Stavros Tavoularis

Experiments in nearly homogenous turbulent shear flow with a uniform mean temperature gradient. Part 1

A reasonably uniform mean temperature gradient has been superimposed upon a nearly homogeneous turbulent shear flow in a wind tunnel. The overheat is small enough to have negligible effect on the turbulence. Away from the wind-tunnel entrance, the transverse statistical homogeneity is good and the temperature fluctuations and their integral scales grow monotonically like the corresponding velocity fluctuations (Harris, Graham & Corrsin 1977). Measurements of several moments, one- and two-point correlation functions, spectra, integral scales, microscales, probability densities, and joint probability densities of the turbulent velocities, temperature fluctuations, and temperature-velocity products are reported. The heat-transport characteristics are much like those of momentum transport, with the turbulent Prandtl number nearly 1. The temperature fluctuation is better correlated with the streamwise than the transverse velocity component, and the cross-component D 12 of the turbulent diffusivity tensor has sign opposite to and about twice the magnitude of the diagonal component D 22 . Some resemblance of directional properties (relative magnitudes of correlation functions, integral scales, microscales) of the temperature with those of the streamwise velocity is also observed. Comparisons of the present data with measurements in the inner part of a heated boundary layer and a fully turbulent pipe flow ( x 2 / d = 0·25) show comparable magnitudes of temperature-velocity correlation coefficients, turbulent Prandtl numbers and ratios of turbulent diffusivities, and show similar shapes of two-point correlation functions.

Further experiments on the evolution of turbulent stresses and scales in uniformly sheared turbulence

Measurements of the Reynolds stresses, integral lengthscales and Taylor microscales are reported for several cases of uniformly sheared turbulent flows with shear values in a range substantially wider than those of previous measurements. It is shown that such flows demonstrate a self-preserving structure, in which the dimensionless Reynolds stress ratios and the dissipation over production ratio, e/ P , remain essentially constant. Flows with sufficiently large

Temperature fluctuations and scales in grid-generated turbulence

k_{\rm s} = (1/\overline{U_{\rm c}}){\rm d}\overline{U_1}dx_2

Velocity-derivative skewness in small Reynolds number, nearly isotropic turbulence

have exponentially growing stresses and e/ P ≈ 0.68; a linear relationship between the coefficient in the exponentiallaw and k s is shown to be compatible with measurements having k s > 3. The possibility of a self-preserving structure with asymptotically constant stresses and e/ P ≈ 1.0 is also compatible with measurements, corresponding to flows with small values of k s . The integral lengthscales appear to grow according to a power law with an exponent of about 0.8, independent of the mean shear, while the Taylor microscales, in general, approach constant values. Various attempts to scale the stresses and to predict their evolution are discussed and the applicability of Hasens theory is scrutinized. Finally, an ‘exact’ expression for the pressure-strain rate covariance is derived and compared to some popular models.

Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient. Part 2. The fine structure

To study the mixing of a passive scalar in nearly isotropic turbulence, experiments have been made in isotropically mixed thermal fields with thermal mesh size M θ ( a ) equal to the momentum mesh size M , ( b ) larger than M (obtained by heating only alternate rods of the turbulence generating grid), and ( c ) smaller than M . This last condition was achieved by inserting a fine heating screen with M θ M , at locations downstream of the turbulence grid. The heating screen was designed to produce negligible statistical change in the velocity field a short distance downstream. In all the heated grid experiments, for a given initial configuration of the thermal field, the intensity of temperature fluctuations θ normalized by the mean temperature rise Δ T , and the decay rate of

The structure of turbulent flow in a rectangular channel containing a cylindrical rod – Part 2: phase-averaged measurements

\overline{\theta^2}

Asymptotic laws for transversely homogeneous turbulent shear flows

were both independent of the temperature of the grid. The principal effect of having M θ > M was an increase in the relative intensity of temperature fluctuations compared with the M θ = M case, and a marginal increase in their decay rate; contrary to expectation, the ratio R of temperature to velocity integral scales in the region of approximate homogeneity did not differ from that corresponding to M θ = M . In heated screen experiments, the relative decay rate was independent of M θ / M and Δ T . For the three locations of the heating screen used in these experiments, the decay rate was also independent of the relative distance x s of the heating screen from the turbulence generating grid; however, larger x s was associated with larger relative intensity of fluctuations. To a first approximation, the ratio R approached unity according to the empirical relation R = 1 − A exp [− α x θ /( UT 0 )], where x θ is downstream distance measured from the heating screen, and T 0 is a characteristic turbulence decay time scale at x 0 = 0. It was also verified that the skewness of the streamwise temperature derivative is approximately zero sufficiently downstream of the heating screen. Where the present study overlaps with previous measurements, an extensive comparison reveals several points of agreement as well as departure.

Measurements of the velocity field of a wing-tip vortex, wandering in grid turbulence

Previous measurements in the moderate to small Reynolds number range of isotropic turbulence have all shown the skewness factor

Reynolds number effects on the fine structure of uniformly sheared turbulence

S\equiv -{\overline{(\partial u/\partial x)^3}}/[\overline{(\partial u/\partial x)^2}]^{\frac{3}{2}}

Measurements of heat diffusion from a continuous line source in a uniformly sheared turbulent flow

of the streamwise velocity derivative to increase with decreasing Reynolds number. This ‘paradoxical’ trend was found for 150 ≥ R λ ≥ 4. New data covering the range 4 ≥ R λ ≥ 1 show a maximum S for R λ between 4 and 3 and a rapid decrease for R λ