Results from full numerical simulations of the Navier–Stokes equations for three-dimensional, stationary, and isotropic turbulence are used (1) to study the scaling properties of two-time modal velocity correlations and (2) to determine the dominant process in the decorrelation of the small-scale velocities. The main results obtained are (1) that the convective sweeping of the small scales by the energy-containing large scales determines the scaling property of the inertial- and near-dissipation ranges and (2) that the sweeping effect is dominant in the decorrelation of the small scales. Reynolds-number dependence of the decorrelation is also considered.

Helicity production in a homogeneous fluid is numerically demonstrated by using steady and unsteady forced Navier-Stokes equations: Even if all Fourier components of the force do not have helicity, nonlinear interactions of the zero-helicity components can generate helicity in the flow. When the Reynolds number increases, the flow nature changes from steady to temporally periodic to chaotic. The produced helicity has the largest time-averaged value in the periodic motion.

Recently, Smith and Reynolds [Phys. Fluids A 3, 992 (1991)] suggested that the turbulent energy spectrum with exponential decaying form E(k)=CKε2/3k−5/3 exp(−σk) (CK is Kolmogorov constant, ε is the energy dissipation rate, and σ is some constant) may be a poor model, because it does not give velocity derivative skewness in good agreement with experimental value. On the other hand, some direct numerical simulations of the Navier–Stokes equation demonstrate the above exponential form in the dissipation range. This disagreement is resolved by considering a model spectrum based on direct numerical simulation.

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