Showing papers on "Turbulence published in 1988"

Direct simulation of a turbulent boundary layer up to R sub theta = 1410

Abstract: The turbulent boundary layer on a flat plate, with zero pressure gradient, is simulated numerically at four stations between R sub theta = 225 and R sub theta = 1410. The three-dimensional time-dependent Navier-Stokes equations are solved using a spectra method with up to about 10 to the 7th power grid points. Periodic spanwise and stream-wise conditions are applied, and a multiple-scale procedure is applied to approximate the slow streamwise growth of the boundary layer. The flow is studied, primarily, from a statistical point of view. The solutions are compared with experimental results. The scaling of the mean and turbulent quantities with Reynolds number is examined and compared with accepted laws, and the significant deviations are documented. The turbulence at the highest Reynolds number is studied in detail. The spectra are compared with various theoretical models. Reynolds-stress budget data are provided for turbulence-model testing.

Eddies, streams, and convergence zones in turbulent flows

Abstract: Recent studies of turbulent shear flows have shown that many of their important kinematical and dynamical properties can be more clearly understood by describing the flows in terms of individual events or streamline patterns These events or flow regions are studied because they are associated with relatively large contributions to certain average properties of the flow, for example kinetic energy, Reynolds stress, or to particular processes in the flow, such as mixing and chemical reactions, which may be concentrated at locations where streamlines converge for fast chemical reactions (referred to as convergence or C regions), or in recirculating eddying regions for slow chemical reactions The aim of this project was to use the numerical simulations to develop suitable criteria for defining these eddying or vortical zones The C and streaming (S) zones were defined in order to define the whole flow field It is concluded that homogeneous and sheared turbulent flow fields are made up of characteristic flow zones: eddy, C, and S zones A set of objective criteria were found which describe regions in which the streamlines circulate, converge or diverge, and form high streams of high velocity flow

The compressible turbulent shear layer: an experimental study

Abstract: The growth rate and turbulent structure of the compressible, plane shear layer are investigated experimentally in a novel facility. In this facility, it is possible to flow similar or dissimilar gases of different densities and to select different Mach numbers for each stream. Ten combinations of gases and Mach numbers are studied in which the free-stream Mach numbers range from 0.2 to 4. Schlieren photography of 20-ns exposure time reveals very low spreading rates and large-scale structures. The growth of the turbulent region is defined by means of Pitot-pressure profiles measured at several streamwise locations. A compressibility-effect parameter is defined that correlates and unifies the experimental results. It is the Mach number in a coordinate system convecting with the velocity of the dominant waves and structures of the shear layer, called here the convective Mach number. It happens to have nearly the same value for each stream. In the current experiments, it ranges from 0 to 1.9. The correlations of the growth rate with convective Mach number fall approximately onto one curve when the growth rate is normalized by its incompressible value at the same velocity and density ratios. The normalized growth rate, which is unity for incompressible flow, decreases rapidly with increasing convective Mach number, reaching an asymptotic vaue of about 0.2 for supersonic convective Mach numbers.

The dynamics of coherent structures in the wall region of a turbulent boundary layer.

Abstract: We have modelled the wall region of a turbulent boundary layer by expanding the instantaneous field in so-called empirical eigenfunctions, as permitted by the proper orthogonal decomposition theorem (Lumley 1967, 1981). We truncate the representation to obtain low-dimensional sets of ordinary differential equations, from the Navier–Stokes equations, via Galerkin projection. The experimentally determined eigenfunctions of Herzog (1986) are used; these are in the form of streamwise rolls. Our model equations represent the dynamical behaviour of these rolls. We show that these equations exhibit intermittency, which we analyse using the methods of dynamical systems theory, as well as a chaotic regime. We argue that this behaviour captures major aspects of the ejection and bursting events associated with streamwise vortex pairs which have been observed in experimental work (Kline et al. 1967). We show that although this bursting behaviour is produced autonomously in the wall region, and the structure and duration of the bursts is determined there, the pressure signal from the outer part of the boundary layer triggers the bursts, and determines their average frequency. The analysis and conclusions drawn in this paper appear to be among the first to provide a reasonably coherent link between low-dimensional chaotic dynamics and a realistic turbulent open flow system.

Laminar Flamelet Concepts in Turbulent Combustion

Abstract: The laminar flamelet concept covers a regime in turbulent combustion where chemistry (as compared to transport processes) is fast such that it occurs in asymptotically thin layers—called flamelets—embedded within the turbulent flow field. This situation occurs in most practical combustion systems including reciprocating engines and gas turbine combustors. The inner structure of the flamelets is one-dimensional and time dependent. This is shown by an asymptotic expansion for the Damkohler number of the rate determining reaction which is assumed to be large. Other non-dimensional chemical parameters such as the nondimensional activation energy or Zeldovich number may also be large and may be related to the Damkohler number by a distinguished asymptoiic limit. Examples of the flamelet structure are presented using onestep model kinetics or a reduced four-step quasi-global mechanism for methane flames. For non-premixed combustion a formal coordinate transformation using the mixture fraction Z as independent variable leads to a universal description. The instantaneous scalar dissipation rate χ of the conserved scalar Z is identified to represent the diffusion time scale that is compared with the chemical time scale in the definition of the Damkohler number. Flame stretch increases the scalar dissipation rate in a turbulent flow field. If it exceeds a critical value χ q the diffusion flamelet will extinguish. Considering the probability density distribution of χ , it is shown how local extinction reduces the number of burnable flamelets and thereby the mean reaction rate. Furthermore, local extinction events may interrupt the connection to burnable flamelets which are not yet reached by an ignition source and will therefore not be ignited. This phenomenon, described by percolation theory, is used to derive criteria for the stability of lifted flames. It is shown how values of ∋ q obtained from laminar experiments scale with turbulent residence times to describe lift-off of turbulent jet diffusion flames. For non-premixed combustion it is concluded that the outer mixing field—by imposing the scalar dissipation rate—dominates the flamelet behaviour because the flamelet is attached to the surface of stoichiometric mixture. The flamelet response may be two-fold: burning or non-burning quasi-stationary states. This is the reason why classical turbulence models readily can be used in the flamelet regime of non-premixed combustion. The extent to which burnable yet non-burning flamelets and unsteady transition events contribute to the overall statistics in turbulent non-premixed flames needs still to be explored further. For premixed combustion the interaction between flamelets and the outer flow is much stronger because the flame front can propagate normal to itself. The chemical time scale and the thermal diffusivity determine the flame thickness and the flame velocity. The flamelet concept is valid if the flame thickness is smaller than the smallest length scale in the turbulent flow, the Kolmogorov scale. Also, if the turbulence intensity v′ is larger than the laminar flame velocity, there is a local interaction between the flame front and the turbulent flow which corrugates the front. A new length scale L G =v F 3 /∈ , the Gibson scale, is introduced which describes the smaller size of the burnt gas pockets of the front. Here v F is the laminar flame velocity and ∈ the dissipation of turbulent kinetic energy in the oncoming flow. Eddies smaller than L G cannot corrugate the flame front due to their smaller circumferential velocity while larger eddies up to the macro length scale will only convect the front within the flow field. Flame stretch effects are the most efficient at the smallest scale L G . If stretch combined with differential diffusion of temperature and the deficient reactant, represented by a Lewis number different from unity, is imposed on the flamelet, its inner structure will respond leading to a change in flame velocity and in some cases to extinction. Transient effects of this response are much more important than for diffusion flamelets. A new mechanism of premixed flamelet extinction, based on the diffusion of radicals out of the reaction zone, is described by Rogg. Recent progress in the Bray-Moss-Libby formulation and the pdf-transport equation approach by Pope are presented. Finally, different approaches to predict the turbulent flame velocity including an argument based on the fractal dimension of the flame front are discussed.

Reynolds-stress and dissipation-rate budgets in a turbulent channel flow

Abstract: The budgets for the Reynolds stresses and for the dissipation rate of the turbulence kinetic energy are computed using direct simulation data of a turbulent channel flow. The budget data reveal that all the terms in the budget become important close to the wall. For inhomogeneous pressure boundary conditions, the pressure-strain term is split into a return term, a rapid term, and a Stokes term. The Stokes term is important close to the wall. The rapid and return terms play different roles depending on the component of the term. A split of the velocity pressure-gradient term into a redistributive term and a diffusion term is proposed, which should be simpler to model. The budget data is used to test existing closure models for the pressure-strain term, the dissipation rate, and the transport rate. In general, further work is needed to improve the models.

Hydraulic Stream Ecology: Observed Patterns and Potential Applications

Abstract: Although it is well known that metabolism, feeding, and behaviour of lotic organisms is influenced by various flow characteristics, hydraulic variables usually are not accurately measured in lotic ecology studies. Using an approach we call "hydraulic stream ecology", we link organismic responses to a more comprehensive treatment of the physical environment. Since a unified analytical solution for all important hydraulic variables in running waters does not exist at the moment, we advocate a simpler view of the physical system. We demonstrate methods for estimating complex hydraulic key characteristics, like turbulence in the free flow, turbulence close to the stream bottom, and the force of flow prevailing at the bottom. Calculations of these complex key characteristics require measurement of simple hydraulic characteristics like mean velocity, water surface slope, depth, bottom roughness, kinematic viscosity, and density of the water. The hydraulic environment shows characteristic patterns within whole c...

The force exerted on a body in inviscid unsteady non-uniform rotational flow

Abstract: A general expression is derived for the fluid force on a body of simple shape moving with a velocity v through inviscid fluid in which there is an unsteady non-uniform rotational velocity field uo(x,t) in two or three dimensions. It is assumed that the radius is small compared with the scale over which the strain rate changes, though for the sphere it is also assumed that the changes in the ambient velocity field over the scale of the sphere are small compared with the velocity of the body relative to the flow. Given these approximations it is shown that the effects of the rate of change of the vorticity of the ambient flow is of second order and can be neglected. However the rate of change of the irrotational straining motion is included in the analysis. It is shown that the inertial forces derived by many authors for irrotational flow can be simply added to a generalization of the lift force derived by Auton (1987) in a companion paper. It is shown how this lift force is made up of a rotational and an inertial or added-mass component. For three-dimensional bluff bodies the latter is generally larger (by a factor of three for a sphere), and can be simply calculated from the added-mass coefficient. For illustration, the general expression is used to derive formulae for (i) the motion of a spherical bubble in a steady non-uniform flow to contrast with the motion in an unsteady flow, and (ii) the motion of rigid volumes of neutral density across an inviscid shear flow. These results show how added-mass (and lift) forces lead to different motions for a sphere and a cylinder. The general expression is useful in two-phase flow calculations, and for indicating the forces and motions of 'lumps of fluid' in turbulent flows.

Investigations of round vertical turbulent buoyant jets

Abstract: The axial and radial velocity components w and u, and the concentration c of a Rhodamine 6G dye were measured simultaneously in a turbulent buoyant jet, using laser-Doppler anemometry combined with a recently developed laser-induced-fluorescence concentration measurement technique. These non-intrusive techniques enable measurements in a region of plume motion where conventional probe-based techniques have had difficulties. The results of the study show that the asymptotic decay laws for velocity and concentration of a tracer transported by the flow are verified experimentally in both jets and plumes. The momentum and volume fluxes and the mean dilution factor are determined in dimensionless form as a function of the normalized distance from the flow source. Contradictory results from earlier experimental plume investigations concerning the decay laws of w and c and the plume width ratio b_c/b_w are discussed. The turbulence properties and the transition from momentum-driven jets to buoyancy-driven plumes are presented. The turbulence is found to scale with the mean flow as predicted by dimensional analysis and self-similarity. Buoyancy-produced turbulence is found to transport twice as much tracer as jet turbulence. Although velocity statistics in jets and plumes are found to be highly self-similar there is a strong disparity in the distribution of tracer concentration in the two flows. This occurs in the time-average mean flows as well as the r.m.s. turbulent quantities. Instantaneous concentration fluctuations are found to exceed time averages by as much as a factor of 3. The experimental results should provide a reasonable basis for validation of computer models of axisymmetric plumes.

Defining a universal and continuous Strouhal–Reynolds number relationship for the laminar vortex shedding of a circular cylinder

Abstract: The existence of a discontinuity in the Strouhal–Reynolds number relationship for the laminar vortex shedding of a cylinder is found to be caused by a change in the mode of oblique shedding. By ‘‘inducing’’ parallel shedding (from manipulating end conditions) the resulting Strouhal curve becomes completely continuous and agrees very well with the oblique‐shedding data, if it is transformed by S0=Sθ/cos θ (where Sθ is the Strouhal number corresponding with the oblique‐shedding angle θ). The curve also agrees with data from a completely different facility. This provides evidence that this Strouhal curve (S0) is universal (for a circular cylinder).

Turbulent shear flows over low hills

Abstract: A general analysis is developed for turbulent shear flows over two- and three-dimensional hills with low-slopes which allows for a wide range of upwind velocity profiles, such as those caused by wakes of upwind hills, roughness changes, or changes in stratification. In this paper the atmosphere is assumed to be neutrally stable and the half-lengths of the hills, L, are large compared with their heights, H, which are very large compared with the roughness length zo. The general structure of the solution is defined by dividing the flow into two regions, each of which is divided into two sublayers: an inviscid outer region composed of an upper layer in which there is potential flow when the atmosphere is neutrally stable, and a middle layer in which the wind shear dominates; and an inner region of thickness l ≤ L in which the effects of perturbation shear stresses are confined. The latter region is divided into two: a shear stress layer where the shear stresses, although weak, determine that the maximum of the perturbation velocity is located in this layer; and an inner surface layer of thickness ls where the shear stress gradient varies rapidly and the perturbation velocity tends to zero. The details of the middle layer are given here for different kinds of upwind profiles, including logarithmic, ‘power law’ and linear profiles. It is shown that the analysis can be extended to allow for nonlinear inertial effects in the middle layer. Analytical solutions are derived for the inner region as asymptotic expansions in δ = [ln(l/zo)]−1, which is assumed to be small, and this shows that ls ∼ zo(l/zo)1/2. The results of the analytical model are compared with our own and with previously published numerical computations of the full equations (applying the same assumptions used for calculating the turbulent shear stresses as used in the analytical work), which have largely been validated against full-scale measurements. These results confirm that the relative increase of surface stress is significantly greater than the increase of wind speed near the surface except when there is no upwind shear (as for example in a logarithmic boundary layer when the roughness length tends to zero). Finally, the paper shows that the outer regions of laminar (or constant eddy viscosity) and of turbulent flows over hills are broadly similar, but that the effects of the flow in the inner region on the outer regions are much smaller in the latter case.

Spectral wave attenuation by bottom friction: theory

Abstract: Based on the linearized form of the boundary layer equations and a simple eddy viscosity formulation of shear stress, the turbulent bottom boundary layer flow is obtained for a wave motion specified by its directional spectrum. Closure is obtained by requiring the solution to reduce, in the limit, to that of a simple harmonic wave. The resulting dissipation is obtained in spectral form with a single friction factor determined from knowledge of the bottom roughness and an equivalent monochromatic wave having the same root-mean-square near-bottom orbital velocity and excursion amplitude as the specified wave spectrum. The total spectral dissipation rate is obtained by integration and compared with the average dissipation obtained from a model considering the statistics of individual waves defined by their maximum orbital velocity and zero-crossing period. The agreement between the two different evaluations of total spectral dissipation supports the validity of the spectral dissipation model.

The fluctuating wall‐shear stress and the velocity field in the viscous sublayer

Abstract: The fluctuating wall‐shear stress was measured with various types of hot‐wire and hot‐film sensors in turbulent boundary‐layer and channel flows. The rms level of the streamwise wall‐shear stress fluctuations was found to be 40% of the mean value, which was substantiated by measurements of the streamwise velocity fluctuations in the viscous sublayer. Heat transfer to the fluid via the probe substrate was found to give significant differences between the static and dynamic response for standard flush‐mounted hot‐film probes with air or oil as the flow medium, whereas measurements in water were shown to be essentially unaffected by this problem.

Instability mechanisms in shear-flow transition

Abstract: Developing an understanding of turbulent shear flow at high Reynolds numbers has been a central problem in the theory of fluid motion for over a century Like all turbulent flows, turbulent shear flow is a fluid motion of complex and irregular character whose exact behavior is very sensitive to small changes in initial or boundary conditions Turbulent shear flows are further characterized by a large range of length and time scales, with energy and momentum transfer predominantly affected by nonlinear (iner­ tial) processes between eddies of different scales In many situations of interest, the external conditions are geometrically and temporally simple, and the flow equations admit a correspondingly simple solution: one example is Hagen-Poiseuille flow in a pipe with a constant pressure gradi­ ent Simple, or laminar, flow is generally preferred at low or moderate Reynolds numbers, while turbulent flow is preferred at high Reynolds

A linear-eddy model of turbulent scalar transport and mixing

Abstract: Transport and mixing of diffusive scalars in turbulent flows are simulated computationally based on a novel representation of the temporal evolution along a transverse line moving with the mean fluid velocity. The scalar field along this line evolves by Fickian diffusion, representing molecular processes, and by randomly occurring events called block inversions. Block inversion, representing the effect of turbulent convection, consists of the random selection of an interval (Y0 − 1/2, Y0 + 1/2) of the line, where the interval size l may he either fixed or randomly selected, and replacement of the scalar field θ(y) within that interval by θ(2y0 For fixed l, the model requires a single input parameter, the Peclet number. To demonstrate the performance of the model, this formulation is used to compute the spatial development of diffusive scalar fields downstream of several source configurations in homogeneous turbulence. Generalization to inhomogeneous turbulence is discussed, as well as a formulati...

Spectral analysis of large-eddy simulations of the convective boundary layer

Abstract: To examine the fidelity of the simulated turbulent flow, we analyzed the spectra of 96×&96×96 large-eddy-simulation results. We derived expressions for the inertial-range spectra of a filtered wind field, compared our computed spectra with the theoretical predictions, and drew two main conclusions. First, the wave cutoff filter is more appropriate for our large-eddy-simulation model than the Gaussian filter. Second, only a certain combination of the subgrid-scale parameters for the dissipation rate and eddy viscosity provides good inertial-range spectra. We offer an explanation for the unreasonably large sugrid temperature and moisture variances reported in Deardorff's 1974 lame-eddy-simulation results, and show that moment statistics up to third order are not sensitive to moderate changes in the subgrid-scale parameters.

Stochastic estimation of organized turbulent structure - Homogeneous shear flow

Abstract: A generalization of the conditional-eddy concept is proposed in which the conditional event specifies the local kinematic state in terms of the velocity and the deformation. Results are presented for stochastically estimated conditional eddies given the local kinematics. The equation governing the probability density function of a kinematic state has been derived for constant-property incompressible flow, providing a link between coherent flow structures corresponding to the conditional eddies and the modelling of turbulent transport. The primary contributions to the second-quadrant and fourth-quadrant Reynolds-stress events in homogeneous shear flow are shown to come from flow induced through the 'legs' and close to the 'heads' of upright and inverted 'hairpins', respectively.

Optimal excitation of perturbations in viscous shear flow

Abstract: Evidence, both theoretical and experimental, is accumulating to support a mechanism for transition to turbulence in shear flow based on the 3‐D secondary instability of finite 2‐D departures from plane parallelism. It is of central importance for using this mechanism to understand how the finite amplitude 2‐D disturbances arise. To be sure, it is possible that in many experiments the disturbance is produced by the intervention of a mechanism that directly injects the requisite disturbance energy without calling on the store of kinetic energy inherent in the shear flow. It is shown here that it is also possible to tap the mean shear energy using properly configured perturbations that develop into the required primary disturbance on time scales comparable to those associated with the secondary instabilities even though the shear flow is stable or supports, at most, weak exponential instability.

Modelling of the interaction of small and large eddies in two dimensional turbulent flows

Abstract: L'amplitude des petits tourbillons decroit exponentiellement vers une valeur petite. On en deduit une loi d'interaction simplifiee des petits et grands tourbillons

Growth and decay of turbulence in a stably stratified shear flow

Abstract: The behaviour of an evolving, stably stratified turbulent shear flow was investigated in a ten-layer, closed-loop, salt-stratified water channel. Simultaneous single-point measurements of the mean and fluctuating density and longitudinal and vertical velocities were made over a wide range of downstream positions. For strong stability, i.e. a mean gradient Richardson number Ri greater than a critical value of Ricr ≈ 0.25, there is no observed growth of turbulence and the buoyancy effects are similar to those in the unsheared experiments of Stillinger, Helland & Van Atta (1983) and Itsweire, Helland & Van Atta (1986). For values of Richardson number less than Ricr the turbulence grows at a rate depending on Ri and for large evolution times the ratio between the Ozmidov and turbulent lengthscale approaches a constant value which is also a function of Richardson number.Normalized velocity and density power spectra for the present experiments conform to normalized spectra from previous moderate- to high-Reynolds-number studies. With increasing or decreasing stability, the stratified shear spectra exhibit greater portions of the universal non-stratified spectrum curve. The shapes of the shear-stress and buoyancy-flux cospectra confirm that they act as sources and sinks for the velocity and density fluctuations.

Turbulence structure in a deciduous forest

Abstract: Three-dimensional wind velocity components were measured at two levels above and at six levels within a fully-leafed deciduous forest. Greatest shear occurs in the upper 20% of the canopy, where over 70% of the foliage is concentrated. The turbulence structure inside the canopy is characterized as non-Gaussian, intermittant and highly turbulent. This feature is supported by large turbulence intensities, skewness and kurtosis values and by the large infrequent sweeps and ejections that dominate tangential momentum transfer. Considerable day/night differences were observed in the vertical profiles of the mean streamwise wind velocity and turbulence intensities since the stability of the nocturnal boundary layer dampens turbulence above and within the canopy.

Turbulent Transport on the Endwall in the Region Between Adjacent Turbine Blades

Abstract: The complex three-dimensional flow in the endwall region near the base of a turbine blade has an important impact on the local heat transfer. The initial horseshoe vortex, the passage vortex, and resulting corner vortices cause large variations in heat transfer over the entire endwall region. Due to these large surface gradients in heat transfer, conventional measurement techniques generally do not provide in accurate determination of the local heat transfer coefficients. In the present study the heat/mass transfer analogy is used to examine the local transport coefficients for two different endwall boundary layer thicknesses and two free-stream Reynolds numbers. A linear turbine blade cascade is used in conjunction with a removable endwall plate. Napthalene (C{sub 10}H{sub 8}) is cast into a mold on the plate and the rate of naphthalene sublimation is determined at 6,000+ locations on the simulated endwall by employing a computer-aided data acquisition system. This technique allows one to obtain detailed contour plots of the local convection coefficient over the entire endwall. By examining the mass transfer contours, it is possible to infer information on three-dimensional flow in the passage between the blades. Extremely high transport coefficients on the endwall indicate locations of potential overheating and failuremore » in actual turbine.« less

On the resuspension of small particles by a turbulent flow

Abstract: Presents a new approach to the way small particles are resuspended from a surface exposed to a turbulent flow. In contrast to current force balance models, this approach recognises the influence of turbulent energy transferred to a particle from the resuspending flow. This energy maintains the particle in motion on the surface within a surface adhesive potential well. The particle is detached from the surface when it has accumulated enough vibrational energy to escape from the well. Such considerations lead to a formula for the rate constant for long-term resuspension.

Closure of the Reynolds stress and scalar flux equations

Abstract: A second‐order, single‐point closure model for calculating the transport of momentum and passive scalar quantities in turbulent flows is described. Of the unknown terms that appear in the Reynolds stress and scalar flux balance equations, it is those which involve the fluctuating pressure that exert a dominant influence in the majority of turbulent flows. A closure approximation (linear in the Reynolds stress) has been formulated for the velocity‐pressure gradient correlation appearing in the Reynolds stress equation. When this is used in conjunction with previous proposals for the other unknown terms in the stress equation, the proposed model closely simulates most of the data on high Reynolds number homogeneous turbulent flows. For the fluctuating scalar‐pressure gradient correlation appearing in the scalar flux equation, an approximation has been devised that satisfies the linear transformation properties of the exact equation. Additional characteristics of the fluctuating scalar field are obtained from the solution of modeled balance equations for the scalar variance and its ‘‘dissipation’’ rate. The resulting complete scalar field model is capable of reproducing measured data in decaying scalar grid turbulence and strongly sheared, nearly homogeneous flow in the presence of a mean scalar gradient. In addition, applications to the thermal mixing layer developing downstream from a partially heated grid and to a slightly heated plane jet issuing into stagnant surrounds result in calculated profiles in close agreement with those measured.

Oscillations of drops in zero gravity with weak viscous effects

Abstract: Nonlinear oscillations and other motions of large axially symmetric liquid drops in zero gravity are studied numerically by a boundary-integral method. The effect of small viscosity is included in the computations by retaining first-order viscous terms in the normal stress boundary condition. This is accomplished by making use of a partial solution of the boundary-layer equations which describe the weak vortical surface layer. Small viscosity is found to have a relatively large effect on resonant mode coupling phenomena.

High-Resolution Numerical Experiments for Forced Two-Dimensional Turbulence

Abstract: Forced two-dimensional turbulence is simulated by high-resolution (5122) numerical integrations of the Navier-Stokes equations. Small-scale behaviour differs significantly from the one previously observed at lower resolutions. Coherent structures are observed at the injection scale with spontaneous formation of dipolar and tripolar structures here analysed for the first time.

Observations of the frequencies in a sphere wake and of drag increase by acoustic excitation

Abstract: Vortex shedding and instability wave frequencies have been measured in the wakes of spheres in the Reynolds number range 500