Measurements are presented for different flow rates of the time-averaged wall shear stress and of the root-mean-square value of the turbulent fluctuations along a small-amplitude sinusoidally shaped solid surface. The stresses are found to have a variation along the wave surface which is also sinusoidal. The influence of flow rate and of wavelength on the amplitude and phase angle can be correlated by using a wave-number α+ made dimensionless with wall parameters.

It is found that for α+ > 10−2 a frozen-turbulence assumption can be made whereby the influence of the wave-induced variation of the mixing length can be ignored. For α+ < 10−4 the flow can be described by assuming the Reynolds stresses are given by an equilibrium assumption. The relaxation from this equilibrium condition is characterized by a sharp change in the phase angle for 6 × 10−4 < α+ < 10−3.

This relaxation is associated with physical processes in the viscous wall region which are not yet understood. It is argued that these are principally related to the wave-induced variation of the pressure gradient.

The wave-induced variation of the turbulent fluctuations in the wall shear stress also indicate a relaxation in that the maximum turbulence intensity is located in a region of favourable pressure gradient.

A new method is proposed for the calculation of gravity waves on deep water. This is based on some recently discovered quadratic identities between the Fourier coefficients an in Stokes's expansion. The identities are shown to be derivable from a cubic potential function, which in turn is related to the Lagrangian of the motion. A criterion for the bifurcation of uniform waves into a series of steady waves of non-uniform amplitude is expressed by the vanishing of a particular determinant with elements which are linear combinations of the coefficients an. The critical value of the wave steepness for the symmetric bifurcations discovered by Chen & Saffman (1980) are verified. It is shown that a truncated scheme consisting of only the coefficients a0, a1 and a2 already exhibits Class 2 bifurcation, and similarly for Class 3. Asymmetric bifurcations are also discussed. A recent suggestion by Tanaka (1983) that gravity waves exhibit a Class 1 bifurcation at the point of maximum energy is shown to be incorrect.

The response of single two- and three-dimensional Helmholtz resonators subject to external excitation by a plane acoustic wave is studied. The inviscid linearized problem is solved by the matched-asymptotic-expansion technique in the low-frequency limit, i.e. when the characteristic neck dimension is small compared with the acoustic wavelength. The scale of the cavity is chosen such as to tune the system to the lowest Helmholtz mode. The results are compared with the classical lumped-element model, and refined expressions are derived for the effective mass (added length) and stiffness (effective cavity volume) of the resonator.