The wave-action conservation equation for water waves is always derived from a Lagrangian for irrotational flow. This is quite satisfactory if the whole flow-field (i.e. waves and background current) is irrotational, but is inadequate for a background current with a large-scale (vertical) vorticity, even if the flow has negligible vorticity on the local scale of a few wavelengths. A wave-action conservation equation is derived for this case and equations governing the flow and the waves are given in a simple form closely parallel to the irrotational flow equations.

This paper is concerned with laboratory measurements of turbulence in a mixed layer and through a density interface, in the absence of a mean flow. The present results confirm the conclusion of Hopfinger & Toly (1976) that the turbulence in a mixed layer is not significantly affected by the slow entrainment of fluid across the bounding density interface. In a homogeneous fluid the turbulence intensity is found to be surprisingly non-uniform, even two grid mesh distances away from the grid. Velocity measurements have also been taken through a density interface (at the entraining boundary of a mixed layer) and the turbulence here varies in a manner that bears some resemblance to the theory of Hunt & Graham (1978). These velocity measurements were taken with a laser-Doppler anemometer and they were made possible by a novel experimental technique which eliminates the refractive index variations which normally occur in a turbulent, density-stratified liquid flow.

A simple analysis shows that with a disturbance present the potential jump in a steady flow in a canal is expressed in terms of (1) the effective volume (displaced volume and added mass/density of fluid) and (2) the depth Froude number for either a submerged body or a body with thin waterplane area. For a ship moving in a canal, the expression for potential jump contains a contribution from the line integral term along the intersection between the ship hull and the free surface. When a pressure distribution is given on the free surface, the potential jump can be expressed explicitly in terms of the depth Froude number and the total pressure force, regardless of the shape of the pressure distribution. From the present relations, the added mass of a ship in steady motion in a canal is computed from the potential jump computed previously by the author for various Froude numbers. This added mass plays an essential role in the equation of motion initially when a sudden external force is applied to a steady moving ship. The present analysis is complimentary to that of Newman (1976) and the extension of that to the three-dimensional case. As practical applications of the potential jump, which has had a limited interest, we proposed approximate formulas for speed correction and sinkage of a ship in a towing tank experiment. Also proposed is an approximate formula for the speed correction in a wind tunnel experiment. The present approximate formula is compared with ‘exact’ numerical results obtained by the localized finite element method for both towing tank and wind tunnel experiments. The present speed correction formula is also compared with existing approximate formulas for a wind tunnel experiment. The present formulas compare favourably with the exact numerical results.

We report on a set of turbulent flow experiments of the Taylor type in which the fluid is contained between a rotating inner circular cylinder and a fixed concentric outer cylinder, focusing our attention on very large Taylor number values, i.e. \[ 10^3 \leqslant T/T_c \leqslant 10^5, \] where Tc is the critical value of the Taylor number T for onset of Taylor vortices. At such large values of T, the turbulent vortex flow structure is similar to the one observed when T – Tc is small and this structure is apparently insensitive to further increases in T. These flows are characterized by two widely separated length scales: the scale of the gap width which characterizes the Taylor vortex flow and a much smaller scale which is made visible by streaks in the form of a ‘herring-bone’-like pattern visible at the walls. These are conjectured to be Görtler vortices which arise as a result of centrifugal instability in the wall boundary layers. Ideas of marginal instability by which we postulate that both the Taylor and Görtler vortex structures are marginally unstable on their own scale seem to provide good quantitative agreement between predicted and observed Görtler vortex spacings.

The method of characteristics is used to calculate the unsteady one-dimensional flow produced by the convection of a temperature disturbance, contained between two contact surfaces, in high subsonic flow through a nozzle. The results show the development of the pressure disturbances which are associated with the force perturbation needed to accelerate the temperature disturbance at the same rate as the surrounding gas and propagate in both the upstream and downstream directions. Using a simple flow model, expressions for the mean pressure disturbances are derived and shown to be in good agreement with numerical solutions. Other numerical solutions which show the effect of changing the various flow parameters and the nozzle shape are presented. In all of the cases considered, the pressure disturbances caused by a 10 % change in the inlet temperature are significantly large and may be an important part of ‘excess’ noise.

The motion behind the head of a gravity current advancing over a no-slip horizontal surface is a complex three-dimensional flow. There is intense mixing between the current and its surroundings and the foremost part of the head is raised above the surface. Experimental results are obtained from (i) an apparatus in which the head is brought to rest by using an opposing flow and a moving floor and (ii) a modified lock exchange flow. The dimensionless velocity of advance, rate of mixing between the two fluids and the depth of the mixed layer left behind the head and above the following gravity current are determined for an extended range of the dimensionless gravity current depth. The mixing between the two fluids is the result of gravitational and shear instabilities at the gravity current head. A semi-empirical analysis is presented to describe the results. The influence of Reynolds number is discussed and comparison with a documented atmospheric flow is presented.

To gain insight into the orbital motion in waves on the point of breaking, we first study the trajectories of particles in some ideal irrotational flows, including Stokes’ 120° corner-flow, the motion in an almost-highest wave, in periodic deep-water waves of maximum height, and in steep, solitary waves.

In Stokes’ corner-flow the particles move as though under the action of a constant force directed away from the crest. The orbits are expressible in terms of an elliptic integral. The trajectory has a loop or not according as q [sqcup ] c where q is the particle speed at the summit of each trajectory, in a reference frame moving with speed c. When q = c, the trajectory has a cusp. For particles near the free surface there is a sharp vertical gradient of the horizontal displacement.

The trajectories of particles in almost-highest waves are generally similar to those in the Stokes corner-flow, except that the sharp drift gradient at the free surface is now absent.

In deep-water irrotational waves of maximum steepness, it is shown that the surface particles advance at a mean speed U equal to 0·274c, where c is the phase-speed. In solitary waves of maximum amplitude, a particle at the surface advances a total distance 4·23 times the depth h during the passage of each wave. The initial angle α which the trajectory makes with the horizontal is close to 60°.

The orbits of subsurface particles are calculated using the ‘hexagon’ approximation for deep-water waves. Near the free surface the drift has the appearance of a thin forwards jet, arising mainly from the flow near the wave crest. The vertical gradient is so sharp, however, that at a mean depth of only 0.01L below the surface (where L is the wavelength) the forwards drift is reduced to less than half its surface value. Under the action of viscosity and turbulence, this sharp gradient will be modified. Nevertheless the orbital motion may contribute appreciably to the observed ‘winddrift current’.

Implications for the drift motions of buoys and other floating bodies are also discussed.

Weis-Fogh discovered a remarkable new principle of aerodynamic lift. Hovering wasps exploit the principle and fly with an aerodynamic performance superior in some respects to anything previously known. In this paper we address the question of whether the Weis-Fogh effect can be exploited in turbomachinery. We think the answer is yes.

Normal turbomachinery design is based on the analysis of isolated cascades of blades with steady entry and exit flows. The interactions between adjacent cascades and nonuniformities of the flow are usually regarded as problems which have to be minimized. Unsteadiness gives rise to noise. In this paper we take the opposite view and examine a novel type of turbomachinery stage that depends on the interaction between rotor and stator for its normal operation. The stage exploits the Weis-Fogh principle and has the unusual property that when started from rest it generates a pressure rise without shedding any vorticity into the fluid. We argue that there may be a performance advantage for stages of this new type.

Experiments were done to check the validity of the theoretical model and these are described. The results seem to show that under certain circumstances a strong rotor-stator interaction can result in an improved stage performance, and we suggest that this improvement may be due to the Weis-Fogh effect.

Our 1975 paper reported the results of experiments on shock reflexion in a wind tunnel and a shock tube; further results are presented here. For strong shocks it is shown that transition to Mach reflexion takes place continuously at the shock wave incidence angle ω0 corresponding to the normal shock point ω0 = ωN, unless the downstream boundaries form a throat. In this event transition can be promoted anywhere within the range ω0 [les ] ωN, and it is even possible to suppress regular reflexion altogether! However when ω0 < ωN the transition is discontinuous and accompanied by hysteresis. Again for strong shocks evidence is presented which suggests that the famous persistence of regular reflexion beyond the ωN point ω0 > ωN is spurious. For weak shocks the transition condition is not known but it is found that even for regular reflexion a marked discrepancy between theory and experiment develops as the shocks become progressively weaker. Also when weak shocks diffract over single concave corners there is a somewhat surprising discontinuity in the regular reflexion range. It seems that none of these phenomena can be adequately explained by real gas effects such as viscosity and variation of specific heats.

Results from a series of pipe-flow experiments using a range of water-soluble drag-reducing polymers are presented. Degradation has been investigated by means of multiple passes of the solutions through a pipe. A theory predicting drag reduction in pipe flow has been devised which agrees with the experimental results. Changes in polymer molecular weight due to degradation are taken into account. The analysis is then applied to a turbulent boundary layer with polymer injection.

The streamwise and spanwise velocity components and the gradients of these components normal to the wall were examined by using hot-film sensors and flush-mounted wall elements to study the vortex structures associated with the bursting phenomenon. Quadrant probability analysis and conditional sampling techniques indicated that pairs of counter-rotating streamwise vortices occur frequently in the wall region of a bounded turbulent shear flow. A streamwise momentum defect occurred between the vortices as low-speed fluid was ‘pumped’ away from the wall by the vortex pair. The defect region was long and narrow and possibly forms the low-speed streak as observed in visualization studies. The velocity defect was terminated by a strong acceleration followed by a high speed region.

The disturbing motion of plane Couette and Poiseuille flow is described using three parameters: two amplitudes corresponding to the disturbance of the parallel flow and the cellular motion, respectively, and the angle ϕ0 which defines the orientation of the vortex blobs with respect to the parallel flow. Equations of motion for these parameters are obtained using a Ritz-Galerkin method. For Reynolds numbers above a critical value sufficiently big disturbances will grow until a steady finite amplitude state is achieved. The energy of the disturbance remains finite, in spite of the highly truncated field representation using only three parameters. This is possible because of the nonlinear dependence of the field functions on ϕ0. The critical values of Reynolds number, above which finite amplitude states exist, are computed for the plane Couette flow and the Poiseuille channel flow.