Volume 25, Issue 10, October 1982
Index of content:

The nonunique rate of spread of the two‐dimensional mixing layer
View Description Hide DescriptionThe rate of spread of a plane, incompressible, turbulent shearlayer was determined experimentally. The velocity ratio was constant, while the actual velocities were altered. It was established that the divergence of the flow with downstream distance was not uniquely determined by the velocity ratio in the range of variables considered. It is believed that an instability is responsible for this behavior.

The lifetime of nonlinear whistlers
View Description Hide DescriptionThe newly found time‐derivative‐dependent ponderomotive force and velocity modulation contributions in nonlinear whistler wave propagation are incorporated into the multidimensional stability analysis. It is shown by the Liapunov method that stable one‐dimensional whistler solitons exist. As a further result, it is demonstrated that the growth rate of the transverse bending instability, which is driven by the time‐derivative‐dependent ponderomotive force, is insignificant. This implies the observability of whistler solitons.

Flux loss during the equilibrium phase of field‐reversed configurations
View Description Hide DescriptionField‐reversed configurations are consistently formed at low filling pressures in the FRX‐C device, with decay time of the trapped flux after formation much larger than the stable period. This contrasts with previous experimental observations.

Reduction in hot electron transport on dielectric targets at high laser irradiance
View Description Hide DescriptionConducting properties of the target material are shown to affect both the penetration depth and lateral extent of hot electron transport in experiments with nsec‐CO_{2}‐laser pulses incident on various planar layered targets. At an irradiance around 5×10^{13} W/cm^{2} on metal targets most hard x‐rays are emitted outside the focal spot. The hard x‐ray emission area is reduced by a factor of ten when the conducting target material is replaced by a dielectric of similar Z. The inward transport is likewise reduced. Strong electric fields produced by a local negative charge accumulation in a dielectric may explain the transport reductions.

Boundary effects on the dynamics of channels generated by laser‐initiated discharges
View Description Hide DescriptionThe dynamics of unbounded and bounded reduced density channels have been characterized by means of ruby laser schlieren photography. These channels are produced by CO_{2} laser‐initiated discharges in clean atmospheric pressure air. Bounded channels exhibit a significant compression in width and earlier onset of fine scale turbulence. These results could impact proposed designs for inertial fusion reactors relying upon reduced density channels for particle transport through gas blankets.

A shear instability induced by a composite internal wave
View Description Hide DescriptionExperiments have been performed in a thermally stratified two‐layer shear flow with a nonzero mean velocity to observe the effects of artifically introduced low frequency internal waves on higher frequency, Kelvin–Helmholtz waves growing spatially on the density interface. Phillips’ model for wave‐induced shear across an interface is extended to the two first‐mode wave trains which can propagate in such a flow. It is shown that the Richardson number becomes a function of the phase of the internal composite waves and that its minimum value is either at the front or at the back face of the waveform depending on the sign of the background vorticity. Measurements are presented of the phase‐averaged temperature and velocity fields of generated internal waves and show the waves breaking down on the face where the Richardson number was found to be at a minimum. The breakdown is characterized by the rapid growth of high frequency waves which appear to be phase locked on the parent internal gravity wave. Possible instances where this type of breakdown could occur in nature are discussed.

The inviscid stability of Long’s vortex
View Description Hide DescriptionThe inviscid stability of Long’s vortex, which is believed to model tornado‐like flows, is investigated using a finite‐difference method. Flows of this type are found to be generally unstable to small, short‐wave, helical disturbances, while no instabilities to axisymmetric modes have been found using this method. This instability provides a possible mechanism for the development of ’’suction vortices’’ in tornadoes.

Kelvin–Helmholtz instability for parallel flow in porous media: A linear theory
View Description Hide DescriptionTwo fluid layers in fully‐saturated porous media are considered. The lighter fluid is above the heavier one so that in the absence of motion the arrangement is stable and the interface is flat. It is shown that when the fluids are moving parallel to each other at different velocities, the interface may become unstable (the Kelvin–Helmholtz instability). The corresponding conditions for marginal stability are derived for Darcian and non‐Darcian flows. In both cases, the velocities should exceed some critical values in order for the instability to manifest itself. In the case of Darcy’s flow, however, an additional condition, involving the fluids’ viscosity and density ratios, is required.

Stability of an expanding cylindrical plasma envelope: Rayleigh–Taylor instability
View Description Hide DescriptionThe stability of a cylindrically symmetric plasma envelope driven outward by blast waves is considered. The plasma fluid is assumed to be a compressible, isentropic gas describable as an ideal gas ( p = aρ^{γ}, γ≳1). The stability problem of such an envelope undergoing self‐similar motion is solved by considering the initial‐value problem. It is shown that in the early phase of an expansion, the envelope is unstable to Rayleigh–Taylor modes which develop at the inner surface. In the later phase of the expansion, the Rayleigh–Taylor modes are weakened due to the geometrical divergence effect. The implications of the time‐dependent behavior of the Rayleigh–Taylor instability for plasma switches are discussed.

Mechanism of atomization of a liquid jet
View Description Hide DescriptionIn the atomization regime of a round liquid jet, a diverging spray is observed immediately at the nozzle exit. The mechanism that controls atomization has not yet been determined even though several have been proposed. Experiments are reported with constant liquid pressures from 500 psia (33 atm) to 2500 psia (166 atm) with five different mixtures of water and glycerol into nitrogen, helium, and xenon with gas pressures up to 600 psia (40 atm) at room temperature. Fourteen nozzles were used with length‐to‐diameter ratios ranging from 85 to 0.5 with sharp and rounded inlets, each with an exit diameter of about 340 μm. An evaluation of proposed jet atomization theories shows that aerodynamic effects, liquid turbulence, jet velocity profile rearrangement effects, and liquid supply pressure oscillations each cannot alone explain the experimental results. However, a mechanism that combines liquid–gas aerodynamic interaction with nozzle geometry effects would be compatible with our measurements but the specific process by which the nozzle geometry influences atomization remains to be identified.

Experimental study of an ‘‘incipient spot’’ in a transitional boundary layer
View Description Hide DescriptionA turbulent spot was created artificially in a transitional boundary layer by means of a point disturbance which was made as reproducible as possible. Single‐probe hot‐wire measurements of the streamwise velocity component were used to study the structure of the disturbance prior to its breakdown into a spot. The ’’incipient spot’’ in this experiment is found to be highly evolutionary, its length increasing by almost 100% during transit past a fixed location. The contour of the incipient spot, when projected on a plane parallel to the wall, is arrowheaded in shape with an apex which is considerably sharper than that of a turbulent spot. In the plane of symmetry, rapid fluctuations are observed far from the wall; closer to the wall, a velocity excess occurs and regions of streamwise momentum defect and excess develop alternately in the spanwise direction. Time history at a fixed streamwise location shows that the central excess region is crossed by a ’’defect bridge’’ connecting the downstream ends of the adjacent defect regions. The incipient spots in this experiment propagate considerably faster than the three‐dimensional wave packets, which have been investigated by others who applied the same, yet much weaker, disturbance source.

Period between bursting in turbulent boundary layers
View Description Hide DescriptionAvailable measurements in turbulent boundary layers having zero, favorable, or adverse pressure gradients have been used here to show that a universal value of the nondimensional period between bursting does not exist.

The probability density function of a passive scalar in turbulent shear flows
View Description Hide DescriptionThe transport equation for the probability density function of a scalar in turbulent shear flow is analyzed and the closure based on the gradient flux model for the turbulent flux and an integral model for the scalar dissipation term is put forward. The probability density function equation is complemented by a two‐equation turbulence model. Application to several shear flows proves the capability of the closure model to determine the probability density function of passive scalars.

Focusing of waves in turbulent inhomogeneous media
View Description Hide DescriptionGrowth of large fluctuations in the amplitude of high‐frequency waves or shocks propagating through turbulent, inhomogeneous media is investigated stochastically with geometrical acoustics. Previous efforts use linearization which is not uniformly valid at large distances and large variations in the ray tube area. The present analysis retains the nonlinear terms crucially important to focusing and growth of singular fluctuations in the amplitude. It is shown, in two dimensions, that the fluctuations of the ray‐tube area grow exponentially and caustics occur on every ray, repeatedly, on a distance scale of a σ^{−2/3}, where the fluctuations in ray directions are still small, O(σ^{2/3}). Here, σ≪1 is the standard deviation and a is the correlation length of the wave velocity distribution in the medium. Probability densities for the occurrence of caustics are given. Also, the moments of the ray‐tube area distribution and amplitude related statistics are developed for distances well into the region of caustic formation. Finally, a method is presented for relating the theoretical predictions to measurements on an image plane.

Bipolar model for traveling‐wave induced nonequilibrium double‐layer streaming in insulating liquids
View Description Hide DescriptionA model is proposed for the time evolution of ion concentrations in a thin charge layer near an interface between an insulating solid and a semi‐insulating bipolar liquid, subjected to an applied electric field. Given the specific case of a traveling‐wave applied field of peak magnitude E _{0} and planar geometry, solutions for the charge density and electric field in the layer are used to calculate the time‐average stress moment and, hence, the pumping velocity of the liquid. Analytic solutions, valid in the regimes of small applied field magnitude (E _{0} L _{D}/V _{ t }≪1, where L _{0} and V _{ t } are the Debye length and thermal voltage, respectively) or frequency (ωε/σ≪1, ω the angular frequency and ε and σ the permittivity and equilibrium conductivity, respectively), predict charge layers with a characteristic dimension of the Debye length and fluid pumping in the direction of propagation of the traveling wave (forward). Numerical solutions, in the regime of large magnitude fields with ωε/σ∼1, predict either forward or backward pumping, as well as a charge layer with thickness on the order of a migration length (L = 2πb E _{0}/ω, where b is the ion mobility). Parameters such as ion mobility, thermal generation rate, and level of ionization in the liquid are important in determining the rate (and even direction) of the pumping.

Experiments on the influence of magnetic fields on the viscosity of water and a water‐NaCl solution
View Description Hide DescriptionThe influence of external magnetic fields on the viscosity of water at 295 K was investigated in a differential experiment. With fields up to 2.3 T either parallel to or perpendicular to the flow, an upper limit to relative changes was established as 3×10^{−5}. This result is contradictory to earlier results by other authors, who reported relative viscosity increases up to 3×10^{−3} at comparable field strengths.

Operation limits of multipole ion sources
View Description Hide DescriptionExperiments in which the effective anode area of a multipole ion source is reduced, in order to enhance its ionization and gas efficiency, show that there is a minimum area below which efficient operation becomes impossible. This phenomena is analyzed in terms of a model based on particle balance equations and is shown to be closely related to the reversal in plasma potential with respect to anode potential. The theoretically predicted operation regime is shown to be in reasonable agreement with that found in a variety of multipole sources. Comparison is also made with the limitations set by cathode area.

Hamiltonian formulation of guiding center motion and of the linear and nonlinear gyrokinetic equation
View Description Hide DescriptionThis derivation of the gyrokinetic equations is based on the Hamiltonian formulation of the guiding center motion. The transformation to guiding center variables is accomplished by a sequence of canonical transformations. The kinetic equation is determined by Liouville’s equation. This equation is then ordered in accordance with the gyrokinetic ordering, and analyzed order by order to obtain the linear and nonlinear gyrokinetic equations.

Finite‐β stabilization of the universal drift instability: Revisited
View Description Hide DescriptionThe stabilization of the universal drift instability due to finite β effects (i.e., electromagnetic coupling and ∇B orbit modifications) is studied numerically and a marginal stability curve (as a function of β and k) is presented. It is found that the most difficult modes to stabilize have arbitrarily small wavenumbers and the critical value of β is β_{cr} ≃0.135 for T _{ e } = T _{ i }.

Beat excitation of whistler waves
View Description Hide DescriptionA detailed calculation is made of the nonlinear excitation of a low‐frequency whistler due to the beat of two high‐frequency electromagnetic waves. The whistler is excited near the reflection layers of the high‐frequency pumps where an effective antenna is generated by the beat ponderomotive force acting on electrons. Results relevant to ionospheric and laboratory experiments are obtained.