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Detailed computations were made of energy transfer among the scales of motion in incompressible turbulent fields at low Reynolds numbers generated by direct numerical simulations. It was observed that although the transfer resulted from triad interactions that were nonlocal in k space, the energy always transferred locally. The energy transfer calculated from the eddy-damped quasinormal Markovian (EDQNM) theory of turbulence at low Reynolds numbers is in excellent agreement with the results of the numerical simulations. At high Reynolds numbers the EDQNM theory predicts the same transfer mechanism in the inertial range that is observed at low Reynolds numbers, i.e., predominantly local transfer caused by nonlocal triads. The weaker, nonlocal energy transfer is from large to small scales at high Reynolds numbers and from small to large scales at low Reynolds numbers.

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Solving Navier-Stokes equations using monotone algorithms often produces results that are consistent with the dynamics of high Reynolds number turbulence despite formally insufficient numerical resolution to capture all physically relevant scales of motion. It is frequently argued that the truncation error of a numerical scheme provides a mechanism for the energy dissipation and serves as an implicit subgrid scale model. Such an approach to turbulence modeling, known loosely as the Monotonically Integrated LES (MILES), was originally proposed by Boris et al. (1992) and reviewed recently by Grinstein and Fureby (2002). The primary effect of a numerical discretization in MILES, which is similar to the effects of explicit SGS models, is the dissipation of turbulent kinetic energy. Despite its importance, very little is known about details of numerical dissipation in MILES methods and, more importantly, its relation (or lack of it) to the actual dissipative effects of turbulence. We describe a method for computing effective numerical eddy viscosity, useful for assessing numerical dissipation of such approaches. The method is evaluated on an example of a specific nonoscillatory finite volume scheme MPDATA developed for simulations of geophysical flows. A series of numerical simulations of homogeneous, isotropic turbulence are performed and the numerical eddy viscosities are determined. The detailed quantitative comparisons are made between the numerical eddy viscosities and the theoretical eddy viscosity as well as intrinsic eddy viscosities computed exactly from the velocity fields by introducing artificial wave number cutoffs. A typical example of such a comparison is shown in the enclosed figure.

The mean velocity profile scaling and the vorticity structure of a stably stratified, initially turbulent wake of a towed sphere are studied numerically using a high-accuracy spectral multi-domain penalty method model. A detailed initialization procedure allows a smooth, minimum-transient transition into the non-equilibrium (NEQ) regime of wake evolution. A broad range of Reynolds numbers,Re= UD/ν ∈ [5 × 103, 105] and internal Froude numbers,Fr= 2U/(ND) ∈ [4, 64] (U,Dare characteristic velocity and length scales, andNis the buoyancy frequency) is examined. The maximum value ofReand the range ofFrvalues considered allow extrapolation of the results to geophysical and naval applications.At higherRe, the NEQ regime, where three-dimensional turbulence adjusts towards a quasi-two-dimensional, buoyancy-dominated flow, lasts significantly longer than at lowerRe. AtRe= 5 × 103, vertical fluid motions are rapidly suppressed, but atRe= 105, secondary Kelvin–Helmholtz instabilities and ensuing turbulence are clearly observed up toNt≈ 100. The secondary motions intensify with increasing stratification strength and have significant vertical kinetic energy.These results agree with existing scaling of buoyancy-driven shear onRe/Fr2and suggest that, in the field, the NEQ regime may last up toNt≈ 1000. At a given highRevalue, during the NEQ regime, the scale separation between Ozmidov and Kolmogorov scale is independent ofFr. This first systematic numerical investigation of stratified turbulence (as defined by Lilly,J. Atmos. Sci.vol. 40, 1983, p. 749), in a controlled localized flow with turbulent initial conditions suggests that a reconsideration of the commonly perceived life cycle of a stratified turbulent event may be in order for the correct turbulence parametrizations of such flows in both geophysical and operational contexts.