The structure of the intense-vorticity regions is studied in numerically simulated homogeneous, isotropic, equilibrium turbulent flow fields at four different Reynolds numbers, in the range Re, = 35-170. In accordance with previous investigators this vorticity is found to be organized in coherent, cylindrical or ribbon-like, vortices ('worms'). A statistical study suggests that they are simply especially intense features of the background, O(o'), vorticity. Their radii scale with the Kolmogorov microscale and their lengths with the integral scale of the flow. An interesting observation is that the Reynolds number y/v, based on the circulation of the intense vortices, increases monotonically with ReA, raising the question of the stability of the structures in the limit of Re,-z co. Conversely, the average rate of stretching of these vortices increases only slowly with their peak vorticity, suggesting that self-stretching is not important in their evolution. One-and two-dimensional statistics of vorticity and strain are presented; they are non-Gaussian and the behaviour of their tails depends strongly on the Reynolds number. There is no evidence of convergence to a limiting distribution in this range of Re,, even though the energy spectra and the energy dissipation rate show good asymptotic properties in the higher-Reynolds-number cases. Evidence is presented to show that worms are natural features of the flow and that they do not depend on the particular forcing scheme.

A direct numerical simulation of a supersonic turbulent boundary layer has been performed. We take advantage of a technique developed by Spalart for incompressible flow. In this technique, it is assumed that the boundary layer grows so slowly in the streamwise direction that the turbulence can be treated as approximately homogeneous in this direction. The slow growth is accounted for by a coordinate transformation and a multiple-scale analysis. The result is a modified system of equations, in which the flow is homogeneous in both the streamwise and spanwise directions, and which represents the state of the boundary layer at a given streamwise location. The equations are solved using a mixed Fourier and B-spline Galerkin method.Results are presented for a case having an adiabatic wall, a Mach number of M = 2.5, and a Reynolds number, based on momentum integral thickness and wall viscosity, of Reθ′ = 849. The Reynolds number based on momentum integral thickness and free-stream viscosity is Reθ = 1577. The results indicate that the Van Driest transformed velocity satisfies the incompressible scalings and a small logarithmic region is obtained. Both turbulence intensities and the Reynolds shear stress compare well with the incompressible simulations of Spalart when scaled by mean density. Pressure fluctuations are higher than in incompressible flow. Morkovin's prediction that streamwise velocity and temperature fluctuations should be anti-correlated, which happens to be supported by compressible experiments, does not hold in the simulation. Instead, a relationship is found between the rates of turbulent heat and momentum transfer. The turbulent kinetic energy budget is computed and compared with the budgets from Spalart's incompressible simulations.

The variational multiscale method is applied to the large eddy simulation ͑LES͒ of homogeneous, isotropic flows and compared with the classical Smagorinsky model, the dynamic Smagorinsky model, and direct numerical simulation ͑DNS͒ data. Overall, the multiscale method is in better agreement with the DNS data than both the Smagorinsky model and the dynamic Smagorinsky model. The results are somewhat remarkable when one realizes that the multiscale method is almost identical to the Smagorinsky model ͑the least accurate model!͒ except for removal of the eddy viscosity from a very small percentage of the lowest modes.

The statistical properties of the strong coherent vortices observed in numerical simulations of isotropic turbulence are studied. When compiled at axial vorticity levels ω/ω′∼Re1/2λ, where ω′ is the r.m.s. vorticity magnitude for the flow as a whole, they have radii of the order of the Kolmogorov scale and internal velocity differences of the order of the r.m.s. velocity of the flow u′. Theoretical arguments are given to explain these scalings. It is shown that the filaments are inhomogeneous Burgers' vortices driven by an axial stretching which behaves like the strain fluctuations of the background flow. It is suggested that they are the strongest members in a class of coherent objects, the weakest of which have radii of the order of the Taylor microscale, and indirect evidence is presented that they are unstable. A model is proposed in which this instability leads to a cascade of coherent filaments whose radii are below the dissipative scale of the flow as a whole. A family of such cascades separates the self-similar inertial range from the dissipative limit. At the vorticity level given above, the filaments occupy a volume fraction which scales as Re−2λ, and their total length increases as O(Reλ). The length of individual filaments scales as the integral length of the flow, but there is a shorter internal length of the order of the Taylor microscale.

Energy transfers and spectral eddy viscosity in large-eddy simulations of homogeneous isotropic turbulence: Comparison of dynamic Smagorinsky and multiscale models over a range of discretizations Large-eddy simulation ͑LES͒ with regular explicit filtering is investigated. The filtered-scale stress due to the explicit filtering is here partially reconstructed using the tensor-diffusivity model: It provides for backscatter along the stretching direction͑s͒, and for global dissipation, both also attributes of the exact filtered-scale stress. The necessary LES truncations ͑grid and numerical method͒ are responsible for an additional subgrid-scale stress. A natural mixed model is then the tensor-diffusivity model supplemented by a dynamic Smagorinsky term. This model is reviewed, together with useful connections to other models, and is tested against direct numerical simulation ͑DNS͒ of turbulent isotropic decay starting with Re ϭ90 ͑thus moderate Reynolds number͒: LES started from a 256 3 DNS truncated to 64 3 and Gaussian filtered. The tensor-diffusivity part is first tested alone; the mixed model is tested next. Diagnostics include energy decay, enstrophy decay, and energy spectra. After an initial transient of the dynamic procedure ͑observed with all models͒, the mixed model is found to produce good results. However, despite expectations based on favorable a priori tests, the results are similar to those obtained when using the dynamic Smagorinsky model alone in LES without explicit filtering. Nevertheless, the dynamic mixed model appears as a good compromise between partial reconstruction of the filtered-scale stress and modeling of the truncations effects ͑incomplete reconstruction and subgrid-scale effects͒. More challenging 48 3 LES are also done: Again, the results of both approaches are found to be similar. The dynamic mixed model is also tested on the turbulent channel flow at Re ϭ395. The tensor-diffusivity part must be damped close to the wall in order to avoid instabilities. Diagnostics are mean profiles of velocity, stress, dissipation, and reconstructed Reynolds stresses. The velocity profile obtained using the damped dynamic mixed model is slightly better than that obtained using the dynamic Smagorinsky model without explicit filtering. The damping used so far is however crude, and this calls for further work.