No abstract

Measurements are presented of the velocity structure function on the axis of a turbulent jet at Reynolds numbers Rλ ≤ 852 and in a turbulent duct flow at Rλ = 515. Moments of the structure function up to the eighteenth order were calculated, primarily with a view to establish accurately the dependence on the order of the inertial range power-law exponent and to draw conclusions about the distribution of energy transfer in the inertial range. Adequate definition of the probability density of the structure function was achieved only for moments of order n ≤ 10. It is shown, however, that, although the values of moments of n > 10 diverges from their true values, the dependence of the moment of the structure function on the separation r is still given to a fair accuracy for moments up to n ≈ 18. The results demonstrate that the inertial-range power-law exponent is closely approximated by a quadratic dependence on the power which for lower-order moments (n [lsim ] 12) would be consistent with a lognormal distribution. Higher-order moments diverge, however, from a lognormal distribution, which gives weight to Mandelbrot's (1971) conjecture that ‘Kolmogorov's third hypothesis’ is untenable in the strict sense. The intermittency parameter μ, appearing in the power-law exponent, has been determined from sixth-order moments 〈(δμ)6〉 ∼ r2−μ to be μ = 0.2 ± 0.05. This value coincides with that determined from non-centred dissipation correlations measured in identical conditions.

The turbulence generated by a vertically oscillating grid in a water tank and the entrainment across a salinity interface caused by this turbulence have been investigated experimentally. Measurements were carried out in a homogeneous layer of fluid as well as a two-layered fluid, which permitted us to determine the decay law of this turbulence and the way in which the structure of the turbulence depends on the mesh size and on the frequency and amplitude of the grid oscillation. It was found that the turbulent kinetic energy decays with distance from the grid according to a power law$\overline{q^2}\propto z^{-n}$, withnclose to 2, and that the turbulent Reynolds number remains approximately constant during decay. The linear dependence of the r.m.s. turbulent velocity on the grid oscillation frequency found by Thompson & Turner (1975) in the case of a square-bar grid has been confirmed. It is shown here that this linear relation remains valid when an interface is present and consequently the dependence of the entrainment velocity on the local Richardson number is of the form$u_e/u \propto Ri^{-\frac{3}{2}}$, the Péclet number being high. While the bearing of these results on the problem of the thermocline or an inversion is clear we wish to emphasize that the spatial decay of turbulence is interesting in itself.