Jonathan Morrison

Scaling of the streamwise velocity component in turbulent pipe flow

Statistics of the streamwise velocity component in fully developed pipe flow are examined for Reynolds numbers in the range 5.5 x 10^4 ≤ ReD ≤ 5.7 x 10^6. Probability density functions and their moments (up to sixth order) are presented and their scaling with Reynolds number is assessed. The second moment exhibits two maxima: the one in the viscous sublayer is Reynolds-number dependent while the other, near the lower edge of the log region, follows approximately the peak in Reynolds shear stress. Its locus has an approximate (R^+)^{0.5} dependence. This peak shows no sign of ‘saturation’, increasing indefinitely with Reynolds number. Scalings of the moments with wall friction velocity and

Pitot probe corrections in fully developed turbulent pipe flow

(U_{cl}-\overline{U})

The interaction between inner and outer regions of turbulent wall-bounded flow

are examined and the latter is shown to be a better velocity scale for the outer region, y/R > 0.35, but in two distinct Reynolds-number ranges, one when ReD 7 x 10^4. Probability density functions do not show any universal behaviour, their higher moments showing small variations with distance from the wall outside the viscous sublayer. They are most nearly Gaussian in the overlap region. Their departures from Gaussian are assessed by examining the behaviour of the higher moments as functions of the lower ones. Spectra and the second moment are compared with empirical and theoretical scaling laws and some anomalies are apparent. In particular, even at the highest Reynolds number, the spectrum does not show a self-similar range of wavenumbers in which the spectral density is proportional to the inverse streamwise wavenumber. Thus such a range does not attract any special significance and does not involve a universal constant.

BURSTS AND THE LAW OF THE WALL IN TURBULENT BOUNDARY LAYERS

Mean flow measurements taken in fully developed turbulent pipe flow over a wide Reynolds number range are used to evaluate current methods of correcting Pitot probe data. Based on this evaluation, a new form for the displacement correction is proposed which appears to be more accurate over a wider range of conditions than those currently available. The difficulty of obtaining the true near-wall velocity profile near the wall is explored.

Relaminarisation of Reτ = 100 channel flow with globally stabilising linear feedback control

The nature of the interaction between the inner and outer regions of turbulent wall-bounded flow is examined. Townsends theory of inactive motion is shown to be a first-order, linear approximation of the effect of the large eddies at the surface that acts as a quasi-inviscid, low-frequency modulation of the shear-stress-bearing motion. This is shown to be a ‘strong’ asymptotic condition that directly expresses the decoupling of the inner-scale active motion from the outer-scale inactive motion. It is further shown that such a decoupling of the inner and outer vorticity fields near the wall is inappropriate, even at high Reynolds numbers, and that a ‘weak’ asymptotic condition is required to represent the increasing effect of outer-scale influences as the Reynolds number increases. High Reynolds number data from a fully developed pipe flow and the atmospheric surface layer are used to show that the large-scale motion penetrates to the wall, the inner–outer interaction is not describable as a linear process and the interaction should more generally be accepted as an intrinsically nonlinear one.

Anisotropy and energy flux in wall turbulence

The bursting mechanism in two different high-Reynolds-number boundary layers has been analysed by means of conditional sampling. One boundary layer develops on a smooth, flat plate in zero pressure gradient; the other, also in zero pressure gradient, is perturbed by a rough-to-smooth change in surface roughness and the new internal layer has not yet recovered to the local equilibrium condition at the measurement station. Sampling on the instantaneous uv signal in the logarithmic region confirms the presence of two related structures, ‘ejections’ and ‘sweeps’ which, in the smooth-wall layer, appear to be responsible for most of the turbulent energy production, and to effect virtually all that part of the spectral energy transfer that is universal. Ejections show features similar to those of Falcos ‘typical eddies’ while sweeps appear to be inverted ejections moving down towards the wall. The inertial structures associated with ejections show attributes of the true universal motion (Townsends ‘attached’ eddies) of the inner layer and these are therefore identified as ‘bursts’. In the outer layer, these become ‘detached’ from the wall. The large-scale structures associated with sweeps also appear to be ‘detached’ eddies (‘splats’), but these induce low-wave-number inactive motion near the wall and this is not universal even though the sweep itself is. Neither ejections nor sweeps detected in the rough-to-smooth layer are near a condition of energy equilibrium. The relation of ejections and sweeps to the law of the wall and other accepted laws is discussed.

Similarity of the streamwise velocity component in very-rough-wall channel flow

The problems of nonlinearity and high dimension have so far prevented a complete solution of the control of turbulent flow. Addressing the problem of nonlinearity, we propose a flow control strategy which ensures that the energy of any perturbation to the target profile decays monotonically. The controller’s estimate of the flow state is similarly guaranteed to converge to the true value. We present a one-time off-line synthesis procedure, which generalises to accommodate more restrictive actuation and sensing arrangements, with conditions for existence for the controller given in this case. The control is tested in turbulent channel flow (Re_τ = 100) using full-domain sensing and actuation on the wall-normal velocity. Concentrated at the point of maximum inflection in the mean profile, the control directly counters the supply of turbulence energy arising from the interaction of the wall-normal perturbations with the flow shear. It is found that the control is only required for the larger-scale motions, specifically those above the scale of the mean streak spacing. Minimal control effort is required once laminar flow is achieved. The response of the near-wall flow is examined in detail, with particular emphasis on the pressure and wall-normal velocity fields, in the context of Landahl’s theory of sheared turbulence.

Conditional-sampling schemes for turbulent flow, based on the variable-interval time averaging (VITA) algorithm

A term-by-term wavelet decomposition of the equation for turbulence kinetic energy in turbulent channel flow is used to provide a dual space-scale description of the production and flux of energy. Wavelet filtering, analogous to that used in large-eddy simulation, is performed on the nonlinear term that constitutes the energy flux. Meneveaus term, π (m) sg[i] is used to represent forward scatter and backscatter. This term is highly intermittent, much more so than the equivalent terms for production at the same scale. Virtually all of π (m) sg[i] appears in only two components that involve subgrid flux of streamwise momentum in the wall-normal and spanwise directions. An equivalent term that is the wavelet transform of the pressure-gradient term is shown to be several orders of magnitude smaller, consistent with its neglect in current subgrid modelling techniques. However, the mean-square pressure-gradient fluctuations (that reach a maximum in the range of wavenumbers in which the velocity spectra exhibit a -5/3 slope) are responsible for the significant spatial intermittency observed in the energy flux

IUTAM Symposium on Flow Control and MEMS

The streamwise velocity component is studied in fully developed turbulent channel flow for two very rough surfaces and a smooth surface at comparable Reynolds numbers. One rough surface comprises sparse and isotropic grit with a highly nonGaussian distribution. The other is a uniform mesh consisting of twisted rectangular elements which form a diamond pattern. The mean roughness heights (± the standard deviation) are, respectively, about 76(±42) and 145(±150) wall units. The flow is shown to be two-dimensional and fully developed up to the fourth-order moment of velocity. The mean velocity profile over the grit surface exhibits self-similarity (in the form of a logarithmic law) within the limited range of 0.04 y/h 0.06, but the profile over the mesh surface does not, even though the mean velocity deficit and higher moments (up to the fourth order) all exhibit outer scaling over both surfaces. The distinction between self-similarity and outer similarity is clarified and the importance of the former is explained. The wake strength is shown to increase slightly over the grit surface but decrease over the mesh surface. The latter result is contrary to recent measurements in rough-wall boundary layers. Single- and twopoint velocity correlations reveal the presence of large-scale streamwise structures with circulation in the plane orthogonal to the mean velocity. Spanwise correlation length scales are significantly larger than corresponding ones for both internal and external smooth-wall flows.

Flow estimation of boundary layers using DNS-based wall shear information

The variable-interval time-averaging (“VITA”) algorithm has been tested in a variety of turbulent boundary layers for its ability to detect shear-stress-producing motions from hot-wire signals. A “VITA + LEVEL” scheme (which uses criteria for both short-time variance and short-time average, i.e.“level”) has been devised, and used in several different boundary layers. This scheme yields length-scale statistics that are acceptably independent of the conditioning criteria, which the VITA scheme does not.