W. C. Reynolds

The structure of turbulent boundary layers

Extensive visual and quantitative studies of turbulent boundary layers are described. Visual studies reveal the presence of surprisingly well-organized spatially and temporally dependent motions within the so-called ‘laminar sublayer’. These motions lead to the formation of low-speed streaks in the region very near the wall. The streaks interact with the outer portions of the flow through a process of gradual ‘lift-up’, then sudden oscillation, bursting, and ejection. It is felt that these processes play a dominant role in the production of new turbulence and the transport of turbulence within the boundary layer on smooth walls. Quantitative data are presented providing an association of the observed structure features with the accepted ‘regions’ of the boundary layer in non-dimensional co-ordinates; these data include zero, negative and positive pressure gradients on smooth walls. Instantaneous spanwise velocity profiles for the inner layers are given, and dimensionless correlations for mean streak-spacing and break-up frequency are presented. Tentative mechanisms for formation and break-up of the low-speed streaks are proposed, and other evidence regarding the implications and importance of the streak structure in turbulent boundary layers is reviewed.

The production of turbulence near a smooth wall in a turbulent boundary layer

The structure of the flat plate incompressible smooth-surface boundary layer in a low-speed water flow is examined using hydrogen-bubble measurements and also hot-wire measurements with dye visualization. Particular emphasis is placed on the details of the process of turbulence production near the wall. In the zone 0 y + The uncertainties in the bubble data are large, but they have the distinct advantage of providing velocity profiles as a function of time and the time sequences of events. These data show that the velocity profiles during bursting periods assume a shape which is qualitatively distinct from the well-known mean profiles. The observations are also used as the basis for a discussion of possible appropriate mathematical models for turbulence production.

The mechanics of an organized wave in turbulent shear flow

Some preliminary results on the behaviour of controlled wave disturbances introduced artificially into turbulent channel flow are reported. Weak plane-wave disturbances are introduced by vibrating ribbons near each wall. The amplitude and relative phase of the streamwise component of the induced wave is educed from a hot wire signal, allowing the wave speed and attenuation characteristics and the wave shape to be traced downstream. The normal component and wave Reynolds stress have been inferred from these data. It appears that Orr–Sommerfeld theories attempted to date are inadequate for description of these waves.

The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments

The dynamical equations governing small amplitude wave disturbances in turbulent shear flows are derived. These equations require additional equations or assumptions about the wave-induced fluctuations in the turbulence Reynolds stresses before a closed system can be obtained. Some simple closure models are proposed, and the results of calculations using these models are presented. When the predictions are compared with our data for channel flow, we find it essential that these oscillations in the Reynolds stresses be included in the model. A simple eddy-viscosity representation serves surprisingly well in this respect.

Evaluation of subgrid-scale models using an accurately simulated turbulent flow

A calculation of periodic homogeneous isotropic turbulence is used to simulate the experimental decay of grid turbulence. The calculation is found to match the experiment in a number of important aspects and the computed flow field is then treated as a realization of a physical turbulent flow. From this flow, a calculation is conducted of the large eddy field and the various averages of the subgrid-scale turbulence that occur in the large eddy simulation equations. These quantities are compared with the predictions of the models that are usually applied in large eddy simulation. The results show that the terms which involve the large-scale field are accurately modeled but the subgrid-scale Reynolds stresses are only moderately well modeled. It is also possible to use the method to predict the constants of the models without reference to experiment. Attempts to find improved models have not met with success.

Three-dimensional simulations of large eddies in the compressible mixing layer

The effect of Mach number on the evolution of instabilities in the compressible mixing layer is investigated. The full time-dependent compressible Navier–Stokes equations are solved numerically for a temporally evolving mixing layer using a mixed spectral and high-order finite difference method. The convective Mach number Mc (the ratio of the velocity difference to the sum of the free-stream sound speeds) is used as the compressibility parameter. Simulations with random initial conditions confirm the prediction of linear stability theory that at high Mach numbers (Mc > 0.6) oblique waves grow more rapidly than two-dimensional waves. Simulations are then presented of the nonlinear temporal evolution of the most rapidly amplified linear instability waves. A change in the developed large-scale structure is observed as the Mach number is increased, with vortical regions oriented in a more oblique manner at the higher Mach numbers. At convective Mach numbers above unity the two-dimensional instability is found to have little effect on the flow development, which is dominated by the oblique instability waves. The nonlinear structure which develops from a pair of equal and opposite oblique instability waves is found to resemble a pair of inclined A-vortices which are staggered in the streamwise direction. A fully nonlinear computation with a random initial condition shows the development of large-scale structure similar to the simulations with forcing. It is concluded that there are strong compressibility effects on the structure of the mixing layer and that highly three-dimensional structures develop from the primary inflexional instability of the flow at high Mach numbers

Compressible mixing layer - Linear theory and direct simulation

Results from linear stability analysis are presented for a wide variety of mixing layers, including low-speed layers with variable density and high Mach number mixing layers. The linear amplification predicts correctly the experimentally observed trends in growth rate that are due to velocity ratio, density ratio, and Mach number, provided that the spatial theory is used and the mean flow is a computed solution of the compressible boundary-layer equations. It is found that three-dimensional modes are dominant in the high-speed mixing layer above a convective Mach number of 0.6, and a simple relationship is proposed that approximately describes the orientation of these waves. Direct numerical simulations of the compressible Navier-Stokes equations are used to show the reduced growth rate that is due to increasing Mach number. From consideration of the compressible vorticity equation, it is found that the dominant physics controlling the nonlinear roll-up of vortices in the high-speed mixing layer is contained in an elementary form in the linear eigenfunctions. It is concluded that the linear theory can be very useful for investigating the physics of free shear layers and predicting the growth rate of the developed plane mixing layer

Active control of streamwise vortices and streaks in boundary layers

Coherent structures play an important role in the dynamics of turbulent shear flows. The ability to control coherent structures could have significant technological benefits with respect to flow phenomena such as skin friction drag, transition, mixing, and separation. This paper describes the development of an actuator concept that could be used in large arrays for actively controlling transitional and turbulent boundary layers. The actuator consists of a piezoelectrically driven cantilever mounted flush with the flow wall. When driven, the resulting flow disturbance over the actuator is a quasi-steady pair of counter-rotating streamwise vortices with common-flow away from the wall. The vortices decay rapidly downstream of the actuator; however, they produce a set of high- and low-speed streaks that persist far downstream (well over 40 displacement thicknesses). The amplitude of the actuator drive signal controls the strength of the generated vortices. The actuator is fast, compact, and generates a substantial disturbance in the flow. Its performance has been demonstrated using a small array of sensors and actuators in low-speed water laminar boundary layers with imposed steady and unsteady disturbances. Experiments are reported in which transition from a large disturbance was delayed by 40 displacement thicknesses, and in which the mean and spanwise variation of wall shear under an array of high- and low-speed streaks was substantially reduced downstream of a single transverse array of actuators.

One-point turbulence structure tensors

The dynamics of the evolution of turbulence statistics depend on the structure of the turbulence. For example, wavenumber anisotropy in homogeneous turbulence is known to affect both the interaction between large and small scales (Kida & Hunt 1989), and the non-local effects of the pressure–strain-rate correlation in the one-point Reynolds stress equations (Reynolds 1989; Cambon et al . 1992). Good quantitative measures of turbulence structure are easy to construct using two-point or spectral data, but one-point measures are needed for the Reynolds-averaged modelling of engineering flows. Here we introduce a systematic framework for exploring the role of turbulence structure in the evolution of one-point turbulence statistics. Five one-point statistical measures of the energy-containing turbulence structure are introduced and used with direct numerical simulations to analyse the role of turbulence structure in several cases of homogeneous and inhomogeneous turbulence undergoing diverse modes of mean deformation. The one-point structure tensors are found to be useful descriptors of turbulence structure, and lead to a deeper understanding of some rather surprising observations from DNS and experiments.

Stability of turbulent channel flow, with application to Malkus's theory

The Orr-Sommerfeld stability problem has been studied for velocity profiles appropriate to turbulent channel flow. The intent was to provide an evaluation of Malkuss theory that the flow assumes a state of maximum dissipation, subject to certain constraints, one of which is that the mean velocity profile is marginally stable. Dissipation rates and neutral stability curves were obtained for a representative two-parameter family of velocity profiles. Those in agreement with experimental profiles were found to be stable; the marginally stable profile of greatest dissipation was not in good agreement with experiments. An explanation for the apparent success of Malkuss theory is offered.