The whistle in a steam kettle provides a near-perfect example of a hole tone system, in which two orifice plates are held a short distance apart in a cylindrical duct. This setup leads to distinct audible tones for a large range of flow rates. The main objective of the current paper is to understand the physical mechanism behind the generation of hole tones (whistling of steam kettles). A variety of experiments were undertaken, primarily focusing on how the acoustics of the hole tone system varied depending on the flow rate, whistle geometry, and upstream duct length. These were supplemented by flow visualisation experiments using water. The results show that the whistle's behaviour is divided into two regions of operation. The first, occurring at Reynolds numbers (based on orifice diameter and jet velocity) below Reδ ≈ 2000, exhibits a near-constant frequency behaviour. A mathematical model based on a Helmholtz resonator has been developed for this part of the mechanism. The second, for Reynolds numbers greater than Reδ ≈ 2000, the whistle exhibits a constant Strouhal number behaviour. A physical model has been developed to describe this part of the mechanism where the resonant modes of the upstream duct are coupled with the vortex shedding at the jet exit.

The current state of knowledge about the structure of wall-bounded turbulent flows is reviewed, with emphasis on the layers near the wall in which shear is dominant, and particularly on the logarithmic layer. It is shown that the shear interacts with scales whose size is larger than about one third of their distance to the wall, but that smaller ones, and in particular the vorticity, decouple from the shear and become roughly isotropic away from the wall. In the buffer and viscous layers, the dominant structures carrying turbulent energy are the streamwise velocity streaks, and the vortices organize both the dissipation and the momentum transfer. Farther from the wall, the velocity remains organized in streaks, although much larger ones than in the buffer layer, but the vortices lose their role regarding the Reynolds stresses. That function is taken over by wall-attached turbulent eddies with sizes and lifetimes proportional to their heights. Two kinds of eddies have been studied in some detail: vortex clusters, and ejections and sweeps. Both can be classified into a detached background, and a geometrically self-similar wall-attached family. The latter is responsible for most of the momentum transfer, and is organized into composite structures that can be used as models for the attached-eddy hierarchy hypothesized by Townsend [“Equilibrium layers and wall turbulence,” J. Fluid Mech.11, 97–120 (1961)]. The detached component seems to be common to many turbulent flows, and is roughly isotropic. Using a variety of techniques, including direct tracking of the structures, it is shown that an important characteristic of wall-bounded turbulence is temporally intermittent bursting, which is present at all distances from the wall, and in other shear flows. Its properties and time scales are reviewed, and it is shown that bursting is an important part of the production of turbulent energy from the mean shear. It is also shown that a linearized model captures many of its characteristics.

The relevance of Orr's inviscid mechanism to the transient amplification of disturbances in shear flows is explored in the context of bursting in the logarithmic layer of wall-bounded turbulence. The linearized problem for the wall normal velocity is first solved in the limit of small viscosity for a uniform shear and for a channel with turbulent-like profile, and compared with the quasiperiodic bursting of fully turbulent simulations in boxes designed to be minimal for the logarithmic layer. Many properties, such as time and length scales, energy fluxes between components, and inclination angles, agree well between the two systems. However, once advection by the mean flow is subtracted, the directly computed linear component of the turbulent acceleration is found to be a small part of the total. The temporal correlations of the different quantities in turbulent bursts imply that the classical model, in which the wall-normal velocities are generated by the breakdown of the streamwise-velocity streaks, is a better explanation than the purely autonomous growth of linearized bursts. It is argued that the best way to reconcile both lines of evidence is that the disturbances produced by the streak breakdown are amplified by an Orr-like transient process drawing energy directly from the mean shear, rather than from the velocity gradients of the nonlinear streak. This, for example, obviates the problem of why the cross-stream velocities do not decay once the streak has broken down.