The deflection of flow around an isolated obstacle in a rotating homogeneous fluid is investigated. Criteria for the onset of closed streamlines over an isolated obstacle are reviewed. In the flow regime where no closed streamlines exist, steady solutions for the stream function are obtained for both quasigeostrophic and finite-Rossby-number flows. A measure is proposed to allow quantitative evaluation of the flow patterns, and the dependence of deflection on obstacle volume and aspect ratio is examined. In the regime where closed streamlines can exist, the presence of a trapped vortex to the right (looking downstream) of the obstacle is investigated by means of time integration of the shallow-water equations. The significance of the trapped vortex for a real fluid is then tested through the addition of the frictional effect of Eckman pumping.

Measurements have been made of the pressure distribution and turbulent-boundary-layer development on the afterbody of a model engine nacelle with a jet exhausting from the base and with the jet replaced by a parallel solid sting. It was found that the effect of replacing the jet by a solid body was to increase the pressure recovery over the afterbody and hence give a lower drag than with the jet. These changes in the pressure distribution affected the boundary-layer development and turbulence structure by different methods based on a momentum integral equation and the kinetic equation for the turbulence. Both methods approximately incorporate the effects of convergence and divergence of the flow caused by changes in transverse curvature of the surface. Neither method was completely satisfactory for the prediction of the overall boundary-layer development.

It was also found that, near the tail of the model, where the body radius is decreasing rapidly, the Reynolds shear stress was much lower than it would be in a two-dimensional boundary layer with the same pressure gradient. Calculations and analysis based on earlier work show that this reduction is directly related to the rates of strain associated with the convergence of the streamlines over the afterbody.

Observed statistics of non-breaking ocean-surface gravity waves shoaling between 4 and 1 m depths are compared with the predictions of linear finite-depth theory and a nonlinear model. The linear theory included effects of the directional distribution of energy within each frequency component. The nonlinear model, which does not consider directional effects, is based on Boussinesq-type equations for a sloping bottom (Freilich & Guza 1984). Given initial conditions in 4 m depth, the nonlinear model more accurately predicts the evolution of energy spectra, coherence and phase speed between sensors, and lengths of runs of high waves than does the linear theory. In four out of five cases, observed trends in the evolution of sea-surface-elevation skewness are predicted by the nonlinear model, while linear theory predicts zero skewness. Neither model can explain changes in the directional spectra observed between 9 and 4 m depths.

The model penetrative-convection problem of ice–water convection is considered. Analytical progress is made through the remarkable simplification that horizontally long convection cells are preferred when the heat flux is fixed on the boundaries (Chapman & Proctor 1980). However, a linear analysis shows that long horizontal scales are preferred only when the convection is mildly penetrative (i.e. the overlying layer of stable fluid is not deep). A straightforward nonlinear asymptotic analysis of the convection only provides the relatively uninteresting information that the convection is subcritical. Using the technique of reconstitution (Roberts 1985) to provide higher-order corrections to the asymptotic theory, flow properties at larger amplitudes are calculated and predictions about the extent of the subcriticality are made.

The marginal separation of a laminar incompressible boundary layer on the line of symmetry of a three-dimensional body is discussed. The interaction itself is taken to be quasi-two-dimensional but the results differ from those for a two-dimensional boundary layer in that the effect of the gradient of the crossflow is included. Solutions of the resulting integral equation are computed for two values of the additional parameter, and comparisons made with an analytical prediction of the asymptotic form as the length of the separation bubble tends to infinity. The occurrence of the phenomenon is confirmed by an examination of the results of an existing numerical integration of the boundary-layer equations for the line of symmetry of a paraboloid.

In order to model the fluid dynamics of Korotkoff sound generation when the artery under the cuff is fully collapsed during most of the heart cycle, the characteristics of pressure-wave propagation in a long silicone-rubber tube were studied experimentally. The central portion of this tube was designed to collapse to zero cross-sectional area as a result of high negative transmural pressure, thus simulating a collapsed artery. Propagation of a single half-sinusoidal pressure wave in and around this segment was studied in detail by pressure, velocity and tube-longitudinal-shape measurements.

A very steep wave front (shock wave) capable of producing a short tapping sound was formed by an overtaking phenomenon in the fully collapsed tube segment and it propagated into the inflated tube distal to the collapsed segment. An empirical equation relating the flow rate penetrating into the collapsed segment, the incident-wave pressure and the external pressure Pc over the collapsed segment was obtained. This equation predicts that the pressure-wave propagation in a fully collapsed segment depends only on the flow rate into the collapsed segment.

The initial internal pressure of the tube distal to the collapsed segment Pd is one independent variable in the high-cuff-pressure condition. The amplitude of the steep wave front and the shape of the pressure wave in the inflated tube distal to the collapsed segment are governed by Pc–Pd and the flow rate penetrating the collapsed segment. For the same flow rate, if Pc–Pd is lower than a critical value, the amplitude of the pressure in the distal tube decreases with increasing Pd because of positive pressure-wave reflection at the exit of the collapsed segment. On the other had, if Pc–Pd is higher than that value, no wave reflection occurs and the amplitude of the pressure wave is independent of Pd. In the latter case a severe constriction exists near the distal end of the collapsed segment, and flow occurs as two thin high-speed jets.

We have developed a compact and cost-effective shock tube to simulate the static and dynamic pressures of blast waves. The shock tube is open at both ends and is driven by high explosives distributed over a finite length of the tube near one end. The overall charge length is determined by the simulation time of interest, and the charge-density distribution is tailored to produce the pressure-waveform shape desired. For the shock tube to simulate a typical blast wave, the charge density must be highest at the charge front (closest to the test section) and gradually reduced towards the back. The resulting shock tube is an order of magnitude shorter than a conventional dynamic airblast simulator (DABS) in which concentrated explosives are used to drive the shock.

Tailored charges designed using this method were built and tested in a simulation development programme sponsored by the U.S. Defense Nuclear Agency (DNA). The pressures measured for several charge distributions agreed very well with SRI's PUFF hydrocode computations and demonstrated the feasibility of the compact simulator under realistic test conditions.

Wave-power absorption by an oscillating water column in a channel is studied within linear theory, and for different boundary conditions regarding the regions between the absorber and the channel walls. Particular attention is given to the effect of placing projecting sidewalls in front of the column.

The dynamics of two-dimensional uniform wavetrains on the interface between a viscoelastic compliant coating and a boundary-layer flow are explored theoretically. The coating is treated as a single-layer isotropic Voigt material of finite thickness that is bonded to a rigid half-space. The flow is modelled first by potential theory and then modified to incorporate pressure phase shifts and magnitudes found in boundary-layer flow over wavy walls. The consideration of viscoelastic effects has led to an important dimensionless damping parameter γt = Ct τt/d (where τt is the strain relaxation time, Ct is the elastic shear-wave speed and d is the layer depth) that seems to have been overlooked by experimentalists. The flow and the damping are found to have dramatic effects on wave propagation. Using flow pressure and material-damping parameters typical of experiments, the results show that both upstream- and downstream-propagating waves exist at low flow speeds. At higher flow speeds, shorter waves can no longer propagate upstream. At still higher velocities, two instabilities, ‘static divergence’ and ‘flutter’, are found. Static divergence occurs for flow speeds above 2.86Ct and consists of slow waves moving with speeds of about 0.02Ct. These results compare fairly well with published experimental data. Static divergence is found to be a damping instability for these coating systems. When the flow speed is increased further, the flutter instability appears consisting of waves with phase speeds about equal to Ct.

This paper studies the propagation of a wave packet in regions where the central packet frequency ω is close to the local maximum of the effective Väisälä frequency Nf(z) = N(z)/[1 − k·U(z)/ω], where k is the central wavevector of the packet and U is the mean current with a vertical velocity shear. The wave approaches the layer ω = Nfm asymptotically, i.e. trapping of the wave takes place. The trapping of guided internal waves is investigated within the framework of the linearized equations of motion of an incompressible stratified fluid in the WKB approximation, with viscosity, spectral bandwidth of the packet, vertical shear of the mean current and non-stationarity of the environment taken into account. As the packet approaches the layer of trapping, the growth of the wavenumber k is restricted only by possible wave-breaking and viscous dissipation. The growth of k is accompanied by the transformation of the vertical structure of internal-wave modes. The wave motion focuses at a certain depth determined by the maximum effective Väisälä frequency Nfm. The trapping of the wave packet results in power growth of the wave amplitude and steepness. At larger times the viscous dissipation becomes a dominating factor of evolution as a result of strong slowing down of the packet motion.

The role of trapping in the energy exchange of internal waves, currents and small-scale turbulence is discussed.

A solid sphere falling through a Bingham plastic moves in a small envelope of fluid with shape that depends on the yield stress. A finite-element/Newton method is presented for solving the free-boundary problem composed of the velocity and pressure fields and the yield surfaces for creeping flow. Besides the outer surface, solid occurs as caps at the front and back of the sphere because of the stagnation points in the flow. The accuracy of solutions is ascertained by mesh refinement and by calculation of the integrals corresponding to the maximum and minimum variational principles for the problem. Large differences from the Newtonian values in the flow pattern around the sphere and in the drag coefficient are predicted, depending on the dimensionless value of the critical yield stress Yg below which the material acts as a solid. The computed flow fields differ appreciably from Stokes’ solution. The sphere will fall only when Yg is below 0.143 For yield stresses near this value, a plastic boundary layer forms next to the sphere. Boundary-layer scalings give the correct forms of the dependence of the drag coefficient and mass-transfer coefficient on yield stress for values near the critical one. The Stokes limit of zero yield stress is singular in the sense that for any small value of Yg there is a region of the flow away from the sphere where the plastic portion of the viscosity is at least as important as the Newtonian part. Calculations For the approach of the flow field to the Stokes result are in good agreement with the scalings derived from the matched asymptotic expansion valid in this limit.

A numerical simulation of turbulent natural convection (the Rayleigh–Bénard problem) has been conducted using large-eddy-simulation (LES) methods and the results compared with several experiments. The development of the LES equation is outlined and discussed. The modelling of the small-scale turbulent motion (called subgrid modelling) is also discussed. The resulting LES equations are solved and data collected over a short period of time in a similar manner to the direct simulation of the governing conservation equations. An explicit, second-order accurate, finite-difference scheme is used to solve the equations. Various average properties of the resulting flow field are calculated from the data and compared with experimental data in the literature. The use of a subgrid model allows a higher value of Ra to be simulated than was previously possible with a direct simulation. The highest Ra successfully simulated was 2.5 × 106. The problems at higher values of Ra are discussed and suggestions for improvements made.

The propagation of flexural waves in floating ice plates is governed by two restoring forces – elastic bending of the plate, and the tendency of gravity to make the upper surface of the supporting water horizontal. This paper studies steady wave patterns generated by a steadily moving source on a water–ice system that is assumed to be homogeneous and of infinite horizontal extent, using asymptotic Fourier analysis to give a simple description of the wave pattern far from the source. Short-wavelength elastic waves propagate ahead, while the long gravity waves appear behind; and, depending on the system parameters, one, two or no caustics may appear. Wavecrest patterns are shown, and the amplitude variation with direction from the source is given. Where the two caustics just merge together, a special mathematical function analogous to the Airy function is introduced to describe wave amplitudes. These waves can be detected by a strainmeter embedded in the ice, and we compare its theoretical response with some experimental measurements.

The stability of fully developed pipe-Poiseuille flow to finite-amplitude axisymmetric and non-axisymmetric disturbances has been studied using the equilibrium-amplitude method of Reynolds & Potter (1967). In both the cases the least-stable centre-modes were investigated. Also, for the non-axisymmetric case the mode investigated was the one with azimuthal wavenumber equal to one. Many higher-order Landau coefficients were calculated, and the Stuart-Landau series was analysed by the Shanks (1955) method and by using Padé approximants to look for the existence of possible equilibrium states. The results show in both cases that, for each value of the Reynolds number R, there is a preferred band of spatial wavenumbers α in which equilibrium states are likely to exist. Moreover, in both cases it was found that the magnitude of the minimum threshold amplitude for a given R decreases with increasing R. The scales of the various quantities obtained agree very well with those deduced by Davey & Nguyen (1971).

Two- and three-lobed oscillations of a rotating liquid drop immersed in an immiscible fluid of comparable density and the same angular velocity were studied experimentally. Using acoustically suspended drops, it has been found that the relative change in the resonance frequencies of the axisymmetric drop-shape oscillations Δωl/ωl(0) is proportional to the square of the normalized angular speed (Ω/ωl(0))2 when ωl > 2Ω. This is in agreement with a recent analytical study of the same problem. Some preliminary results regarding the effect of rotation on the free-decay rate of the two-lobed oscillations are also presented.

A literature survey (Berger, Talbot & Yao 1983) indicates that laminar viscous flow in curved pipes has been extensively investigated. Most of the existing analytical results deal with the case of circular cross-section. The important studies dealing with elliptical cross-sections are mainly due to Thomas & Walters (1965) and Srivastava (1980). The analysis of Thomas & Walters is based on Dean's (1927, 1928) approach in which the simplified forms of the momentum and continuity equations have been used. The analysis of Srivastava is essentially a seminumerical approach, in which no explicit expressions have been presented.

In this paper, using elliptic coordinates and following the unsimplified formulation of Topakoglu (1967), the flow in a curved pipe of elliptical cross-section is analysed. Two different geometries have been considered: (i) with the major axis of the ellipse placed in the direction of the radius of curvature; and (ii) with the minor axis of the ellipse placed in the direction of the radius of curvature. For both cases explicit expressions for the first term of the expansion of the secondary-flow stream function as a function of the ellipticity ratio of the elliptic section have been obtained. After selecting a typical numerical value for the ellipticity ratio, the secondary-flow streamlines are plotted. The results are compared with that of Thomas & Walters. The remaining terms of the expansion of the flow field are not included, but they will be analysed in a future paper.

A method for solving the Navier–Stokes equations in domains with moving boundaries is proposed. By means of a coordinate transformation, the region under consideration is converted to a region with known boundaries which are coordinate surfaces. An appropriate difference scheme with an algorithm for its implementation is constructed. The method is applied to the case of steady incompressible viscous flow past a resting deformable bubble. Results are obtained for wide ranges for Reynolds and Weber numbers and compared with other theoretical or experimental works in the common regions for the governing parameters. A separation of the flow and the occurrence of a toroidal vortex in the rear of the bubble is observed and verified through a number of computations. Typical flow patterns as well as a variety of practically important relations between the parameters of the flow are shown graphically.

Two formulas, based on analytical considerations, which are capable of predicting the wedge angle of transition from Mach to regular reflection over cylindrical concave wedges, are developed. They are derived using Hornung, Oertel & Sandeman's (1979) conclusion that a Mach reflection can exist only if the corner-generated signals can catch up with the incident shock wave. The good agreement between the present models and the experimental results confirm Hornung et al.'s (1979) concept. The predictions of these models are in better agreement with experimental results than the predictions of Itoh, Okazaki & Itaya's (1981) model. The present models are very simple to use and apply but, like Itoh et al.'s (1981) model, they also lack the ability to account for the dependence of the transition angle on the radius of curvature of the cylindrical wedge.

Vertical forcing of a fluid layer leads to standing waves by means of a subharmonic instability. When the driving amplitude and frequency are chosen to be near the intersection of the stability boundaries of two nearly degenerate modes, we find that they can compete with each other to produce either periodic or chaotic motion on a slow timescale. We utilize digital image-processing methods to determine the time-dependent amplitudes of the competing modes, and local-sampling techniques to study the onset of chaos in some detail. Reconstruction of the attractors in phase space shows that in the chaotic regime the dimension of the attractor is fractional and at least one Lyapunov exponent is positive. The evidence suggests that a theory incorporating four coupled slow variables will be sufficient to account for the mode competition.

The early phase of the establishment of the flow past a circular cylinder started impulsively into rotation and translation is investigated by visualizing the flow patterns with solid tracers and by analysing qualitatively (flow topology) and quantitatively (velocity distributions and singular-point trajectories) the corresponding photographs. The range considered corresponds to moderate Reynolds numbers (Re [les ] 1000). The rotating-to-translating-speed ratio α increases from 0 to 3.25 and the motion covers a period during which the cylinder translates 4.5 or even 7 times its diameter. The details of the mechanisms of the near-wake formation are considered in particular and the increase of the flow asymmetry with increase in rotation is pointed out. Thus the existence of two regimes has been confirmed with the creation or non-creation of alternate eddies after an initial one E1 Furthermore, the new phenomena of saddle-point transposition and intermediate-eddy coalescence have been identified in the formation or shedding of respectively the odd and even subsequent eddies Ei (i = 2,3,…) when they exist. The very good agreement between these experimental data and the numerical results of Badr & Dennis (1985), obtained by solving the Navier-Stokes equations and presented in a parallel paper, confirms their respective validity and permits the determination of the flow characteristics not accessible, or accessible only with difficulty, to the present experiments. These flow properties such as drag and vorticity are capable of providing information on the Magnus effect for the former property and on unsteady separated flows for the latter.