L. Fulachier

A DESCRIPTION OF THE ORGANIZED MOTION IN THE TURBULENT FAR WAKE OF A CYLINDER AT LOW REYNOLDS NUMBER

The topology of the organized motion has been obtained in the slightly heated self-preserving far wake of a circular cylinder at a Reynolds number, based on the cylinder diameter, of about 1200. In a frame of reference moving with the organized motion, the toplogy in the plane of main shear reduces to a succession of centres and saddles, located at about the wake half-width. Centres are identifiable by large values of spanwise vorticity associated with the coherent large-scale motion. Saddles occur at the intersection of converging and diverging separatrices, the latter being identifiable with the high strain rate due to the large-scale motion. Large values of the longitudinal turbulence intensity associated with the smaller-scale motion occur at the centres. High values of the normal and shear stresses, the temperature variance and heat fluxes associated with the large-scale motion occur on either side of each saddle point along the direction of the diverging separatrix. Contours for the production of energy and temperature variance associated with the small-scale motion are aligned along the diverging separatrices, and have maxima near the saddle point. Contours for one component of the dissipation of small-scale temperature variance also have a high concentration along the diverging separatrix. Flow visualizations in the far wake suggest the existence of groups of three-dimensional bulges which are made up of clusters of vortex loops.

Topology of a turbulent boundary layer with and without wall suction

Measurements of velocity and temperature fluctuations are made in a turbulent boundary layer with nominally zero pressure gradient for two different slightly heated wall conditions: impermeable and porous surfaces. The temperature fluctuations are measured at three points in the flow to permit the identification of two spatially coherent events: coolings and heatings. Conditional velocity vectors in the plane of mean shear are viewed in a reference frame which translates at a constant velocity. Conditioning is on coolings, heatings or a combination of these events. Sectional streamlines, derived from the velocity vector data, show a succession of critical points: saddles and unstable foci. Coolings are aligned with diverging separatrices through the saddles whereas heatings are identified with the foci. Coolings are associated with a large strain rate and also a large spanwise vorticity: this result seems consistent with the presence of hairpin vortices which extend to different distances from the wall. In contrast, the strain rate and spanwise vorticity are small at the foci. The stabilising influence of suction is observed in the topology of the organised motion and in the contribution from this motion to the conventional stresses, temperature variance and heat fluxes.

Correlation between the longitudinal velocity fluctuation and temperature fluctuation in the near-wall region of a turbulent boundary layer

Abstract Measurements of the longitudinal velocity fluctuation u and of the temperature fluctuation θ in a turbulent boundary layer indicate a strong correlation between u and θ in the immediate vicinity of the wall, the absolute value of the correlation coefficient approaching unity at the wall. The importance of low-speed or high-temperature streaks is examined and quantified by considering joint probability and spectral density functions of u and θ.

Spectral analogy between temperature and velocity fluctuations in several turbulent flows

Abstract The analogy between the spectral distributions of the temperature variance and the turbulent kinetic energy, established by Fulachier and Dumas in the case of a turbulent boundary layer with zero pressure gradient over a uniformly slightly heated surface, is tested in different turbulent flows. These flows include a boundary layer subjected to the sudden application of wall suction, a moderately unstable boundary layer over a rough wall, the atmospheric surface layer at very high Reynolds numbers and with different stability conditions, a plane jet, a plane wake and nearly homogeneous turbulence with uniform mean velocity and mean temperature gradients. The analogy works well except in the atmospheric surface layer when conditions become increasingly stable. In the case of natural convection and supersonic boundary layer flows, the information on the velocity field is incomplete but, the available results do not invalidate the analogy.

Turbulent Prandtl number and spectral characteristics of a turbulent mixing layer

Abstract Measurements have been made of all three velocity fluctuations and of the temperature fluctuations in a thermal mixing layer associated with a turbulent plane jet. In a region of the flow for which the Reynolds stresses and heat fluxes are large, the turbulent Prandtl number is equal to about 0.4. The small magnitude of the turbulent Prandtl number in the present and other mixing layer investigations seems to reflect the relatively strong coherence of the flow. Spectra and cross spectra of velocity and temperature fluctuations exhibit a pronounced peak at the average frequency of the coherent motion. A close similarity is noted between the spectrum of the lateral velocity fluctuation and the temperature spectrum.

Average wavelength of organised structures in the turbulent far wake of a cylinder

The average wavelength of organised structures in the far wake of a circular cylinder is inferred from several different estimates based primarily on wind tunnel measurements. Spectra of the lateral velocity fluctuation and cross-spectra between this fluctuation and the temperature fluctuation, at either the same point or at a different point in space, provide relatively unambiguous estimates of the average wavelength of the structures. Dye photographs in a water tunnel provide a less accurate estimate of the average wavelength of the structures. However, all estimates indicate that the average wavelength increases with streamwise distance, at a rate consistent with the self-preserving growth of the wake.

Effect of wall suction on bursting in a turbulent boundary layer

The effect of suction on the wall region of a turbulent boundary layer over a slightly heated wall has been quantified in terms of several aspects of the motion that are related to bursts and sweeps. These events are detected by the modified u‐level method (with alignment on the ends of bursts), the uv‐quadrant 2 method, and the uv‐quadrant 4 method. The mean periods of bursts and sweeps are increased by suction. The regions upstream from u‐level detected bursts are more coherent than the bursts themselves. Suction substantially increases the relative contributions from the organized motion to momentum and heat fluxes, ∼(uv), ∼(uθ), and ∼(vθ), and has a lesser effect on contributions to ∼(u2), ∼(v2), and ∼(θ2).

Spectral relationships between velocity and temperature fluctuations in turbulent shear flows

The frequency dependence of a turbulent Prandtl number, defined using the Reynolds shear stress and normal heat flux co‐spectra, in various turbulent shear flows accentuates the inadequacy of the Reynolds analogy from a spectral point of view. For the same flows, the analogy between spectral distributions of the kinetic energy and the temperature variance is validated over a significant frequency domain. This analogy suggests a spectral parameter which is very close to unity in this frequency range for all the flows considered.

Normalization for a turbulent boundary layer with wall suction

When a moderate suction rate is applied at the wall of a turbulent boundary layer, the normalized distributions of the Reynolds stresses, temperature variance, and heat fluxes in the inner region are analogous to those obtained without suction, provided the normalization is based on local maxima of the Reynolds shear stress and turbulent heat flux instead of the wall shear stress and the wall heat flux.

Turbulent Reynolds and Péclet numbers re-defined

Abstract It is suggested that the use of the fluctuating velocity vector u i may yield a more meaningful comparison between turbulent Reynolds and Peclet numbers.