High Reynolds Number Case Research Articles

Dynamic structures of a submerged jet interacting with a free surface

The spatial structures of a submerged jet interacting with a free surface were examined experimentally. The time-resolved PIV technique was used for the quantitative measurements. Two Reynolds numbers (1920, 3480) were examined for a configuration, in which the depth of the jet beneath the free surface was fixed to H=2D. The dynamics of the flow structures were examined further using the space–time proper orthogonal decomposition (POD) analysis technique. Some common characteristics were found in both jet flows, which are believed to be the general features of the free-surface jet flows. On the other hand, the dynamic characteristics of the large-scale turbulent motions differed significantly with respect to the Reynolds number. In the low Reynolds number case, three dominant dynamic structures were found: flapping motion of the jet, very large scale vortical structure interacting with the free surface at the right side, and the transverse stretching of large scale structure due to the presence of free surface. The reconstructed fluctuating velocity fields and the swirling strength contours demonstrated that the very large scale structures began to move downward at about 10D downstream the initial interaction. In the high Reynolds number case, the first two dominant spatial modes showed the momentum exchange process between the jet flow and the free surface. The third mode displayed a vortex just below the free surface at the left side and the fourth mode showed the elongated vortex structures. The scale of vortical structures was much smaller in the high Reynolds number case than that in the low Reynolds case, and the downward motion of large scale structures was not found in the high Reynolds number case.

A DNS evaluation of mixing models for transported PDF modelling of turbulent nonpremixed flames

Transported probability density function (TPDF) methods are well suited to modelling turbulent, reacting, variable density flows. One of the main challenges to the successful deployment of TPDF methods is accurately modelling the unclosed molecular mixing term. This study examines three of the most widely used mixing models: the Interaction by Exchange with the Mean (IEM), Modified Curl (MC) and Euclidean Minimum Spanning Tree (EMST) models. Direct numerical simulation (DNS) data-sets were used to provide both initial conditions and inputs needed over the course of the runs, including the mean flow velocities, mixing frequency, and the turbulent diffusion coefficient. The same chemical mechanism and thermodynamic properties were used, allowing the study to focus on the mixing model. The simulation scenario was a one-dimensional, nonpremixed, turbulent jet flame burning either a syngas or ethylene fuel stream that featured extinction and reignition. This test scenario was selected because extinction and reignition phenomena are sensitive to the mixing model. Three DNS cases were considered for both the syngas and ethylene cases with a parametric variation of Reynolds and Damköhler numbers, respectively. Extinction events became more prevalent with increasing Reynolds number in the syngas cases and with decreasing Damköhler number in the ethylene cases. The model was first tested with the mixing frequency defined from the dissipation rate and variance of mixture fraction. With this definition, for the syngas cases this study finds that the TPDF method is successful at predicting flame extinction and reignition using all three mixing models for the relatively lower and intermediate Reynolds number cases, but that all models under-predict reignition in the relatively higher Reynolds number case. In the ethylene fuelled cases, only the EMST mixing model correctly predicts the reignition event for the two higher Damköhler number cases, however, in the lowest Damköhler number case the EMST model over-predicts reignition and the IEM and MC models under-predict it. Mixing frequency was then modelled based on the turbulence frequency and a model constant Cϕ, the ratio of scalar to mechanical mixing rates. The DNS cases were reexamined with this definition and the results suggested that the optimal value for Cϕ is mixing model and case dependent. In particular, it was found in the ethylene case considered that reignition could be achieved with the IEM and MC models by adjusting the value of Cϕ.

Large-eddy simulation of pulsed high-speed subsonic jets in a turbulent crossflow

The jet in crossflow problem has been extensively studied, mainly because of its application to film cooling and injector design. It has been established that in low-speed flow, pulsing the jet significantly enhances mixing and jet penetration. This work investigates the effects of pulsing of high-speed subsonic jets (Ma∼0.47−0.77) on mixing and jet trajectory in turbulent subsonic crossflows by using large-eddy simulation. Jets with different density and momentum ratios are pulsed from an injector into a crossflow for a range of Strouhal numbers. Results are compared with the earlier low-speed cases to determine the sensitivity of jet penetration scaling on the relatively high Reynolds and Mach numbers of the current pulsed jets. It is shown that the classical momentum-ratio-based scaling (which reduces to the velocity ratio scaling in equal density low-speed case) can still be used for these high Reynolds and jet Mach number cases, although the scaling constant is slightly different. However, when the jet momentum ratio is different for the same Strouhal, Reynolds and Mach numbers, there is a significant change in the scaling constant, suggesting a sensitivity that could impact the original scaling relationship itself.

Validation of a CFD model of Taylor flow hydrodynamics and heat transfer

The growing importance of the Taylor flow regime in microchannel flow and heat transfer has led to the need for validated CFD models. Experimental data for Taylor flow of water/nitrogen and ethylene glycol/nitrogen in a 2 mm diameter channel having Reynolds numbers in the range 22–1189 and Capillary number of 0.003–0.160 are used to validate a CFD model developed in ANSYS Fluent. The model simulates two-dimensional, periodic flow and heat transfer in a unit cell (comprising a single bubble and its adjacent half slugs) in a frame of reference moving with the bubble. The simulation results show excellent agreement with the bubble shape, film thickness, bubble velocity and homogeneous void fraction. The above data and the pressure drop data are compared with the available correlations and are shown to agree well, linking the experimental data, CFD results and established correlations in one validation exercise. Heat transfer simulations also reproduce the data well with a maximum difference of 15% except for high Reynolds number cases ( Re TP ≥951). It is shown that in this case the assumption of two-dimensional, axisymmetric flow is no longer valid.

A modified blade element theory for estimation of forces generated by a beetle-mimicking flapping wing system

We present an unsteady blade element theory (BET) model to estimate the aerodynamic forces produced by a freely flying beetle and a beetle-mimicking flapping wing system. Added mass and rotational forces are included to accommodate the unsteady force. In addition to the aerodynamic forces needed to accurately estimate the time history of the forces, the inertial forces of the wings are also calculated. All of the force components are considered based on the full three-dimensional (3D) motion of the wing. The result obtained by the present BET model is validated with the data which were presented in a reference paper. The difference between the averages of the estimated forces (lift and drag) and the measured forces in the reference is about 5.7%. The BET model is also used to estimate the force produced by a freely flying beetle and a beetle-mimicking flapping wing system. The wing kinematics used in the BET calculation of a real beetle and the flapping wing system are captured using high-speed cameras. The results show that the average estimated vertical force of the beetle is reasonably close to the weight of the beetle, and the average estimated thrust of the beetle-mimicking flapping wing system is in good agreement with the measured value. Our results show that the unsteady lift and drag coefficients measured by Dickinson et al are still useful for relatively higher Reynolds number cases, and the proposed BET can be a good way to estimate the force produced by a flapping wing system.

Characteristics of vortex formation and thrust performance in drag-based paddling propulsion

Several characteristics of drag-based paddling propulsion are studied with a simple mechanical model and a measurement technique for mapping three-dimensional flow fields. In drag-based propulsion, the temporal change of the vortex strength is an important parameter in the relationship between vortex formation and thrust generation. Our results indicate that spanwise flow behind the paddling propulsor significantly affects tip vortex development and thrust generation. The distribution of spanwise flow is dependent on the propulsor shape and the Reynolds number. A delta-shaped propulsor generates strong spanwise flow compared with a rectangular propulsor. For the low Reynolds number case, spanwise flow is not as strong as that for the high Reynolds number case. Without sacrificing total impulse, the flexible propulsor can smooth out thrust peaks during sudden stroke motions, which is favorable for avoiding structural failures and stabilizing body motion. We also explored the role of stopping vortex shedding in efficient thrust generation by determining the relationship between stroke angles and total impulses generated by paddling propulsors.

Hybrid RANS/LES of flow and heat transfer in round impinging jets

Fluid flow and convective heat transfer predictions are presented of round impinging jets for several combinations of nozzle–plate distances H/ D = 2, 6 and 13.5 (where D is the nozzle diameter) and Reynolds numbers Re = 5000, 23,000 and 70,000 with the newest version of the k– ω model of Wilcox (2008) and three hybrid RANS/LES models. In the RANS mode of the hybrid RANS/LES models, the k– ω model is recovered. Three formulations are considered to activate the LES mode. The first model is similar to the hybrid models of Davidson and Peng (2003) and Kok et al. (2004). The turbulent length scale is replaced by the grid size in the destruction term of the k-equation and in the definition of the RANS eddy viscosity. As grid size, a maximum measure of the hexahedral grid cell is used. The second model has the same k-equation, but the eddy viscosity is the minimum of the k– ω eddy viscosity and the Smagorinsky eddy viscosity, following a proposal by Batten et al. (2004). The Smagorinsky eddy viscosity is formed with the cube root of the cell volume. The third model has, again, the same k-equation, but has an eddy viscosity which is an intermediate between the eddy viscosities of the first and second models. This is reached by using the cube root of the cell volume in the eddy viscosity formula of the first model. The simulation results are compared with experimental data for the high Reynolds number cases Re = 23,000 and Re = 70,000 and LES data for the low-Reynolds number case Re = 5000. The Reynolds numbers are defined with the nozzle diameter and the bulk velocity at nozzle outlet. At low nozzle–plate distance (the impingement plate is in the core of the jet), turbulent kinetic energy is overpredicted by RANS in the stagnation flow region. This leads to overprediction of the heat transfer rate along the impingement plate in the impact zone. At high nozzle–plate distance (the impingement plate is in the mixed-out region of the jet), the turbulence mixing is underpredicted by RANS in the shear layer of the jet which gives a too high length of the jet core. This also results in overprediction of the heat transfer rate in the impingement zone caused by too big temperature gradients at impingement. All hybrid RANS/LES models are able to correct the heat transfer overprediction of the RANS model. For good predictions at low nozzle–plate distance, it is necessary to sufficiently resolve the formation and development of the near-wall vortices in the jet impingement region. At high nozzle–plate distance, the essence is to capture the evolution and breakup of the flow unsteadiness in the shear layer of the jet, so that accurate mean and fluctuating velocity profiles are obtained in the impingement region. Although the models have a quite different theoretical justification and generate a quite different eddy viscosity in some flow regions, their overall results are very comparable. The reason is that in zones that are crucial for the results, the models behave similarly.

Flow Within a Pipe Annulus With Injection and Suction Through a Porous Wall With High Wall Reynolds Numbers

An approximate solution to the Navier–Stokes equations was found for the case describing two-dimensional steady-state laminar flow over an array of porous pipes with high wall Reynolds number. The Navier–Stokes equations in cylindrical coordinates reduced to a fourth-order nonlinear differential equation, which was solved for high wall Reynolds number flows through the porous wall using a zeroth- and first-order singular perturbation method. Our analytic solution for the high wall Reynolds number case is consistent with solutions found from the low Reynolds number case and that found using finite element analysis.

Experimental study of three-dimensional vortex structures in translating and rotating plates

Motivated by the unsteady force generation of flying animals, vortex formation and vorticity transport processes around small aspect-ratio translating and rotating plates with a high angle of attack are investigated. Defocusing Digital Particle Image Velocimetry was employed to explore the structure and dynamics of the vortex generated by the plates. For both translating and rotating cases, we observe the presence of a spanwise flow over the plate and the consequent effect of vorticity transport due to the tilting of the leading-edge vortex. While the spanwise flow is confined inside the leading-edge vortex for the translating case, it is widely present over the plate and the wake region of the rotating case. The distribution of the spanwise flow is a prominent distinction between the vortex structures of these two cases. As the Reynolds number decreases, due to the increase in viscosity, the leading-edge and tip vortices tend to spread inside the area swept by the rotating plate. The different vorticity distributions of the low and high Reynolds number cases are consistent with the difference in measured lift forces, which is confirmed using the vorticity moment theory.

Characteristics of Three-dimensional Vortex Formation and Propulsive Performance in Flapping Locomotion

Three-dimensional vortex formation and propulsive performance were studied experimentally to identify some of the main characteristic mechanisms of flapping locomotion. Mechanical models with thin plates were used to simulate flapping and translating motions of animal propulsors. Three-dimensional flow fields were mapped quantitatively using defocusing digital particle image velocimetry. First, vortex structures made by impulsively translating low aspect-ratio plates were studied. The investigation of translating plates with a 90 degree angle of attack is important since it is a fundamental model for a better understanding of drag-based propulsion systems. Rectangular flat-rigid, flexible, and curved-rigid thin plastic plates with the same aspect ratio were used to compare their vortex structures and hydrodynamic forces. The interaction of the tip flow and the nearby vortex is a critical flow phenomenon to distinguish vortex patterns among these three cases. In the flexible plate case, slow development of the vortex structure causes a small initial peak in hydrodynamic force during the acceleration phase. However, after the initial peak, the flexible plate generates large force magnitude comparable to that of the flat-rigid plate case. Drag-based paddling propulsion was also studied to explain some of the fundamental differences in vortex formation of lift-based and drag-based propulsions. While the temporal change of the inner area enclosed by the vortex loop is an important factor in thrust generation of lift-based propulsion, the temporal change of the vortex strength becomes more important in drag-based propulsion. Spanwise flow behind the paddling plate plays an important role in tip vortex motion and thrust generation. The distribution of spanwise flow depends on the propulsor shape and the Reynolds number. A delta-shaped propulsor generates strong spanwise flow compared to a rectangular propulsor. For the low Reynolds number case, the spanwise flow is not as strong as that of the high Reynolds number case. The flexible propulsor can smooth out force peaks during impulsive motions without sacrificing total impulse, which is advantageous in avoiding structural failures and stabilizing body motion. The role of the stopping vortex was addressed in optimizing a stroke angle of paddling animals. In addition, vortex formation of clapping propulsion was investigated by varying aspect ratio and stroke angle. A low aspect-ratio propulsor produces larger total impulse than a high aspect-ratio propulsor. As the aspect ratio increases, circulation of the vortex is strengthened, and the inner area enclosed by the vortex structure tends to enlarge. Moreover, in terms of thrust, the advantage of a single plate over double clapping plates is larger for the lower aspect-ratio case. These results offer information to better understand the benefit of low aspect-ratio wings in force generation under specific locomotion modes. When a pair of plates claps, a vortex loop forms from two counter-rotating tip vortices by a reconnection process. The dynamics of wake structures are dependent on the aspect ratio and the stroke angle. Vortex formation and vorticity transport processes of translating and rotating plates with a 45 degree angle of attack were investigated as well. In both translating and rotating cases, the spanwise flow over the plate and the vorticity tilting process inside the leading-edge vortex were observed. The distribution of spanwise flow is a prominent distinction between the vortex structures of these two cases. While spanwise flow is confined inside the leading-edge vortex for the translating case, it is widely present over the plate and the wake region of the rotating case. As the Reynolds number decreases, due to the increase in viscosity, leading-edge and tip vortices tend to spread inside the area swept by the rotating plate, which results in lower lift force generation. Lastly, for translating motion, the dynamics of the vortex in corner regions was compared among three different corner shapes. For a large corner angle, the forward movement of the vortex tends to be uniform along the plate edges. However, for a small corner angle, the vortex close to the corner moves forward following the plate while the vortex away from the corner retards its forward movement.

Effects of Centrifugal Buoyancy and Reynolds Number on Turbulent Heat Transfer in a Two‐Pass Angled‐RIB‐Roughened Channel with Sharp 180∘ Turns Investigated by Using Large Eddy Simulation

The effects of the centrifugal buoyancy and the Reynolds number on heat transfer in a rotating two‐pass rib‐roughened channel with 180∘ sharp turns were numerically investigated by using the large eddy simulation. The effect of the Reynolds number was seen in the finer flow structure. The effect of the aiding/opposing buoyancy contributions was seen more vigorously on the pressure surface than that on the suction surface, though the details depended on the Reynolds number, the rotation number, and the existence of the ribs. As the buoyancy increased, the friction factor dominated by the pressure loss of the sharp turn decreased, and the decreasing rate is smaller for the higher rotation speed case. The Colburn′s j factor stayed almost constant irrespective of the rotation speed. As a result, the heat transfer efficiency index slightly increased by the buoyancy, and it became smaller for the higher rotation speed and higher Reynolds number cases.

1601 後流の影響を受ける高負荷低圧タービン翼列流れにおけるLESパラメータ解析(S35-1 圧縮性流れの基礎と応用(1),S35 圧縮性流れの基礎と応用)

Large Eddy Simulation (LES) of high loaded Low Pressure Turbine (LPT) cascade was performed. A comparison is made with an existing experimental data for the same geometry and operating conditions. The purpose of this work is to clarify the effect of incoming wakes on the boundary layer flow It was demonstrated that the computed results were in good agreement with the experimental data The time-averaged separation region showed that the separation. point shifted downstream and the reattachment point shifted upstream with increasing Strouhal number. The mass-averaged loss coefficients for the low Reynolds number case didn't increase monotonically with the Strouhal number, as opposed to the High Reynolds number cases. This result showed a positive trend of the wake passing from the view point of loss control.

Large Eddy Simulation of Homogeneous Isotropic Turbulent Flow Using the Finite Element Method

This paper presents results of validation study of large eddy simulation (LES) that is applied to homogeneous isotropic turbulence in order to assess its spectral accuracy. The LES is performed by using a streamline-upwind finite element method with second order accuracy both in time and space and the results are compared with those from direct numerical simulation (DNS) based on the spectral method. The validation tests are done by using Standard Smagorinsky Model (SSM) and Dynamic Smagorinsky Model (DSM), and include following two cases: a low Reynolds number case and a higher Reynolds number case. In the former case, the Reynolds number is low enough that the computational grid is capable of resolving all the turbulence scales. In this case our interest is in whether any effects of the subgrid scale (SGS) model should appropriately be dampened out. In the latter case, a relatively large Reynolds number is selected where effects of turbulent eddies that are not resolved by the computational grid should be properly taken into account by the SGS model. It is confirmed that DSM performs better than SSM for both cases and it gives good agreement with DNS results in terms of both spatial spectra and decay of the turbulence statistics. Visualization of the computed flow fields by the DSM also reveals existence of distinct, coherent and tube-like vortical structures similar to those found in instantaneous flow fields computed by the DNS.

NEW LATTICE KINETIC SCHEMES FOR INCOMPRESSIBLE VISCOUS FLOWS

A new two-dimensional lattice kinetic scheme on the uniform mesh was recently proposed by Inamuro, based on the standard lattice Boltzmann method (LBM). Compared with the standard LBM, this scheme can easily implement the boundary condition and save computer memory. In order to remove the shortcoming of a relatively large viscosity at a high Reynolds number, a first-order derivative term is introduced in the equilibrium density distribution function. However, the parameter associated with the derivative term is very sensitive and was chosen in a narrow range for a high Reynolds number case. To avoid the use of the derivative term while removing the shortcoming of a relatively large viscosity, new lattice kinetic schemes are proposed in this work following the original lattice kinetic scheme. In these new lattice kinetic schemes, the derivative term is dropped out and the difficulty of the relatively large viscosity is eased by controlling the time step δt or sonic speed cs. To validate these new lattice kinetic schemes, the numerical simulations of the two-dimensional square driven cavity flow at Reynolds numbers from 100 to 1000 are carried out. The results using the new lattice kinetic schemes are compared with the benchmark data.

Heat Transfer Between Blockages With Holes in a Rectangular Channel

Experiments have been conducted to study steady heat transfer between two blockages with holes and pressure drop across the blockages, for turbulent flow in a rectangular channel. Average heat transfer coefficient and local heat transfer distribution on one of the channel walls between two blockages, and overall pressure drop across the blockages were obtained, for nine different staggered arrays of holes in the blockages and Reynolds numbers of 10,000 and 30,000. For the hole configurations studied, the blockages enhanced heat transfer by 4.6 to 8.1 times, but significantly increased the pressure drop. Smaller holes in the blockages caused higher heat transfer enhancement, but larger increase of the pressure drop than larger holes. The heat transfer enhancement was lower in the higher Reynolds number cases. Because of the large pressure drop, the heat transfer per unit pumping power was lower with the blockages than without the blockages. The local heat transfer was lower nearer the upstream blockage, the highest near the downstream blockage, and also relatively high in regions of reattachment of the jets leaving the upstream holes. The local heat transfer distribution was strongly dependent on the configuration of the hole array in the blockages. A third upstream blockage lowered both the heat transfer and the pressure drop, and significantly changed the local heat transfer distribution.

Interaction between particle clusters and particle-induced turbulence

To investigate the two-way interaction between particles and fluid turbulence, a homogeneous flow field including solid particles was numerically simulated. Spherical particles are falling by gravity with the Reynolds number ranging from 50 to 400, based on slip velocity. Particular attention was focused on the clustering of particles, which might enhance turbulence by energy supply through larger scales in comparison with dispersed particles. In the higher Reynolds number case, particle clusters are formed due to the wake, and vortex shedding enhances them. But clusters cause fluid turbulence resulting in their break-up. The Reynolds-number dependence, the dynamics and the time scale of particle clusters are discussed in this paper.

Some Reynolds number effects on two- and three-dimensional turbulent boundary layers

Experimental data for a two-dimensional (2-D) turbulent boundary layer (TBL) flow and a three-dimensional (3-D) pressure-driven TBL flow outside of a wing/body junction were obtained for an approach Reynolds number based on momentum thickness of Re θ =23,200. The wing shape had a 3:2 elliptical nose, NACA 0020 profiled tail, and was mounted on a flat wall. Some Reynolds number effects are examined using fine spatial resolution (Δy+=1.8) three-velocity-component laser-Doppler velocimeter measurements of mean velocities and Reynolds stresses at nine stations for Re θ =23,200 and previously reported data for a much thinner boundary layer at Re θ =5,940 for the same wing shape. In the 3-D boundary layers, while the stress profiles vary considerably along the flow due to deceleration, acceleration, and skewing, profiles of the parameter \(\)\(\) correlate well and over available Reynolds numbers. The measured static pressure variations on the flat wall are similar for the two Reynolds numbers, so the vorticity flux and the measured mean velocities scaled on wall variables agree closely near the wall. The stresses vary similarly for both cases, but with higher values in the outer region of the higher Re θ case. The outer layer turbulence in the thicker high Reynolds number case behaves similarly to a rapid distortion of the flow, since stream-wise vortical effects from the wall have not diffused completely through the boundary layer at all measurement stations.

Three Dimensional Numerical Analysis for Bubbly Flow around a Circular Cylinder.

A numerical method is developed to simulate a bubbly flow around a circular cylinder with a boundary-fitted coordinate system. In this study, the number density model of a bubbly flow is employed, where the equations of conservations and the group motion of bubbles are solved directly, The three-dimensional simulations have been conducted in the laminar flow conditions at the liquid Reynolds number ranging from 100 to 2000. The void fraction profile behind a cylinder agree with that of experiment and another simulation at the liquid Reynolds number of 430. The Strouhal number at the Reynolds number of 200 and 500 is presented. At the lower Reynolds number, the Strouhal number does not change with the variation of the void fraction. On the contrast, the local maximum point of the Strouhal number is observed in the higher Reynolds number case, which is also observed in the experiment. The bubble accumulation in the Karman vortices is observed in the case of the higher relaxation time of a bubble, where such structures have been also observed in the experiment behind a bluff body.

Organized Turbulence Structures in the Near-Neutral Atmospheric Surface Layer

The Tiederman method, which was originally designed for unambiguous detection of “bursts” in the buffer layer of smooth surface laboratory boundary-layer flow, is shown to work equally well in the neutral atmospheric surface layer. It enables estimation of characteristic timescales of significant structures responsible for the momentum transport: mean duration of and mean interval between bursts (upward transport of momentum deficit) and mean duration and interval between sweeps (downward transport of momentum excess). Data representing near neutral conditions from three field experiments over flat and homogeneous areas but with very different roughness characteristics are used in the analysis. For two low vegetation sites (i.e., the measuring heights are very much larger than the roughness sublayer height), it is found that all above-mentioned timescales are constant for any height and identical at the two sites. Scaling the results with the friction velocity indicates the corresponding scaling height to be proportional to the scaling height of the neutral boundary layer. The third site is a forest site, and the measurements were taken in the roughness sublayer. Here canopy inflection scaling is found to apply. The structures identified with the Tiederman method are shown to be responsible for more than 90% of the momentum flux, most of which is accomplished by a mean flow component within the structures. Results are discussed in light of direct numerical simulation results for fully turbulent but low Reynolds number flow over a dynamically smooth surface and large-eddy simulation results for a high Reynolds number case, and these show encouraging consistencies for the logarithmic layer. Turbulence production at the surface is, however, fundamentally different in the rough atmospheric case compared to the smooth case and is presumably governed by canopy wind profile inflection instability.

Decaying two-dimensional turbulence with rigid walls

Decaying two-dimensional Navier-Stokes turbulence (or turbulence for the corresponding electrostatic “guiding center” plasma) has usually been studied in spatially periodic boundary conditions. It is known to exhibit a variety of features which are different from the three-dimensional case. By means of spectral-method direct numerical computation, we show that circular no-slip boundaries can significantly alter the decay scenario in two dimensions. In particular, the wall functions as an important source of vorticity and vorticity gradient, and the decay of energy is enhanced by this effect, relative to the decay in periodic boundary conditions. In addition, the very slow decay of angular momentum in high Reynolds number cases constrains the evolution in a way that has no analogue for rectangular periodic boundary conditions.