Volume 25, Issue 7, July 1982
Index of content:

Density measurement in compressible flows using off‐resonant laser‐ induced fluorescence
View Description Hide DescriptionMeasurement of molecular number density in compressible flows using laser‐induced fluorescence is complicated by collisional quenching of the excited state. It is shown that by exciting the fluorescence off‐resonance the signal becomes proportional to number density and independent of collisional effects. Quantitative measurement of density in an underexpanded jet of nitrogen is demonstrated using off‐resonant fluorescence from iodine seed molecules irradiated with the 514.5 nm line of the argon‐ion laser.

Analytic model of the radiation‐dominated decay of a compact toroid
View Description Hide DescriptionA simple analytic model of the radiation‐dominated decay of a compact torus is presented. Several striking features of various experiments (finite lifetime, linear current decay, and insensitivity of the lifetime to density or stored magnetic energy) are explained by the model. A simple criterion is given for the maximum tolerable impurity density.

The effect of curvature at the detachment point of a fluid sheet from a rigid boundary
View Description Hide DescriptionThe effect of curvature at the detachment point (the point at which the flow separates from a rigid boundary) of flow of an incompressible, inviscid fluid sheet under the action of gravity over a rounded edge is studied. The fluid sheet flows upstream over a level bottom which joins smoothly with a rounded bed leading to a free overfall downstream. A nonlinear steady state solution of the problem is obtained, partially by a numerical procedure, which differs significantly from the corresponding known solutions for flow over a vertical bed. The location of the detachment point (rather than being specified) is determined as part of the solution and is found to be dependent on both the values of far upstream depth and far upstream Froude number.

An exact solution for the drag of a sphere in low Reynolds number flow with strong uniform suction or blowing
View Description Hide DescriptionAn analytical expression is obtained for the drag of a sphere in low Reynolds number flow with arbitrarily strong uniform suction or blowing.

Steady flow patterns of internal solitary bulges in a stratified fluid
View Description Hide DescriptionSteady streamline patterns are demonstrated of a solitary bulge forming on an interfacial transition region in fresh and salt water. The bulge is composed of a vortex pair at αa≳1.3, with α the inverse of the characteristic thickness and a the bulge amplitude.

Bubble migration in a rotating, liquid‐filled sphere
View Description Hide DescriptionExperiments and analysis concerned with the trajectory of a small gas bubble in a rotating, liquid‐ filled glass sphere show that the bubble migrates inward toward the axis of rotation, thus providing a possible centering mechanism for hollow shell formation processes. The migration time is found to be approximately proportional to the parameter (1/ω)(ν/a ^{2} _{ e }ω), where ν is the kinematic viscosity of the liquid, a _{ e } the bubble radius, and ω the rate of rotation.

Near‐field analysis of a compressive supersonic ramp
View Description Hide DescriptionSteady, two‐dimensional, inviscid, supersonic flow is analyzed for a compressive turn where the wall is contoured to provide a centered compression fan. The focal point of the compression is the origin of the usual (primary) oblique shock wave, a slipstream, and a secondary pressure disturbance. This disturbance can be an expansion, a weak solution shock, or a strong solution shock. In the vicinity of the focal point (the near field) there are seven possibilities, one of which is no real solution. For small wall turn angles, there is a unique near‐field solution where the primary shock is the weak solution. In this case the secondary disturbance, whose strength is quite small, is either an expansion or a weak solution oblique shock wave. For larger turn angles, two near‐field solutions are possible, and for still larger angles, none. At relatively large wall turn angles, where the usual oblique shock equations still provide an attached solution, the near‐field equations do not have a solution when the Mach number is sufficiently large.

New observations on hysteresis effects in Taylor–Couette flow
View Description Hide DescriptionIn this experimental study, laser‐velocimetry has been used to investigate hysteresis phenomena presented by steady flows of a viscous fluid. Dealing with Taylor–Couette flow between concentric cylinders with differential rotation, the experiments were focused on the change‐over between steady states featuring four and six cells as the length of the annular domain is varied continuously. The observations are in broad qualitative agreement with the predictions of abstract mathematical models, but they display new features which appear to be beyond the scope of any quantitative theoretical results yet available.

Influence of the velocity ratio on the spatial instability of mixing layers
View Description Hide DescriptionThe linear spatial instability of the tanh and Blasius mixing layers is studied for different values of the ratio between the difference and the sum of the velocities of the two co‐flowing streams. The growth rate, phase velocity, and perturbation velocity distributions are determined numerically and the results are compared with expansions for small shear or low frequency. It is found that the maximum growth rate is approximately proportional to the velocity ratio. This is shown to be consistent with the observed variation of shear layer spreading rate with velocity ratio and with a recent model of flight effects on jet mixing noise.

Spanwise correlation of temperature in a turbulent boundary layer
View Description Hide DescriptionConventional correlations of temperature in the spanwise direction of a turbulent boundary layer indicate a length scale which is independent of Reynolds number and of the order of the boundary layer thickness.

One‐dimensional stability of self‐similar converging flows
View Description Hide DescriptionA necessary condition for the asymptotic approach of symmetric converging flows to a self‐ similar form is the stability of the one‐dimensional partial differential equations when linearized about the appropriate similarity solutions. For the converging shock problem, and (for sufficiently large adiabatic exponent γ) also for the collapsing free‐surface problem, it is found that (1) the standard, analytic similarity solution is positively stable with respect to symmetric (one‐ dimensional) perturbations, and (2) that all other similarity solutions are positively unstable. For the free‐surface problem when γ is small, there seem to be three regimes: neutral stability, instability of all solutions, and stability of a degenerate solution.

Correlations of squared velocity and temperature derivatives in a turbulent plane jet
View Description Hide DescriptionCorrelations, in a turbulent plane jet, of squared time derivatives of three components of velocity and of squared time and spatial derivatives of temperature indicate a value for the exponent μ of about 0.2 for velocity and 0.25 for temperature.

Nonequilibrium probability distributions for randomly forced two‐ dimensional flows
View Description Hide DescriptionThe general Liouville equation for the evolution of the probability distribution of an ensemble of randomly forced inviscid two‐dimensional flows is specialized for a particular spectrum of random forcing. In that case, the probability distribution depends only on a linear combination of kinetic energy and enstrophy, and the Liouville equation reduces to a one‐dimensional ’’diffusion‐ like’’ equation that can be solved analytically. Random stirring of a fluid initially at rest is treated as an example.

Heat transfer in a rarefied gas enclosed between parallel plates: Role of boundary conditions
View Description Hide DescriptionThe influence of boundary conditions of accomodation coefficients and Maxwellian diffuse specular reflection on heat transfer through a rarefied gas enclosed between two parallel plates is examined. An exact expression for heat transfer for accomodation coefficient boundary conditions and the Bhatnagar–Gross–Krook (BGK) model is constructed by using results of Cercignani and Pagani and Thomas, Chang, and Siewert. These results are compared with some variational results of Cipolla and Cercignani and some exact results of Thomas, Chang, and Siewert and Thomas for the BGK model and Maxwellian diffuse specular reflection boundary conditions. It is concluded that the two boundary conditions provide results that agree within about 3% for a range of Knudsen numbers and boundary parameters. It is found that the variational results are remarkably accurate for the BGK model and both types of boundary conditions. Further, it is noted that the heat transfer between parallel plates with different accommodation coefficients at the two surfaces can be calculated exactly by using a harmonic mean for each surface.

Rarefaction wave in relativistic gasdynamics
View Description Hide DescriptionThe steady flow in relativistic gasdynamics is studied. There are two possible regimes of flow: (1) a uniform flow and (2) the rarefaction wave. The rarefaction wave is similar to one studied in the Newtonian limit and is confined to a sectorial region. The maximum angle of this sector is smaller and the pressure drop is greater than in the Newtonian case. For the ultra‐relativistic fluid the results are described with simple formulae.

Theory of a spheroidal probe in low‐density continuum plasmas
View Description Hide DescriptionA spheroidal probe theory for a low‐density continuum plasma, i.e., one where the electron density is N _{ e } ≲10^{8} cm^{−3} and the gas pressure is P≳1 Torr has been developed using a spheroidal coordinate system in order to properly take into account the effect of the finite length of the probe. The numerical results of both the electron‐ and the ion‐current characteristics are obtained for various values of R _{ p }/λ_{D} ranging from 0 to 1, ε = T _{ i }/T _{ e } from 0.1 to 1, and C _{ p } = L _{ p }/2R _{ p } from 1 to 100, where λ_{D} is the Debye length, R _{ p } and L _{ p } are the probe radius and the probe length, T _{ i } and T _{ e } are the ion and the electron temperature, respectively. Using these results, new methods to determine the electron temperature and the plasma space potential (consequently, the electron density) by practical measurements are also proposed and discussed.

Theory of a spherical probe in a collisionless magnetoplasma
View Description Hide DescriptionA theory is presented for a spherical electrostatic probe in a collisionless, Maxwellian plasma containing a uniform magnetic field. The theory yields two upper bounds and an adiabatic limit for collection of the attracted particle species (either electrons or ions). For the repelled species, it yields a lower and an upper bound. The theory is similar in concept to existing theories for cylindrical probes by Laframboise and Rubinstein. It is applicable when the ratio of probe radius to Debye length is small enough, and/or the probe potential is large enough, that no potential barriers exist near the probe. Otherwise, a theory of Sanmartin applies. The attracted‐particle current in the adiabatic limit, i.e., when mean gyroradius≪Debye length, shows negative‐resistance behavior. One of the upper bounds is based on the use of particle canonical angular momentum conservation to define allowed and forbidden regions for particle orbits, and generalizes an existing theory by Parker and Murphy to include particle thermal motion.

Temperature gradient and electric field driven electrostatic instabilities
View Description Hide DescriptionThe stability of electrostatic waves to thermodynamic and electric potential gradients is investigated. A general instability parameter, ε = 2.6(ε_{ E }+ε_{ p }) +0.2ε_{ T }, is identified which is related to thermodynamic gradients (ε_{ p } and ε_{ T }) and internal electric fields (ε_{ E }). This parameter is evaluated at the instability threshold as a function of T _{ e }/T _{ i } for both ion acoustic and electrostatic ion cyclotron waves. The major virtue of this analysis, other than its overall generality, is to show that thermodynamic gradients drive instabilities even when the internal electric field vanishes. This result does not emerge from previous analyses because skewing of the distribution function was not included in the dielectric.

Quasisteady turbulence driven by runaway electrons
View Description Hide DescriptionThe evolution of the turbulence driven by runaway electrons has been followed by means of a computer code based on the quasilinear equations. The evolution is not characterized by periodic relaxations as claimed in previous works but ends in a quasisteady turbulent, yet very persistent state, accessible from different initial conditions. This discrepancy is clarified as being due to the excessive stiffness of the moment equations used to demonstrate the relaxations. Moreover, a theory is developed to interpret the quasisteady state found.

Consequence of induced bremsstrahlung radiation
View Description Hide DescriptionThe physical meaning of induced bremsstrahlung radiation is clarified by simple considerations. The induced radiation is best understood by picturing a collision process between effective macroparticles in a turbulent plasma. The condition for the negative absorption of an electromagnetic wave is obtained. The induced bremsstrahlung radiation is a new kind of bremsstrahlung instability. The generation mechanism of ordinary mode radiation in the presence of a coherent ion cyclotron wave is discussed. The potential importance of the newly found radiation process to plasma turbulence is stressed.