D. K. Bisset

Spatial organization of large structures in the turbulent far wake of a cylinder

Using an array of x-probes aligned in the plane of mean shear in the turbulent far wake of a circular cylinder, instantaneous velocity vector patterns are obtained from which stream-function approximations and sectional streamlines are derived. Conditional patterns obtained using different methods for detecting the organised motion are essentially independent of the particular method used. The spatial arrangement of the organised motion about the flow centreline varies in a continuous manner between opposing and alternating modes. Results presented include conditional patterns for the opposing and alternating modes and the relative contributions made by each mode to the Reynolds stresses. A modified Rankine vortex kinematic model based as much as possible on experimental data and incorporating both modes, yields mean velocity and Reynolds stress distributions which agree well with experiment. A quasi-three-dimensional version of the model implies that large spanwise vortices and shear-aligned double rollers represent the same three-dimensional organised motion from two different viewpoints.

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.

Effect of Reynolds number on the topology of the organized motion in a turbulent boundary layer

The influence of Reynolds number on the topology of the organised motion in a turbulent boundary layer is studied with the use of an array of eight x-probes in the plane of mean shear. Instantaneous sectional streamlines and contours of large-scale approximations to the spanwise vorticity and strain rate suggest that the motion is relatively complicated at all Reynolds numbers.

Coherent structures in the far field of a turbulent wake

The topology of a typical group of large‐scale coherent structures in the far‐field of a slightly heated cylinder wake is clearly delineated by using averages of the velocity vector components conditioned on the occurrence of spatially coherent temperature fronts. Velocities are determined relative to a frame of reference traveling with the approximate convection velocity of the structures. When the results for a number of positions across the wake are assembled a clear topology picture of a typical group of structures in the plane of the main shear is obtained. The contributions of the coherent and random motions of all structures to the momentum and heat transports have been determined. In all cases the contribution that results from the random motion is larger than that of the coherent motion. This difference is more pronounced for the momentum transport than for the lateral heat transport.

SPANWISE STRUCTURE IN THE NEAR-WALL REGION OF A TURBULENT BOUNDARY LAYER

The behaviour of the stream wise velocity u in the near-wall region of a turbulent boundary layer is obtained by analysing the data from an array of hot wires aligned in the span wise direction. Conventional and conditional statistics are presented, relative to the occurrence of bursts and sweeps detected using a modified u -level method. Sweeps have an average stream wise length which is twice as large as that of bursts while the average span wise extent of sweeps is about 25% larger than that of bursts. Both instantaneous and conditionally averaged information is presented and discussed in the context of bursts and sweeps in the ( x, z )-plane. Dependence on y + is significant, and important differences are observed between instantaneous and conditionally averaged results. Conventional and conditional statistics of the velocity derivatives ∂ u /∂ x and ∂ u /∂ z provide some insight into the anisotropy of the mean-square velocity derivatives in the near-wall region. Conditionally averaged patterns of u compare favourably with the numerical simulations of Kim (1985) in the near-wall region of a turbulent channel flow, at a comparable Reynolds number.

Structure of large-scale vorticity in a turbulent far wake

Simultaneous measurements have been made of large-scale approximations of the three components of the vorticity vector in the far wake of a slightly heated cylinder. Analysis of the results is directed towards the properties of large-scale spanwise vortices and shear-aligned double-roller vortices and the relationship between them. The relationship between vorticity and temperature is also studied.

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).

Topology and transport properties of large‐scale organized motion in a slightly heated rough wall boundary layer

Large‐scale temperature discontinuities are detected in a high Reynolds number boundary layer over a slightly heated rough wall. In the streamwise and normal plane of the measurements, the discontinuities form (as for smooth wall boundary layers) the boundaries between successive spanwise vortexlike structures, flattened against the wall. The regions immediately downstream from the discontinuities are particularly important for the transport of heated, low‐momentum fluid away from the wall. The proportions contributed by the detected organized motion to the velocity and temperature variances are similar to those in smooth wall boundary layers. The proportions contributed to mean products, especially to the Reynolds shear stress, are significantly higher than over smooth walls at similar Reynolds numbers. The detected organized motion in the rough wall boundary layer resembles that in a smooth wall boundary layer of similar skin friction coefficient (and hence much lower Reynolds number).

An eddy viscosity calculation method for a turbulent duct flow

The mean velocity profile across a fully developed turbulent duct flow is obtained from an eddy viscosity relation combined with an empirical outer region wake function. Results are in good agreement with experiments and with direct numerical simulations in the same flow at two Reynolds numbers. In particular, the near-wall trend of the Reynolds shear stress and its variation with Reynolds number are similar to those of the simulations. The eddy viscosity method is more accurate than previous mixing length or implicit function methods.

REYNOLDS NUMBER DEPENDENCE OF THE SECOND-ORDER TURBULENT PRESSURE STRUCTURE FUNCTION

Second-order pressure structure functions, estimated from direct numerical simulations of homogeneous and nonhomogeneous turbulent flows, exhibit a significant Reynolds number dependence in the dissipative range. This dependence mainly reflects the contribution from low wave numbers to the instantaneous pressure gradient.