Real Turbulence Research Articles

Dynamical behavior of the fundamental triad-interaction system in three-dimensional homogeneous turbulence

The fundamental triad-interaction system is the building block of the nonlinear interaction of the three-dimensional Navier–Stokes equations. It satisfies incompressibility, conserves energy and helicity, preserves measure under the time evolution, and involves an arbitrary parameter taking any value in [0,2π]. Under several values of this parameter, it is found that the fundamental triad-interaction system cannot be ergodic on the constant energy-helicity surface because of the extraneous constants of motion other than energy and helicity. This at once implies that isotropy is not possible for the spectral tensor, for isotropy calls for mixing which is a stronger requirement than ergodicity. Although the dynamics of a single triad-interaction system is not directly relevant to real homogeneous turbulence, a theoretical framework to investigate ergodicity and mixing and isotropy of the three-dimensional turbulence model by consistently including many fundamental triad-interaction systems is provided.

Handling Qualities of Aircraft in the Presence of Simulated Turbulence

A previous paper (1977) has presented results from flight simulator experiments on instrument-flight-rule handling-quality studies of a STOL-type aircraft in the presence of various models of simulated turbulence (Gaussian, modified Gaussian, Rayleigh, and variable length and intensity, VLI). In this paper, additional results are presented for flight simulator experiments on visual-flight-rule approach landings of a STOL-type aircraft. Pilot opinion ratings of the landing approach with visual display are analyzed to determine the most realistic turbulence model and to identify the variables that critically affect the handling quality of aircraft in turbulence. It is shown that turbulence simulated by a VLI model adequately match the desired statistical properties of real atmospheric turbulence, and that aircraft handling quality and pilot task performance are critically affected by turbulence. Realistic turbulence models present greater difficulty in controlling the aircraft than a simple Gaussian model.

Stellar occultations by turbulent planetary atmospheres: A heuristic scattering model

A model of ray refraction by an isothermal atmosphere with a scattering screen at the center of bending is used to generate analytic results which simulate the effects of real atmospheric turbulence on occultations. Calculations are carried through for scattering which is constant with height and for exponential height dependence. The effect of the scattering is to bias the the mean intensity of the occulted source, and hence systematically to distort bending angles and height differences obtained from inversion of the intensity data. However, the effect is of order 〈 δϵ 2〉/ ϵ 2 for either model, where 〈 δϵ 2〉 is the mean square scattering angle and ϵ is the average bending angle. The effect turns out to be small for plausible turbulence, since 〈 δϵ 2〉/ gfe 2 is of approximately the same order as the relative mean square density fluctuation. Thus the random effects of turbulence are unlikely to be a source of large systematic error in occultations, provided that the data can be meaningfully averaged either temporally or over a number of occultation events.

Laser beam scintillation beyond the turbulent atmosphere: a numerical computation

The extended Huygens-Fresnel formulation for propagation through turbulence is used to examine scintillation of a finite laser beam. The method is demonstrated analytically for propagation beyond a weak Gaussian phase screen. A numerical integration technique is used to extend the results to a more realistic turbulence model. Results are compared with existing Gaussian beam propagation theory.

Turbulent self-diffusion

A method relating Lagrangian and Eulerian statistics for the diffusion of a particle in a homogeneous stationary velocity field, which was developed for plasma diffusion by Taylor and McNamara and further explained by Montgomery, is shown to be equivalent to a method proposed by Corrsin and used by Saffman. The results are compared with numerical simulations with good agreement for velocity fields which have properties similar to real turbulence.

On the response of low-inertia cup anemometers in real turbulence; a reply

On the response of low-inertia cup anemometers in real turbulence; a reply

Numerical Analysis of Alternating Current Arcs

Solutions of the coupled, non-linear, two-dimensional, non-steady equations of continuity, momentum, and energy have been obtained for an alternating current argon arc located in a constant diameter channel of a converging nozzle configuration. Real gas properties, radiation, convection, viscous dissipation, and turbulence effects were incorporated in the analysis. Spatial and timewise distributions determined included the flow, temperature, and pressure fields, dynamic arc radius, and arc resistance gradient.

Simulated Flight Tests of a Digitally Autopiloted Stol-Craft on a Curved Approach With Scanning Microwave Guidance

A work is described which studied the capabilities of a STOL aircraft equipped with digital minicomputer serving as an autopilot making a curved approach to a runway along a path prescribed by the Air Traffic Control system using radio-navigation data supplied by the developing Scanning Fan Beam Microwave Landing Guidance System. The work involved the development of an ATC scheme for effectively generating a flyable curved approach path and specifying such a path to the aircraft being served. The paths produced are made up of alternating straight and circular segments along which the plane is to maintain prescribed constant airspeeds. The digital autopilot functions include Navigation, Control Trimming, Anticipatory calculations, Generation of Control Commands based on utilization of linear optimal state-feedback control theory, Filtering (including Kalman techniques) of state measurements, and Estimation of prevailing winds. A complete simulation of such a system aboard a McDonnell-Douglas 188/Breguet 941 STOL transport, with realistic winds, turbulence, and measurement noise, was created and exercised on the Purdue University CDC 6500 computer system, and showed the capability of excellent adhesion of the airplane to the commanded flight path.

A Burgers-Type Model of Turbulent Decay in a Non-Newtonian Fluid

To study the effects of the high elongational viscosity on the free (“grid-generated”) turbulence of polymer solutions, a Burgers-type model equation is proposed and formed by replacing the Newtonian viscosity of the original Burgers equation with a non-Newtonian viscosity. By using the proposed model equation, numerical experiments were carried out to compute the energy decays, the changes in the energy spectra, and the variations of the mean square of the velocity gradient with time. Comparisons between the Newtonian and the non-Newtonian cases were based on the same Reynolds numbers and the same initial random velocity fields generated by a Gaussian process with two types of spectrum. Measurements on real grid turbulence are discussed in the light of these calculations. The computational results show, in general, the suppression of “shock waves” because of the non-Newtonian viscosity effect, but the turbulent decay rate at large Reynolds number is not always increased, which is surprising. It appears that the calculations support qualitatively the idea of vortex stretching inhibition in polymer turbulence due to high elongational viscosity.

Time-Dependent Wiener-Hermite Base for Turbulence

A Wiener-Hermite expansion with a time-dependent base for turbulence is tested on Burgers' equation. It is shown that the time-dependent base system improves the rate of series convergence and some useful results can be obtained. The moving-base system, developed by Bodner, allows the equipartition solution to be satisfied exactly with a two-term expansion, and is a modification of Bodner's moving base system for real fluid turbulence.

Equilibrium characteristics of nearly normal turbulence

We discuss some consequences of assuming that two different non-linear model equations, and real turbulence are nearly Gaussian. It is supposed when necessary that the process is driven and it is supposed that the processes have become statistically stationary. These problems are discussed from the viewpoint of the Wiener–Hermite expansion for non-linear, nearly Gaussian processes. Expected equilibria forms are related to corresponding expressions obtained from the zero-fourth-cumulant assumption. The spectrum for Burgers’ model and for incompressible fluid flow problems is found from this viewpoint to beE∼k−2. The kinematical properties leading to such spectra are discussed. It is noted, as has been remarked earlier, that this spectrum is characteristic of flows with near discontinuities. A conjecture is offered concerning how these discontinuities are related to Gaussianity.

Transition from laminar to turbulent flow

A NATO Advanced Study Institute on the topic of transition from laminar flow to turbulence was held at Imperial College, London, from 1 to 6 July 1968. Each morning's session was started with a one-hour general lecture, and was followed by five or six half-hour lectures interspaced with discussion periods. The main lecturers were C. C. Lin (general survey), S. Rosenblat (stability of time-dependent flows), L. S. G. Kovasznay (turbulent, non-turbulent interfaces), L. E. Scriven (free surface effects) and A. A. Townsend (shear turbulence). The idea of the meeting was to bring forth and to discuss current ideas in the subject, both from the point of view of developments out of laminar flow and from that of developments into real turbulence. To this end speakers were chosen to introduce a variety of topics ranging from laminar-flow instabilities (with emphasis on aspects at present imperfectly understood), through non-linear effects to the processes affecting turbulence itself.Many ideas recurred throughout the meeting, both at lectures and in discussion periods. This is true, for example, of several relevant points forcefully made by C. C. Lin. For this reason the present account does not attempt to describe the proceedings of the meeting in chronological order, but rather takes an overall view of the subject matter and points to the areas of agreement and of controversy in relation to various problems.

Forced Model Equation for Turbulence

An artificial random force is introduced into Burgers' model equation for turbulence. This forced model equation is solved numerically as an initial-value problem. Both the driving force and initial velocity field are assumed Gaussian and are generated by a white noise process. Many statistical properties of this model for turbulence are studied. By adjusting the external force, the turbulence can reach an equilibrium state. The velocity correlation function and energy spectrum are calculated for the equilibrium turbulence. It is found that the energy spectrum falls off as the inverse second power of the wavenumber. The velocity correlation function is similar to the result obtained in real turbulence experiments. With Gaussian random driving force and Gaussian initial velocity field, it is found that the velocity field remains very nearly Gaussian by comparing the fourth-order velocity correlation with the quasinormal assumption. Although the process remains very nearly Gaussian, it is found that the projection of the process on the initial white noise process becomes smaller and smaller. This is to be expected, since the dynamic system is escaping from the original random base.

Effect of turbulent fluctuations in an optically active fluid medium.

The effect of a beam traversing an optically active medium of turbulent fluctuations of the index of refraction in the medium is investigated theoretically. The general far-field case is solved by integration of the wave equation with both gain and fluctuations of the index refraction, simplified by neglecting the Laplacian of the fluctuating part of the electric field and one of the time derivatives. The far-field diffraction pattern is identical to that for a nonactive medium. For small to moderate extinction there is a loss of power from the coherent beam but only a slight change in the diffraction pattern, accompanied by wide-angle incoherent scattering. For high-gain cases it is possible to have the extinction coefficient less than the gain, but with complete extinction of the coherent beam and a large incoherent scattering pattern. The use of a more realistic turbulence spectrum than previously used has led to the discovery of a second branch in the curve, in which the far exceeds the previously given limiting resolution as the aperture size is increased beyond a certain limit, and approaches the diffraction pattern based on the aperture, although there may be considerable attenuation in the intensity in the diffraction pattern of the coherent beam. These results are applicable, for example, to the use of large aperture optics in turbulene wind tunnels.