Volume 28, Issue 1, January 1985
Index of content:

The rewetting of an inclined solid surface by a liquid
View Description Hide DescriptionWhen a thin layer of liquid flowing down an inclined solid surface becomes unstable, a dry region may appear. It is of general engineering interest to identify the parameters which control the ability of the liquid to rewet the solid so that a uniform film of liquid can be reestablished. The role played by the contact angle in the rewetting process is investigated by performing a specific set of experiments of the type introduced by Huppert [(Nature 3 0 0, 427 (1982)]. It is found that a small static advancing contact angle promotes rewetting, while a large value of the angle does not.

Vortex pair annihilation in Taylor wavy‐vortex flow
View Description Hide DescriptionWe have made precision measurements of the vortex pair size and wavy mode amplitude of vortices in wavy Taylor–Couette vortex flow. These results are compared to a model advanced by Park and Crawford to account for expulsion of vortex pairs as the Reynolds number is increased in the wavy‐vortex regime.

Intermittency and attractor size in isotropic turbulence
View Description Hide DescriptionQualitative arguments suggest that the Kolmogorov 1941 (K41) inertial range for space dimensionality D3 corresponds to a maximum attractor size if compared with alternative inertial ranges in which intermittency increases as a power of wavenumber. Therefore upper bounds on attractor size consistent with K41 do not either rule out or imply intermittency corrections to the −5/3 law. In contrast, the K41 inertial range corresponds to minimum attractor size if D>4.

The production of highly unidirectional lower‐hybrid waves
View Description Hide DescriptionThe development of a highly unidirectional lower‐hybrid wave source would improve the electron current drive efficiency in tokamaks. Lower‐hybrid waves launched from a phased wave array are shown to be reflected from a grid placed in a cold, low‐density plasma. The antenna–grid combination results in highly unidirectional lower‐hybrid waves.

Anomalous losses from relativistic electron rings in decreasing toroidal fields
View Description Hide DescriptionAnomalously enhanced fast‐electron losses are observed on relativistic E layers in the RECE‐Christa device when the applied toroidal magnetic field decreases to zero in times shorter than ring lifetime. These losses consistently occur in a certain region of the field‐reversal parameter and the ratio of applied toroidal to axial magnetic fields at the ring position. The critical parameter range is independent of the radial gradient of the applied mirror field, the background gas pressure, and the rate‐of‐decay of B _{θ}; however, it depends on the axial length of the rings, and there may be a threshold in d B _{θ}/d t. The observed parameter dependence as well as the absence of any kink or tilt motions point to new orbital resonances as the cause of these losses.

Inverse resonance absorption in an inhomogeneous magnetized plasma
View Description Hide DescriptionThe linear mode conversion of a plasma wave to a light wave in a magnetized plasma has been examined theoretically and by computer simulation. This conversion is the inverse of resonance absorption exhibiting an identical dependence on magnetic field and density scale length with an optimum conversion efficiency of approximately 60%. Radiation from this source may contribute to the harmonic spectra observed from laser‐irradiated plasmas.

Two‐dimensional ray‐trace calculations of thermal whole beam self‐focusing
View Description Hide DescriptionThermal self‐focusing of laser light may be significant when a plasma is irradiated with short‐wavelength laser light. Self‐focusing magnifies the light intensity which can increase absorption by plasma waves (producing hot electrons which may cause preheat), could increase scattering, and could be a perturbation source for the Rayleigh–Taylor instability. We use two‐dimensional hydrodynamic simulations to characterize thermal self‐focusing for parameters of interest to laser fusion applications, and present a simple model. A diverging beam is shown to reduce the self‐focusing.

The separation of viscous jets
View Description Hide DescriptionA viscous jet is not usually observed to separate from a sharp edge in the manner expected theoretically. In the present paper the separation of a creeping jet emerging from a tube with a rounded exit is considered. As a separation criterion, in the absence of surface tension, we propose that the traction normal to the nozzle surface drops to zero at the separation point. Boundary‐element calculations then show a behavior that agrees with experimental data and with previous finite‐element computations. They also permit the Michael condition to be observed at separation, so that the discrepancy between finite‐element calculations and theory is removed.

Fingering with miscible fluids in a Hele Shaw cell
View Description Hide DescriptionUnstable, two‐fluid miscible displacements in a Hele Shaw cell of plate spacing b are analyzed by considering viscous dissipation of energy. A perturbation theory is presented that predicts the wavelength of fingers, λ, as λ≊4b. Experiments with a circular Hele Shaw cell are shown to support this result. In a porous medium, the analogous fingers are demonstrated to be the size of a pore, which is much larger than the corresponding fingers in the analogous Hele Shaw cell. These results provide the lower limits of finger wavelength for the theories of Saffman and Taylor, and Chuoke, van Meurs, and van der Poel.

The stability of buoyancy‐driven rolls aligned with a shear flow when the temperature gradient is nonlinear
View Description Hide DescriptionThe buoyancy driven instability of rolls aligned with a shear flow of a Boussinesq fluid is considered. It is supposed that the temperature varies not only with height but also in the direction of the flow thus allowing the vertical temperature profile to be nonlinear. Conditions are derived for the neglect of the horizontal temperature gradient in the perturbation equations. These are (i) that the vertical temperature gradient varies sufficiently slowly in the direction of the flow and (ii) that Pr h/d≫1, where Pr is the Prandtl number and h and d are the length scales for the vertical variation of velocity and temperature, respectively. Under these conditions, stability is governed by the equation for Bénard convection. The principle of exchange of stabilities is proved for an arbitrary temperature gradient profile, with isothermal, free‐surface boundary conditions, and the equation is solved numerically and by an asymptotic method for a model thermal boundary layer. The analysis is then applied to an experimental study of spoke patterns, observed in the growth of electronic materials. This work also indicates that a previous investigation of the stability of stratified shear flow has a restricted range of validity.

Nonlinear instability at the interface between two viscous fluids
View Description Hide DescriptionCo‐current flow of two viscous fluids in a channel is linearly unstable to long wavelength disturbances. The weakly nonlinear evolution of this instability is examined. It is shown that, because of surface tension and nonlinear effects, the interface can either return to its original undisturbed state or evolve to some finite amplitude steady state.

Capillary‐gravity waves generated in a viscous fluid
View Description Hide DescriptionThe linearized initial‐value problem of capillary‐gravity waves generated by a moving oscillatory surface pressure distribution in a viscous incompressible fluid of infinite depth is solved. It is found that viscosity apart from introducing a damping factor into the amplitude of each wave plays an important role in the critical case. While the solution in the inviscid fluid becomes singular for certain values of the parameters of the problem, the solution in viscous fluid remains valid for all values of the parameters, though the amplitudes are relatively large in the critical case.

Turbulence structures associated with the bursting event
View Description Hide DescriptionTurbulence structures in a wall‐bounded shear layer during the bursting event detected by a conditional sampling technique are investigated using data obtained from large‐eddy simulation of turbulent channel flow. Streamlines are constructed from the ensemble‐averaged velocity field to illustrate the flow patterns associated with the bursting event. They exhibit the ‘‘splatting’’ motions during the sweep event and the existence of a pair of counterrotating streamwise vortices during the ejection process.

A statistically derived system of equations for turbulent shear flows
View Description Hide DescriptionA system of equations governing turbulent shear flows is discussed. In this system the mean velocity, the mean pressure, and four statistical quantities related to the fluctuating field constitute the fundamental quantities for shear flows. A closed system of equations for these quantities is derived statistically with the aid of the two‐scale direct‐interaction approximation, where the Reynolds stress is expressed in the form of the eddy‐viscosity representation. On this basis, some turbulence models are discussed from the statistical viewpoint.

A consistency condition for Reynolds stress closures
View Description Hide DescriptionA new consistency condition is derived for the Reynolds stress turbulent closures. Recommended values of model constants used with the k‐ε model and with various Reynolds stress closures do not satisfy this condition exactly. It is shown that a slight adjustment of certain computer‐optimized constants would make some of these models internally consistent.

Modeling the pressure gradient–velocity correlation of turbulence
View Description Hide DescriptionThe modeling of the pressure gradient–velocity correlation of turbulence is considered. Two distinctly different approaches have been proposed in the turbulence literature: one in which the pressure gradient–velocity correlation is decomposed into a pressure‐strain correlation and a pressure‐diffusion correlation, and another in which the pressure gradient–velocity correlation is split into its deviatoric and isotropic parts. By examining the limit of two‐dimensional turbulence, it is demonstrated that the models obtained from the former approach are inconsistent with the Navier–Stokes equations in a fundamental way, whereas the models obtained from the latter approach are not. Consequently, it appears that the direct modeling of the pressure gradient–velocity correlation in its deviatoric and isotropic parts should be favored. The implications that this result has on turbulence modeling are discussed briefly.

A model for the spectrum of passive scalars in an isotropic turbulence field
View Description Hide DescriptionA simple model is developed for the wavenumber spectrum of the variance of a passive scalar quantity in an isotropic turbulence field. The model can define the spectral distributions at all wavenumbers as an arbitrary function of a scalar Reynolds number Re_{θ}=R Re_{λ} and the Schmidt number Sc=ν/D (where R=τ_{θ}/τ_{ e } is the scalar/kinetic energy time scale ratio and Re_{λ}=u ’λ/ν is the turbulence Reynolds number). The model is compared with one‐dimensional spectral data over a range of Reynolds numbers and for Sc=0.7, 7, and 700; model and data are shown to be in reasonable agreement.

Effect of intake flow on ambient turbulence
View Description Hide DescriptionA small streamlined axisymmetric intake is placed at various locations on the axis of a large axisymmetric turbulent jet. The ratio of the mean velocity in the intake to that of the ambient fluid is varied from zero to thirteen. The effective diameter d* of the intake is determined by its physical size and the range of influence of the intake flow on the ambient jet fluid. Intensities of the components of turbulent velocity are measured in the ambient fluid and in and around the intake. In most cases the intake faced the jet. The ambient turbulence may be idealized as three mutually orthogonal linear vortex filaments of circular cross section and diameter S which is indicative of the scale of energy containing eddies. The vortex filaments deform as the flow is drawn into the intake. In the case d*<S, only parts of vortex filaments of size d* enter the intake. The two effects are used to calculate the intensities of the components of turbulent velocity as a function of d*/S and ratios of mean velocity and density in the intake to their respective values in the ambient fluid. The results agree with experiments within wide ranges of the parameters.

Cusp catastrophe in flow acoustics
View Description Hide DescriptionThe transonic flow in a tube following an abrupt enlargement of the cross section produces self‐induced flow oscillations which generate sound (whistler). The frequency of the oscillation is influenced by the tube length: increasing length leads to a frequency decrease, but only up to a critical length l _{ c } of the tube. If this length is further increased, the frequency will jump to higher values. This jump shows hysteresis: decreasing the tube length again leads to a jump to the lower frequency at a length l _{ c1}<l _{ c }. Having presented details of the above phenomenon, the two mathematical models are then presented, in which the transonic oscillator is represented by two simple nonlinear equations which behave harmonically, and the acoustic resonator, i.e., the tube, is represented by a term including a time lag. It is shown that the hysteresis vanishes for both the experiment and the model if the sound reflection at the end of the tube is decreased below a certain critical value. This behavior is one of the few reported examples of a cusp catastrophe in an oscillating system.