Turbulent motions within the wind-mixed layer, which is advected by near-surface inertial oscillations, excite internal gravity waves in the underlying ocean layers. Momentum transport in the radiated wave field results in a drag force on the inertial currents. Because the magnitude of the inertial currents is large compared with the turbulence intensity, the resultant rate of dissipation of inertial oscillation energy is approximately equal to the energy flux in the radiated wave field. Using linear internal wave theory, asymptotic results are derived for the energy flux in terms of the Brunt-Väisälä frequency N below the mixed layer, the magnitude U0 of the inertial current, the integral length scale l of the mixed-layer turbulence and the mean-square displacement 〈ζ20〉 of the base of the mixed layer. For representative conditions, we estimate an energy flux of 1-10 erg/cm2 s into relatively short (wavelength of order 2πU0/N) high frequency (of order, but less than, N) internal waves. The resultant decay times for inertial oscillation energy range from a day to a week or so, in agreement with reported observations on the decay of inertial oscillations in the upper ocean. The estimated energy flux is comparable in magnitude to estimates for other internal wave generation mechanisms, indicating that, in addition to being a significant sink of inertial energy, this process may locally represent a significant source of internal wave energy in the open ocean.

A technique has been developed to study the phenomenon of ultrasonic emulsification in which oil is dispersed as a fine suspension into water at 20 kHz. It was found that the emulsification takes place in two stages. In the first stage, oil droplets of the order of 70 μm are formed from the instability of interfacial waves. In the second stage these large droplets are successively broken into small droplets by cavitation until a stable droplet size is reached. In this paper, the criterion for the instability of the interfacial waves is developed from a linearized stability analysis of the planar oil-water interface exposed to acoustic excitation. The characteristic droplet diameter produced by the instability is related to the induced capillary wavelength at the interface.

The amplitude of the ultrasonic transducer and the theoretical amplitude of vibration necessary for the instability of the interfacial waves were found to be in agreement. In addition, the sizes of the large droplets present in the suspension systems at short irradiation times agree closely with the predicted droplet diameters.

In discussing turbulent shear layers, experimentalists have divided the flow into a turbulent region, which is vortical, and a non-turbulent region, which is irrotational but unsteady. This paper introduces a theoretical method of decomposing the velocity field into potential and vortical components that is compatible with the experimentalists’ viewpoint. Specifically, only potential motions will exist in the non-turbulent region, while the decomposition shows that the turbulent region consists of both potential and vortical motions. The kinematic decomposition used is called a potential/complex-lamellar decomposition. Compared with the standard Helmholtz decomposition, the complex-lamellar decomposition is not widely known, and this article includes a discussion of its properties and characteristics. The vector components in this decomposition may be represented by three scalar potentials: ϕ, ψ and χ. One of the important physical interpretations of the potentials concerns vortex lines. Vortex lines are defined by the intersection of a surface ψ = constant with a surface χ = constant. Since these surfaces are a function of time, this establishes a sound kinematic theory for following the history of vortex lines in a turbulent or viscous flow.

The spectral method of Orszag & Patterson (1972a, b) is used here to study pressure and velocity fluctuations in axisymmetric, homogeneous, incompressible, decaying turbulence at Reynolds numbers Reλ [lsim ] 40. In real space 323 points are treated. The return to isotropy is simulated for several different sets of anisotropic Gaussian initial conditions. All contributions to the spectral energy balance for the different velocity components are shown as a function of time and wavenumber. The return to isotropy is effected by the pressure-strain correlation. The rate of return is larger at high than at low wavenumbers. The inertial energy transfer tends to create anisotropy at high wavenumbers. This explains the overrelaxation found by Herring (1974). The pressure and the inertial energy transfer are zero initially as the triple correlations are zero for the Gaussian initial values. The two transfer terms are independent of each other but vary with the same characteristic time scale. The pressure-strain correlation becomes small for extremely large anisotropies. This can be explained kinematically. Rotta's (1951) model is approximately valid if the anisotropy is small and if the time scale of the mean flow is much larger than 0·2 Lf/v, which is the time scale of the triple correlations (Lf = integral length scale, v = root-mean-square velocity). The value of Rotta's constant is less dependent upon the Reynolds number if the pressure-strain correlation is scaled by v3/Lf rather than by the dissipation. Lumley & Khajeh-Nouri's (1974) model can be used to account for the influence of large anisotropies. The effect of strain is studied by splitting the total flow field into large- and fine-scale motion. The empirical model of Naot, Shavit & Wolfshtein (1970) has been confirmed in this respect.

We consider the problem of mass injection from a flat plate into uniform supersonic flow when the boundary layer is blown off at the leading edge to form a thin free shear layer separating the inviscid injectant layer from the external flow. The injection is moderate, i.e. of the same order of magnitude as the velocity of entrainment into the base of the shear layer. For simplicity, we consider similarity blowing, proportional to x*−½, where x* is measured along the plate from the leading edge. We find that the solution in the injectant region, based on initial conditions at the leading edge, is non-unique unless fixed by downstream conditions. When injection is cut off at a finite distance along the plate, this enables us to find a solution to the problem in which the shear layer eventually reattaches to the plate and for which the pressure and the height of the injectant layer are continuous at cut-off. The study provides a partial connexion between the earlier studies of weak blowing in which the boundary layer is not blown off and of strong blowing for which the boundary layer is blown off and the entrainment into the shear layer is negligible.

The boundary-layer equations are solved numerically for mainstreams \[ U(x) = x(1-x^2)^{-\alpha}\quad {\rm and}\quad U(x) = (1-x)^{-\alpha}, \] which are both O((1 − x)−α) near x = 1. Series expansions are derived near x = 1. For α > 1, where, for the similarity solution at x = 1, the outer boundary condition is approached through exponentially small terms, a straightforward expansion in powers of 1 − x is possible. For 0 < α < 1, where the decay is only algebraic (Brown & Stewartson 1965), the outer boundary condition cannot be satisfied even with algebraic decay by the higher-order terms in the series and this must be regarded as only an inner expansion. An outer expansion is required which matches with this inner expansion and which approaches the outer boundary condition with exponential decay. For α = 1, the decay is exponential, but not of the same form as for α > 1, and again the outer boundary condition cannot be attained by the higher-order terms in the series. An outer expansion for this case is also derived.

A theoretical model is presented for the liquid-liquid emulsification phenomenon based on the deformation and breakup of an oil droplet exposed to a cavitation shock wave generated by an acoustic field. The model predicts a relationship between the Ohnesorge number and the critical Weber number ratio for long acoustic irradiation times. At short irradiation times, the mean particle size and variance decrease with increasing time of acoustic irradiation. The results show remarkable agreement when compared with results obtained from the studies on liquid droplets exposed to shock impact from a gas stream. The mechanism for acoustic emulsification is that large oil droplets originally formed from the instability oil-water interface are disintegrated into smaller ones by the cavitation until a critical size, characteristic of the particular oil-water system, is reached.

This paper presents an experimental study of the turbulent structure on the centre-line of a two-dimensional impinging jet. The mean velocity, turbulent stresses, triple velocity products and temporal derivatives were measured and the energy balances for the three fluctuating components were calculated. The results indicate a selective stretching of vortices in the direction in which the streamlines spread near the wall, causing anisotropy in this region. The distribution of energy among various frequencies was found from spectral measurements. These measurements revealed the existence of a neutral frequency above which the energy was attenuated by viscous dissipation and below which it was augmented by a vortex-stretching mechanism.

In the present investigation we consider hydromagnetic Stokes flow past a rotating sphere. The magnetic field is produced by a magnetic pole placed at the centre of the sphere. The problem is analysed by a combination of perturbation and numerical methods. It is seen that the flow reversal (due to rotation) at the rear portion of the sphere is enhanced as the strength of the magnetic field increases. In addition, we obtain the simultaneous effects of rotation and a magnetic field on the streamlines.

The temperature and velocity fields in a round heated jet were investigated in detail. Both conventional measurements and conditional measurements (zone averages and point averages) were performed. The probability density functions of the lengths of turbulent and non-turbulent durations were also measured. Filtered correlation measurements show that large-scale turbulent motions were responsible for the bulk of momentum and heat transport, and also that small scales were more efficient in transporting heat than in transporting momentum. In no case was heat transported further or more than momentum, however. These results are discussed in detail, particularly with regard to the entrainment. Conservation equations for turbulent-zone variables and the intermittency factor are derived and a model for some of the resulting higher-order correlations is suggested. An exact equation for the intermittency function is presented.

Erdogan & Chatwin (1967) derived a nonlinear diffusion equation \[ \partial_tc = \partial_z([D_0+(\partial_zc)^2D_2]\partial_zc) \] which models the effect of buoyancy upon the longitudinal dispersion of a solute in pipe flow. The same equation arises more widely as a limiting form in which only the first buoyancy correction is retained. In this paper long-term asymptotic solutions are obtained both for the smearing-out of a concentration jump and for the approach to normality of a finite discharge. A variant of the method provides an approximate solution to the initial-value problem, and a comparison is made with Prych's (1970) experimental results.

The Faxén relations for a rigid particle in an arbitrary Stokes flow are generalized to give expressions for the stresslet (and higher stress moments) exerted by the particle on the fluid, and also to viscous drops immersed in a viscous fluid.

The fully developed laminar flow in a heated curved pipe under the influence of both centrifugal and buoyancy forces is studied analytically. The pipe is assumed to be heated so as to maintain a constant axial temperature gradient. Both horizontal and vertical pipes are considered. Solutions for these two cases are obtained by regular perturbations in the Dean number and the product of the Reynolds and Rayleigh numbers; the solutions are therefore limited to small values of these parameters. Predictions of the axial and secondary flow velocities, streamlines, shear stress, temperature distribution and heat transfer are given for a representative case.

The classical power laws describing the similarity solutions for turbulent jets, wakes and shearing layers are found to determine a fixed turbulent Reynolds number for each flow. The power laws are then derived from the principle of marginal instability without the usual assumptions.

A nonlinear study of harbour resonance is carried out for a rectangular bay indented from a straight coast. Boussinesq equations with nonlinearity and dispersion are used. Simplifying approximations are made for a narrow bay to decouple the nonlinear problem in the bay from the approximately linear problem in the ocean. Harmonic generation in the bay is studied numerically. Experiments for three different bay lengths and three amplitudes are compared with the numerical theory. The relative importance of entrance loss and boundary-layer dissipation to nonlinearity is estimated.

Faulted regions associated with geothermal areas are assumed to be composed of rock which has been heavily fractured within the fault zone by continuous tectonic activity. The fractured zone is modelled as a vertical, slender, two-dimensional channel of saturated porous material with impermeable walls on which the temperature increases linearly with depth. The development of an isothermal slug flow entering the fault at a large depth is examined. An entry solution and the subsequent approach to the fully developed configuration are obtained for large Rayleigh number flow. The former is characterized by growing thermal boundary layers adjacent to the walls and a slightly accelerated isothermal core flow. Further downstream the development is described by a parabolic system. It is shown that a class of fully developed solutions is not spatially stable.

The Lagrangian-history method in turbulence theory (Kraichnan 1977) is modified such that triple moments are expanded in functional powers of the Lagrangian covariance of the symmetric rate-of-strain field instead of the Lagrangian covariance of the velocity field. The simplest approximation which results corresponds to the abridged Lagrangian-history direct-interaction approximation. It is illustrated by application to the Lagrangian properties of a random velocity field whose Eulerian values are frozen in time. Then it is formulated for isotropic Navier-Stokes turbulence. The new approximation is expected to give reduced energy transfer in the dissipation range because the rate of strain along a fluid-element trajectory is statistically stationary in stationary homogeneous turbulence while the derivatives of the Lagrangian velocity with respect to initial position tend to grow and thereby have a longer correlation time. The correlation times of these two entities play corresponding roles in the new and old approximations for energy transfer, respectively.

Small amplitude, axially symmetric waves in a thin-walled viscoelastic tube containing a viscous compressible fluid are considered. Previous authors have found two modes of propagation for such waves but have studied them only in the low frequency, long wavelength limit. We show that there are infinitely many modes and study them at all frequencies. The appropriate dispersion equation was derived previously (Rubinow & Keller 1971) and analysed for an inviscid fluid. Now it is analysed for a viscous fluid. Asymptotic formulae for the propagation constant k are obtained for both low and high frequencies and for various ranges of the parameters characterizing the tube and the fluid. Special attention is paid to the case of a rigid tube and to parameter values that characterize the flow of blood in mammalian arteries. In addition, numerical results are obtained which complement the asymptotic formulae. Graphs of the velocity c vs. the frequency ω are presented for various modes and for various ranges of the parameters. Transmission-line equations and formulae for the impedance and compliance of the fluid-tube system are obtained, together with asymptotic and numerical results.

Several models are developed for the high-wavenumber portion of the spectral transfer function of scalar quantities advected by high-Reynolds-number, locally isotropic turbulent flow. These models are applicable for arbitrary Prandtl or Schmidt number, v/D, and the resultant scalar spectra are compared with several experiments having different v/D. The ‘bump’ in the temperature spectrum of air observed over land is shown to be due to a tendency toward a viscous-convective range and the presence of this bump is consistent with experiments for large v/D. The wavenumbers defining the transition between the inertial-convective range and viscous-convective range for asymptotically large v/D (denoted k* and k1* for the three- and one-dimensional spectra) are determined by comparison of the models with experiments. A measurement of the transitional wavenumber k1* [denoted (k1*)s] is found to depend on v/D and on any filter cut-off. On the basis of the k* values it is shown that measurements of β1 from temperature spectra in moderate Reynolds number turbulence in air (v/D = 0·72) maybe over-estimates and that the inertial-diffusive range of temperature fluctuations in mercury (v/D ≃ 0·02) is of very limited extent.