical wiggler and axial guide magnetic fields. The gyroresonance effect is found to occur at harmonics of the wiggler frequency in addition to the well-known fundamental-harmonic resonance. Resonance at the first negative harmonic is potentially important for providing an explanation of the unexpected observations of a recent free-electron-laser experiment. Exploration of the gyroresonance effect as a harmonic selection mechanism for the free-electron laser is discussed.

We study interfacial pattern formation during directional growth from the isotropic phase of a cholesteric liquid crystal that, at equilibrium, has a length 2π/${\mathit{q}}_0$. We find an oscillatory first instability to the cellular pattern and a second bifurcation to an oscillatory mode (breathing mode) when the pattern’s wave number, q is 0.5${\mathit{q}}_0$<q<${\mathit{q}}_0$. The breathing-mode frequency is linear in q. This is the first observation in pattern-forming systems of an oscillatory mode due to competition between two incommensurate but comparable lengths.

We suggest a mechanism for the appearance of intermittency in fully developed turbulence consistent with the pictures recently presented by Kraichnan [Phys. Rev. Lett. 65, 575 (1990)] and She [Phys. Rev. Lett. 66, 600 (1991)]. The key features in our model are (i) an inverse cascade associated with the spectral density of an additional finite flux motion invariant, leading to (ii) an attempt to form large-scale structures which (iii) are intrinsically unstable to a broadband spectrum of perturbing modes resulting in a secondary transfer of energy to small dissipative scales in intermittent bursts.

The experimental study of a linear array of vortices shows the existence of spatially modulated states of oscillation above onset. A model of coupled oscillators is proposed, and the measurements of the corresponding first- and second-neighbor couplings show that these regimes are the result of frustration.