The nonlinear interaction between the mean flow and a coherent disturbance in a two-dimensional turbulent mixing layer is addressed. Based on considerations from stability theory, previous experimental results, in particular the modification of the mean velocity profile, the peculiar growth of the forced shear-layer thickness and the spatial growth of the disturbance amplitude, are explained. A model that assumes a quasi-parallel mean flow having a self-similar mean velocity profile is developed. The model is capable of predicting the downstream evolution of turbulent mixing layers subjected to external excitations.

The nonlinear interaction between the mean flow and a coherent disturbance in a two-dimensional (2-D) turbulent wake is investigated. Based on considerations from stability theory, a model that assumes a quasiparallel mean flow and constant eddy viscosity is developed. Detailed comparisons between the model and experimental results are made. It is found that for downstream distances, where the wave is still being amplified according to the linear stability theory, the model predicts very well the modification of the mean velocity profile and the spatial growth of both the forced wake and the disturbance amplitude.

A calibration technique for multiple-sensor hot-wire probes is presented. The technique, which requires minimal information about the probe geometry, is tested using a four-sensor and a twelve-sensor probe. Two data reduction algorithms are introduced. The first one assumes a uniform velocity over the probe sensing volume and is applied to the four-sensor probe measurements. The second one assumes a uniform velocity gradient over the sensing volume of the probe. The procedure, when applied to the twelve-sensor probe, is shown to measure the velocity gradient components successfully. In both algorithms, the unknowns (velocity and velocity gradient components) are obtained by solving the resulting systems of nonlinear algebraic equations in a least-squares sense. The performances of the probes and the algorithms are tested with measurements in the wake of a circular cylinder. The statistics and spectra show that the twelve-sensor probe is successful in the simultaneous measurement of all three components of the velocity and all three components of the vorticity vectors.

For wake flows, much knowledge about turbulence structures has been obtained, but the lack of detailed vorticity data hinders understanding of the dynamics of these vortical structures. Previous attempts to measure vorticity components with X-wires in a cylinder wake have been reported by Hussein and Hayakawa [1], Antonia et al. [2] and Bisset et al. [3]. However, to our knowledge the present results are the first simultaneous measurements of all three components of the velocity and vorticity vectors in a wake.

A hot-wire technique is developed to measure simultaneously the 3 components of velocity in turbulent cylinder wake with a miniature 4-sensor probe which consists of 2 orthogonal pairs of V-probes. Jorgensen's law is used to express the effective cooling velocity of each sensor as a nonlinear function of the 3 velocity components. The data reduction is based on an error minimization method using V-probe solutions for initial guesses. The calibration method is independent of probe geometry, sensor orientation, and yields unique solutions for the measured velocity. Velocity is measured at 30 diameters in the wake for Re d ≈ 2050. The measured statistics will be shown and compared to X-probe and V-probe measurements. Other results, including power spectra and Reynolds shear stresses will be discussed. The calibration and data reduction schemes can be extended for simultaneous measurement of velocity and vorticity vectors with a 12-sensor probe which has three 4-sensor units.

The results of experimental studies on the nonlinear evolution of perturbation waves in the turbulent wake behind a flat plate are presented. Sinuous perturbations at several amplitudes and frequencies were introduced into the wake by oscillating a small trailing-edge flap. The Strouhal numbers of the perturbations were specially chosen so that the downstream location of the neutral point (where the spatial amplification rate obtained from linear theory vanishes) was well within the range of measurements. The streamwise evolution of the waves and their effect on the growth of the turbulent wake was investigated. The amplitude of the coherent Reynolds stress varied significantly with x and changed sign downstream of the neutral point. This resulted in rather strong changes in the spreading rate of the mean flow with x. At high forcing levels, dramatic deviations from the square-root behaviour of the unforced wake occurred. Although the development of the mean flow depended strongly on the forcing level, there were some common features in the overall response, which are discussed. The measured coherent Reynolds stress changed sign in the neighbourhood of the neutral point as predicted by linear theory. The normalized mean velocity profiles changed shape as a result of nonlinear interactions but relaxed to a new self-similar shape far downstream from the neutral point Detailed measurements of the turbulent and coherent Reynolds stresses are presented and the latter are compared to linear stability theory predictions.

The evolution of sinuous perturbation waves in the turbulent wake of a flat plate is investigated. The Strouhal number of the perturbations is chosen so that the waves remain amplified over the entire range of measurements. Detailed comparisons between linear stability theory and the phase-averaged measurements of the coherent velocity field are presented. Initially, before significant amplification of the perturbation amplitude occurs, the agreement between the linear theory and the measurements is good. The measured amplitude and phase distributions of the streamwise and lateral components of the coherent or wave-induced velocity field as well as the coherent Reynolds stress show excellent agreement with their linear theory counterparts. The coherent Reynolds stress, which is generated through a nonlinear interaction between the fundamental mode and the mean flow, augments the turbulent Reynolds stress causing the spreading rate of the wake to increase. However, this nonlinear interaction does not affect the shape of the mean velocity profile in the early stages of amplification. The linear theory predictions deteriorate with increasing downstream distance because of nonlinearity and the stronger interaction with the turbulent field as the neutral point of the perturbation is approached. For the unforced flow, the peak in the measured spectrum of the cross-stream (turbulent) velocity fluctuations at any downstream location (in the far wake) corresponds to the local neutral frequency from linear, spatial stability theory for inviscid, parallel flow.

The Orr-Sommerfeld equation admits two solution modes for the two-dimensional plane wake. These are the sinuous mode with antisymmetric streamwise fluctuations and the varicose mode with symmetric streamwise fluctuations. The varicose mode is often ignored because its amplification rates are considerably less than those of the sinuous mode. An experimental investigation of the varicose mode in a two-dimensional turbulent wake was undertaken to determine if this mode of instability agrees as well with linear stability theory, as did the sinuous mode in previous experiments (Wygnanski, Champagne & Marasli 1986). The experiments demonstrated that, although it is possible to generate a nearly pure symmetric disturbance wave, it is very difficult to do as the flow is very sensitive to the slightest asymmetries which might be present in the experiments. These asymmetries are preferentially amplified, resulting in the eventual distortion of an initially prominent symmetric wave. It was therefore necessary to decompose phase-averaged measurements of the streamwise component of the velocity fluctuations into their symmetric and antisymmetric parts, and the results were compared with the appropriate theoretical eigenfunctions from linear stability theory. The lateral distribution of the amplitude and the phase of each mode agree reasonably well with their theoretical counterparts from the Orr-Sommerfeld equation. Slowly diverging linear theory predicts the streamwise variation of the sinuous mode quite well, but fails to do so for the varicose mode. An eddy-viscosity model, coupled with the slowly diverging linear equations, predicts the streamwise variation of both modes reasonably well and describes the transverse distributions of the perturbation amplitudes for both modes, but it fails to predict the distribution of phase for the varicose mode.

A systematic study of two-dimensional, turbulent, small-deficit wakes was carried out to determine their structure and the universality of their self-preserving states. Various wake generators, including circular cylinders, a symmetrical airfoil, a flat plate, and an assortment of screens of varying solidity, were studied for a wide range of downstream distances. Most of the generators were tailored so that their drag coefficients, and therefore their momentum thicknesses, were identical, permitting comparison at identical Reynolds numbers and aspect ratios. The flat plate and airfoil had a small, trailing-edge flap which could be externally driven to introduce forced sinuous oscillations into the wake. The results indicate that the normalized characteristic velocity and length scales depend on the initial conditions, while the shape of the normalized mean velocity profile is independent of these conditions or the nature of the generator. The normalized distributions of the longitudinal turbulence intensity, however, are dependent on the initial conditions.Linear inviscid stability theory, in which the divergence of the mean flow is taken into account, predicts quite well the amplification and the transverse distributions of amplitudes and phases of externally imposed sinuous waves on a fully developed turbulent wake generated by a flat plate. There is a strong indication that the large structures observed in the unforced wake are related to the two-dimensional instability modes and therefore can be modelled by linear stability theory. Furthermore, the interaction of the two possible modes of instability may be responsible for the vortex street-type pattern observed visually in the small-deficit, turbulent wake.