Showing papers on "Turbulence published in 1983"

Equation of motion for a small rigid sphere in a nonuniform flow

Abstract: The forces on a small rigid sphere in a nonuniform flow are considered from first prinicples in order to resolve the errors in Tchen’s equation and the subsequent modified versions that have since appeared. Forces from the undisturbed flow and the disturbance flow created by the presence of the sphere are treated separately. Proper account is taken of the effect of spatial variations of the undisturbed flow on both forces. In particular the appropriate Faxen correction for unsteady Stokes flow is derived and included as part of the consistent approximation for the equation of motion.

Experimental and Theoretical Investigation of Backward-Facing Step Flow

Abstract: Laser-Doppler measurements of velocity distribution and reattachment length are reported downstream of a single backward-facing step mounted in a two-dimensional channel. Results are presented for laminar, transitional and turbulent flow of air in a Reynolds-number range of 70 < Re < 8000. The experimental results show that the various flow regimes are characterized by typical variations of the separation length with Reynolds number. The reported laser-Doppler measurements do not only yield the expected primary zone of recirculating flow attached to the backward-facing step but also show additional regions of flow separation downstream of the step and on both sides of the channel test section. These additional separation regions have not been previously reported in the literature.Although the high aspect ratio of the test section (1:36) ensured that the oncoming flow was fully developed and two-dimensional, the experiments showed that the flow downstream of the step only remained two-dimensional at low and high Reynolds numbers.The present study also included numerical predictions of backward-facing step flow. The two-dimensional steady differential equations for conservation of mass and momentum were solved. Results are reported and are compared with experiments for those Reynolds numbers for which the flow maintained its two-dimensionality in the experiments. Under these circumstances, good agreement between experimental and numerical results is obtained.

An experimental study of entrainment and transport in the turbulent near wake of a circular cylinder

Abstract: This paper describes an experimental investigation of transport processes in the near wake of a circular cylinder at a Reynolds number of 140000. The flow in the first eight diameters of the wake was measured using X-array hot-wire probes mounted on a pair of whirling arms. This flying-hot-wire technique increases the relative velocity component along the probe axis and thus decreases the relative flow angle to usable values in regions where fluctuations in flow velocity and direction are large. One valuable fringe benefit of the technique is that rotation of the arms in a uniform flow applies a wide range of relative flow angles to the X-arrays, making them inherently self-calibrating in pitch. An analog circuit was used to generate an intermittency signal, and a fast surface-pressure sensor was used to generate a phase signal synchronized with the vortex-shedding process. The phase signal allowed sorting of the velocity data into 16 populations, each having essentially constant phase. An ensemble average for each population yielded a sequence of pictures of the instantaneous mean flow field, with the vortices frozen as they would be in a photograph. In addition to globally averaged data for velocity and stress, the measurements yield non-steady mean data (in the sense of an average a t constant phase) for velocity, intermittency, vorticity, stress and turbulent-energy production as a function of phase for the first eight diameters of the near wake. The stresses were resolved into a contribution from the periodic motion and a contribution from the random motion at constant phase. The two contributions are found to have comparable amplitudes but quite different geometries, and the time average of their sum (the conventional global Reynolds stress) therefore has a quite-complex structure. The non-steady mean-vorticity field is obtained with good resolution as the curl of the non-steady mean-velocity field. Less than half of the shed circulation appears in the vortices, and there is a slow decay of this circulation for each shed vortex as it moves downstream. In the discussion, considerable emphasis is put on the topology of the non-steady mean flow, which emerges as a pattern of centres and saddles in a frame of reference moving with the eddies. The kinematics of the vortex-formation process are described in terms of the formation and evolution of saddle points between vortices in the first few diameters of the near wake. One important conclusion is that a substantial part of the turbulence production is concentrated near the saddles and that the mechanism of turbulence production is probably vortex stretching at intermediate scales. Entrainment is also found to be closely associated with saddles and to be concentrated near the upstream-facing interface of each vortex.

Anisotropy in MHD turbulence due to a mean magnetic field

Abstract: The development of anisotropy in an initially isotropic spectrum is studied numerically for two-dimensional magnetohydrodynamic turbulence. The anisotropy develops due to the combined effects of an externally imposed dc magnetic field and viscous and resistive dissipation at high wave numbers. The effect is most pronounced at high mechanical and magnetic Reynolds numbers. The anisotropy is greater at the higher wave numbers.

Small-scale structure of the Taylor–Green vortex

Abstract: The dynamics of both the inviscid and viscous Taylor–Green (TG) three-dimensional vortex flows are investigated. This flow is perhaps the simplest system in which one can study the generation of small scales by three-dimensional vortex stretching and the resulting turbulence. The problem is studied by both direct spectral numerical solution of the Navier–Stokes equations (with up to 256 3 modes) and by power-series analysis in time. The inviscid dynamics are strongly influenced by symmetries which confine the flow to an impermeable box with stress-free boundaries. There is an early stage during which the flow is strongly anisotropic with well-organized (laminar) small-scale excitation in the form of vortex sheets located near the walls of this box. The flow is smooth but has complex-space singularities within a distance $\hat{\delta}(t)$ of real (physical) space which give rise to an exponential tail in the energy spectrum. It is found that $\hat{\delta}(t)$ decreases exponentially in time to the limit of our resolution. Indirect evidence is presented that more violent vortex stretching takes place at later times, possibly leading to a real singularity ( $\hat{\delta}(t) = 0$ ) at a finite time. These direct integration results are consistent with new temporal power-series results that extend the Morf, Orszag & Frisch (1980) analysis from order t 44 to order t 80 . Still, convincing evidence for or against the existence of a real singularity will require even more sophisticated analysis. The viscous dynamics (decay) have been studied for Reynolds numbers R (based on an integral scale) up to 3000 and beyond the time t max at which the maximum energy dissipation is achieved. Early-time, high- R dynamics are essentially inviscid and laminar. The inviscidly formed vortex sheets are observed to roll up and are then subject to instabilities accompanied by reconnection processes which make the flow increasingly chaotic (turbulent) with extended high-vorticity patches appearing away from the impermeable walls. Near t max the small scales of the flow are nearly isotropic provided that R [gsim ] 1000. Various features characteristic of fully developed turbulence are observed near t max when R = 3000 and R λ = 110: a k − n inertial range in the energy spectrum is obtained with n ≈ 1.6–2.2 (in contrast with a much steeper spectrum at earlier times); th energy dissipation has considerable spatial intermittency; its spectrum has a k −1+μ inertial range with the codimension μ ≈ 0.3−0.7. Skewness and flatness results are also presented.

Stratified Turbulence and the Mesoscale Variability of the Atmosphere

Abstract: An analysis is made of Gage's proposal that the horizontal energy spectrum at mesoscale wavelengths is produced by upscale energy transfer through quasi-two-dimensional turbulence. It is suggested that principal sources of such energy can be found in decaying convective clouds and thunderstorm anvil outflows. These are believed to evolve similarly to the wake of a moving body in a stably stratified flow. Following the scale analysis by Riley, Metcalfe and Weissman it is expected that, in the presence of strong stratification, initially three-dimensionally isotropic turbulence divides roughly equally into gravity waves and stratified (quasi-two- dimensional) turbulence. The former then propagates away from the generation region, while the latter propagates in spectral space to larger scales, forming the −5/3 upscale transfer spectrum predicted by Kraichnan. Part of the energy of the stratified turbulence is recycled into three-dimensional turbulence by shearing instability, but the upscale escape ...

A two‐equation turbulence model for two‐phase flows

Abstract: A two-equation turbulence model has been developed for predicting two-phase flows. The two equations describe the conservation of turbulence kinetic energy and dissipation rate of that energy for the carrier fluid in a two-phase flow. They have been derived rigorously from the momentum equations of the carrier fluid. Closure of the time-mean equations is achieved by modeling the turbulent correlations up to third order. The new model eliminates the need to simulate in an ad hoc manner the effects of the dispersed phase on turbulence structure. Preliminary testing indicates that the model is successful in predicting the main features of a round gaseous jet laden with uniform-size solid particles.

Developments in the theory of turbulence

Abstract: The book "presents an introduction to part of what is presently called applied mathematics". It is not. in this reviewer's opinion, a part recognisable as such by most British applied mathematicians. There is no physical modelling involved in this treatise of what seems to be "appl ied" only in that it is not modern "pure mathematics". It is most unlikely that it could prove of general interest to even the more theoretical practitioners of the aeronautical world. The book like many others dealing with analysis contains techniques useful to the manipulation of linear equations, but the mathematical jargon is no more or less amenable to interpretation by most engineers than that already available in pure mathematical texts.

Riblets as a Viscous Drag Reduction Technique

Abstract: T viscous drag of turbulent boundary layers is a significant factor contributing to the fuel costs of the airlines. Several studies have indicated that microsurface geometry variations which change the near-wall structure of the flow have been effective in reducing drag. Summarized here is an investigation into the verification and extension of the most promising of these riblet variations.

Structure of a turbulent separation bubble

Abstract: Flow in the separation bubble formed along the sides of a blunt flat plate with right-angled corners has been studied in terms of extensive single- and two-point measurements of velocity and surface-pressure fluctuations. The cross-correlations between the surface-pressure and velocity fluctuations are found to be useful for the study of large-scale vortex structure in the bubble. Large-scale vortices are shed downstream from the separation bubble with a frequency of about 0.6U∞/xR, where U∞ is the approaching velocity and xR is the time-mean length of the bubble. On top of this regular vortex shedding, there exists a large-scale unsteadiness in the bubble. Vortices which are much larger than the regular vortices are shed with frequencies less than about 0.2U∞/xR. The large-scale unsteadiness is accompanied by enlargement and shrinkage of the bubble and also by a flapping motion of the shear layer near the separation line. The intermittent nature of the flow in the bubble is clarified in some detail. The distributions of the cross-correlations between the pressure and velocity fluctuations demonstrate the vortex structure in the reattaching zone. The longitudinal distance between the vortices is estimated to be (0.7–0.8) xR and their convection velocity is about 0.5U∞ near the reattachment line. The cross-correlations also suggest the existence of a longitudinal counter-rotating system in the bubble. The distance between the axes of the rotation is of the order of 0.6xR. Variations of timescales, lengthscales and phase velocities of the vortices are presented and discussed.

Liftoff characteristics of turbulent jet diffusion flames

Abstract: A theoretical analysis of turbulent jet diffusion flames is developed in which the flame is regarded as an ensemble of laminar diffusion flamelets that are highly distorted. The flow inhomogeneities are considered to be sufficiently strong to produce local quenching events for flamelets as a consequence of excessive flame stretch. The condition for flamelet extinction is derived in terms of the instantaneous scalar dissipation rate, which is ascribed a log-normal distribution. Percolation theory for a random network of stoichiometri c sheets is used to predict quenching thresholds that define liftoff heights. Predictions are shown to be in reasonably satisfactory agreement with experimentally measured liftoff heights of methane jet diffusion flames, within experimental uncertainties. UEL issuing from a tube or duct into an oxidizing atmosphere forms a jet in which combustion may occur. The associated combustion process is the most classical example of a diffusion flame. At sufficiently high velocities of fuel flow (fundamentally, at sufficiently large Reynolds numbers) the entire diffusion flame is turbulent. The turbulent jet diffusion flame begins at the mouth of the duct for a range of values of the exit velocity. When a critical exit velocity is exceeded, the flame abruptly is detached from the duct and acquires a new configuration of stabilization in which combustion begins a number of duct diameters downstream. Flames in this state, stabilized in the mixing region, are termed lifted diffusion flames, and the critical exit velocity at which they appear is called the liftoff velocity. The liftoff height is the centerline distance from the duct exit to the plane of flame stabilization. A further increase in the exit velocity increases the liftoff height without significantly modifying the turbulent flame height (the centerline distance from the duct exit to the plane at which, on the average, combustion ceases). There is a second critical value of the exit velocity, called the blowoff velocity, beyond which the flame cannot be stabilized in the mixing region. The present study addresses questions of the structure of lifted turbulent diffusion flames at exit velocities between liftoff and blowoff values. Attention is focused especially on the calculation of liftoff heights. Liftoff characteristics for turbulent jet diffusion flames are of practical importance in connection with flame stabilization. Conditions for liftoff and blowoff must be known in developing rational designs of burners, e.g., in diffusion-flame combustors for power production or in flaring applications for the petroleum industry. They are also of interest in connection with extinguishment of certain fires that may occur in oil or gas rigs. The present work is directed toward developing an improved fundamental understanding of liftoff phenomena that may later prove useful for these applications.

Plasma Edge Turbulence

Abstract: Model mode-coupling equations for the resistive drift-wave instability are derived and numerically solved to study the properties of turbulence near a plasma edge. The wavenumber spectrum of the turbulence is found to exhibit an inverse cascade to form an isotropic, two-dimensional Kolmogorov spectrum, ${k}^{\ensuremath{-}3}$, in the large-wave-number regime. The turbulence has a broad frequency spectrum with a large saturation level and produces Bohm-type particle diffusion.

Improved turbulence models based on large eddy simulation of homogeneous, incompressible turbulent flows

Abstract: The physical bases of large eddy simulation and subgrid modeling are studied. A subgrid scale similarity model is developed that can account for system rotation. Large eddy simulations of homogeneous shear flows with system rotation were carried out. Apparently contradictory experimental results were explained. The main effect of rotation is to increase the transverse length scales in the rotation direction, and thereby decrease the rates of dissipation. Experimental results are shown to be affected by conditions at the turbulence producing grid, which make the initial states a function of the rotation rate. A two equation model is proposed that accounts for effects of rotation and shows good agreement with experimental results. In addition, a Reynolds stress model is developed that represents the turbulence structure of homogeneous shear flows very well and can account also for the effects of system rotation.

Local Quenching Due to Flame Stretch and Non-Premixed Turbulent Combustion

Abstract: A turbulent non-premixed burning mixture is considered at a state close to extinction. The turbulent flame is conceived as an ensemble of thin laminar diffusion flamelets that are highly distorted and stretched such that they may be quenched locally. The structure of the laminar diffusion flamelets is analysed in the limit of a large activation energy and the results of Linan's analysis of counterflow diffusion flames are used to derive the quenching condition. This condition is expressed by an instantaneous scalar dissipation rate. Statistics of the scalar dissipation rate are discussed on the basis of Kolmogoroff's third hypothesis. Extinction condition of the whole turbulent flame are derived on the basis of the percolation theory.

Dense cores in dark clouds. III. Subsonic turbulence.

Abstract: In 43 dark clouds with narrow molecular lines, significant correlations exist between line width and map size of the form ..delta..vproportionalR/sup 0.5/, and between mean density and map size of the form nproportionalR/sup -1/; and the law of virial equilibrium is closely satisfied. These relations tend to confirm those found earlier for larger clouds, and extend them into the regime of subsonic turbulence. If these relations for large and small clouds reflect the same process, it is still unclear whether this process is a turbulent energy cascade, as in Kolmogorov turbulence, or simply the tendency of clouds with nproportionalR/sup -1/ to be in virial equilibrium. For the smallest clouds (''dense cores'') there is weak support for the turbulent cascade picture. In this picture viscous dissipation of turbulence is likely to play an important role in heating and star formation. The time scale for the free decay of turbulence in dense cores is < or approx. =5 x 10/sup 5/ yr, comparable to the free-fall time. Dense cores can thus form low-mass stars on free-fall time scales if their input of fresh turbulence is sufficiently reduced. This reduction may occur as a result of their small size, or their high densitymore » contrast with surrounding gas. Observed distributions of dense core properties in Taurus, Ophiuchus, and other dark cloud regions appear consistent with dense core evolution toward star formation via dissipation of turbulence. In complexes which are vigorously forming low-mass stars, dense cores are more prevalent, smaller, denser, and have narrower lines than in regions with less star formation.« less

Experiments on the transition of homogeneous turbulence to internal waves in a stratified fluid

Abstract: The evolution of unsheared grid-generated turbulence in a stably stratified fluid was investigated in a closed-loop salt-stratified water channel. Simultaneous single-point measurements of the horizontal and vertical velocity and density fluctuations were obtained, including turbulent mass fluxes central in understanding the energetics of the fluctuating motion. When the buoyancy lengthscale was initially substantially larger than the largest turbulent scales, the initial behaviour of the velocity and density fields was similar to that in the non-stratified case. With further downstream development, the buoyancy lengthscale decreased while the turbulence scale grew. Deviations from neutral behaviour occurred when these two lengthscales became of the same order, after the initially larger inertial forces associated with the initial kinetic energy had become weaker and buoyancy forces became important.Buoyancy forces produced anisotropy in the largest scales first, preventing them from overturning, while smaller-scale isotropic turbulent motions remained embedded within the larger-scale wave motions. These small-scale motions exhibited classical turbulent behaviour and scaled universally with Kolmogorov length and velocity scales. Eventually even the smallest scales of the decaying turbulence were affected by buoyancy, all isotropic motions disappeared, and Kolmogorov scaling failed. The turbulent vertical mass flux decreased to zero for this condition, indicating that the original turbulent field had been completely converted to random internal wave motions.The transition from a fully turbulent state to one of internal waves occurred rapidly in a time less than the characteristic time of the turbulence based on the largest-scale eddies found in the flow at transition. The dissipation rate for complete transition to a wave field was found to be of the order of et = 24.5νN2, where ν is the kinematic viscosity and N the Brunt-Vaisala frequency. This is in fairly good agreement with the value 30νN2 predicted by Gibson (1980, 1981).The present experiments have determined quantitative limits on the range of active turbulent scales in homogeneous stratified turbulence, in terms of an upper limit near the buoyancy lengthscale and a lower limit determined by viscosity in the usual way. This description has been used here to help explain and assimilate the results from the earlier stratified grid-turbulence experiments of Lin & Veenhuizen (1975) and Dickey & Mellor (1980). While some of the features of the present observations may be qualitatively seen in the numerical simulations of the problem of Riley, Metcalfe & Weissman (1981), there are fundamental differences, probably due in part to large differences in initial lengthscale ratios and in the limited range of scales attainable in numerical simulations. The present experiments may serve as a useful test case for future modelling and interpretation of the behaviour of turbulence in stratified flows observed in the oceans and atmosphere.

Structure and dynamics of round turbulent jets

Abstract: Laser‐induced fluorescence and particle streak velocity measurements were conducted to investigate the structure and dynamics of round turbulent jets. The results suggest that the far‐field region of the jet is dominated by large‐scale vortical structures, which appear to be axisymmetric or helical a large part of the time. Entrainment and mixing of the reservoir fluid with the jet fluid is found to be intimately connected with the kinematics of these structures. Unmixed reservoir fluid is found to reach and cross the jet axis.

The effects of crossing trajectories on the dispersion of particles in a turbulent flow

Abstract: The effects of ‘crossing trajectories’ and inertia on the dispersion of particles suspended in a field of grid-generated turbulence were investigated experimentally. The effect of particle trajectories crossing the trajectories of fluid elements, under the influence of a potential field (usually gravity), is to force the particles from one region of highly correlated flow to another. In this manner, particles lose velocity correlation more rapidly than the corresponding fluid points and as a result disperse less.A homogeneous decaying turbulent field was created behind a square biplanar grid in a wind tunnel. Particles were charged by a corona discharge then passed into the test section through a small plastic tube. A uniform electric field within the test section was used to simulate the effect of gravity, forcing the charged particles out of regions of correlated fluid at a higher than normal rate, therefore inducing the effects of crossing trajectories. Two sizes of glass beads (5 μm and 57 μm diameter) were employed in order to observe inertial effects. Laser-Doppler anemometry was used to measure particle mean-square displacement, autocorrelation coefficient, and mean-square velocity, from which dispersion coefficients were calculated.For the two particle sizes used in the tests, it was found that the particle diffusion coefficient, after a suitably long time from their release, was influenced primarily by the effect of crossing trajectories. Only in the particle mean-square velocity was the particle inertia seen to have any effect. The ratio of the particle relaxation time to the Kolmogoroff timescale was found to be a good indicator for the effects of particle inertia.

Scaling of the bursting frequency in turbulent boundary layers

Abstract: The bursting frequency in turbulent boundary layers has been measured over the Reynolds-number range 103 < U∞/ν < 104. When scaled with the variables appropriate for the wall region, the non-dimensional frequency was constant independent of Reynolds number. A strong effect of the sensor size was noted on the measured bursting frequency. Only sensors having a spatial scale less than twenty viscous lengthscales were free from spatial-averaging effects and yielded consistent results. The spatial-resolution problem was apparently the reason for erroneous results reported in the past.

On the structure and resolution of wall-pressure fluctuations associated with turbulent boundary-layer flow

Abstract: In a wind tunnel designed for flow-acoustic measurements, the wall-pressure fluctuations beneath a turbulent boundary layer have been investigated. The measurements were carried out with variously sized pressure transducers (19 [les ] d+ [les ] 333) and with an array of four small transducers (separation distance Δx+ = 75). It is shown that the dimensionless diameter d+ = 19 of the transducers is sufficient to resolve the essential structures of the turbulent pressure fluctuations. The power spectrum Φ(ω+) measured with the smallest transducer d+ = 19 partly exhibits power-law decay , which has been theoretically predicted for locally isotropic turbulence. By visual analysis and signal averaging in the time domain, pressure structures with high amplitudes could be detected which have the shape of short wavetrains or pulses. Their characteristic frequency and longitudinal wavelength have the mean values ω+ = 0.52 and λ+ = 145 respectively, and their mean convection velocity amounts to uc/u∞ = 0.53. It was calculated from the measured probability density that these characteristic structures play an important role, although the probability of their occurrence is low. The sources of these wall-pressure structures can be located in the buffer layer of the boundary layer.

Mean flow in round bubble plumes

Abstract: Previous experimental studies are reviewed and those whose data are deemed reliable are identified. New experiments at larger scale are described and the results are reported. These are combined with the reliable previous studies to form a data set covering heights from 3.66 to 50 m and gasflow rates from 0.0002 to 0.59 normal m3/s. These wide-ranging data are combined with an integral theory for bubble plumes to determine functional relationships between local plume properties and the entrainment coefficient and the fraction of the momentum flux that is carried in the turbulent velocity fluctuations. These relationships together with the integral theory provide a set of equations that are suitable for numerical solution for the mean flow properties of any round bubble plume. Examples of the numerical solutions are presented and a comparison of one of these with existing experimental data is given. The relationships between the local plume properties and the entrainment coefficient and the momentum flux carried by the turbulence are interpreted to provide a qualitative understanding of the parameters involved and their influences on the plume.

Experiments on the turbulence statistics and the structure of a reciprocating oscillatory flow

Abstract: A reciprocating oscillatory turbulent flow in a rectangular duct is investigated experimentally by making use of a laser-Doppler velocimeter, hot-wire anemometers as well as electronic digital sampling and processing equipments.The profiles of the mean velocity, the turbulence intensities, the Reynolds stress and the turbulent-energy production rate are compared for the accelerating and decelerating phases.The characteristics of such a flow are quite different from wall turbulence which is steady in the mean. In the accelerating phase, turbulence is triggered by the shear instability at a slight distance from the wall but is suppressed and cannot develop. However, with the beginning of flow deceleration, turbulence grows explosively and violently and is maintained by the bursting type of motion.The turbulent-energy production becomes exceedingly high in the decelerating phase, but the turbulence is reduced to a very low level at the end of the decelerating phase and in the accelerating stage of reversal flow. Spectra and spatial correlations for the various phases are compared. The spectral decay in the high-frequency range for the decelerating phase with high turbulence is far steeper than that of Kolmogorov's −5/3 power law, indicating remarkably high energy dissipation by high-frequency turbulence.Notwithstanding the great difference between the ensemble-averaged characteristics of the oscillatory flow and those of steady wall turbulence, its basic processes such as ejection, sweep and interactions directed towards and away from the wall are the same as those of ‘steady’ wall turbulence.

Low-dimensional chaos in a hydrodynamic system

Abstract: Evidence is presented for low-dimensional strange attractors in Couette-Taylor flow data. Computations of the largest Lyapunov exponent and metric entropy show that the system displays sensitive dependence on initial conditions. Although the phase space is very high dimensional, analysis of experimental data shows that motion is restricted to an attractor of dimension 5 for Reynolds numbers up to 30% above the onset of chaos. The Lyapunov exponent, entropy, and dimension all generally increase with Reynolds number.

Large-Scale Two-Dimensional Turbulence in the Atmosphere

Abstract: Global FGGE data are used to investigate several aspects of large-scale turbulence in the atmosphere. The approach follows that for two-dimensional, nondivergent turbulent flows which are homogeneous and isotropic on the sphere. Spectra of kinetic energy, enstrophy and available potential energy are obtained for both the stationary and transient parts of the flow. Nonlinear interaction terms and fluxes of energy and enstrophy through wavenumber space are calculated and compared with the theory. A possible method of parameterizing the interactions with unresolved scales is considered. Two rather different flow regimes are found in wavenumber space. The high-wavenumber regime is dominated by the transient components of the flow and exhibits, at least approximately, several of the conditions characterizing homogeneous and isotropic turbulence. This region of wavenumber space also displays some of the features of an enstrophy-cascading inertial subrange. The low-wavenumber region, on the other hand, ...