At most air-liquid interfaces stressed by a static perpendicular electric field, a monolayer of charge is induced that shields the field from the liquid. For relatively inviscid and highly insulating liquids, the electrohydrodynamics can dominate in determining the monolayer and field distributions associated with additional dynamic field components. Electric shear stresses lead to a convection of surface charge that distorts the field, much as though the liquid were conducting. A configuration for studying the monolayer dynamics is developed in which a uniform field is used to induce a uniform monolayer on the interface of a liquid layer having thickness c. Superimposed is a travelling wave of potential \[ {\rm Re}\,\hat{V}_0\exp i(\omega t - kz), \] imposed in a plane parallel to, and a t a distance a above, the interface. Mechanisms for charge redistribution are reflected in the frequency response of the field transmitted through the interface to a second plane bounding the liquid layer from below. A model is developed which accounts for the self-consistent electromechanics in terms of the lumped surface parameters of surface charge σ0 and surface mobility bs, and a bulk conductivity σ. According to this model, interfacial convection dominates a t low frequencies in attenuating the field induced below the interface. For layers which are thick compared with the viscous skin depth, there is a resonance in the response a t the frequency \[ \begin{array}{@{}l@{\qquad\qquad}c@{}} &\omega = \omega_i(2^{\frac{1}{3}}),\\ {\rm where} & \omega_i = \{k\sigma^2_0/\epsilon_0(\rho\eta)^{\frac{1}{2}}[\cot {\rm h}\, ka +(\epsilon/\epsilon_0)\cot {\rm h}\,kc]\}^{\frac{2}{3}} \end{array} \] and ρ, η, ε0 and ε are the liquid mass density, liquid viscosity, and permittivities of air and the liquid, respectively. Surface and bulk conduction, characterized by the relaxation time \[ \tau_b = \epsilon_0(\cot h\,ka + (\epsilon/\epsilon_0)\cot {\rm h}\,kc)/[\sigma_0b_sk + \sigma\cot {\rm h}\,kc], \] result in a broadening of the resonance which is appreciable even for ωτb ∼ 5. At frequencies high compared with both wi and i/Tb) the response is uninfluenced by the charge monolayer. Experiments substantiate the electroviscous resonance. A time-average surface force density, and associated steady convection of the liquid, is also theoretically shown to be a consequence of the phase shifts caused by the electroviscous resonance. This is qualitatively demonstrated by measurement of the steady shear stress induced on the plane bounding the liquid from below.

The stability of laminar axisymmetric jets and wakes, the two prominent examples of free shear layers, is investigated with respect to linear azimuthally periodic disturbances. The complete viscous disturbance equations are integrated numerically and the eigenvalues are obtained by matching the numerically advanced solutions to the asymptotic solutions at a large radius. Both spatial and temporal stability are examined for inviscid and viscid flows. It is found that the critical Reynolds number for the jet and the wake are not much different while the amplification rates for the wake become considerably greater than those for the jet as the Reynolds number increases. The axisymmetric shear-layer flows also seem to be more stable than the corresponding plane flows.

The stability of a potential vortex with a rotating and a non-rotating jet core is analysed. Eigenvalues are calculated numerically for different values of the ratio of the strength of the vortex to the axial velocity. These results show that the potential vortex becomes unstable in the presence of a jet.

The interaction of a vortex ring with a sharp density interface is investigated in the laboratory. Attention is restricted to the case where the Froude number based on the density difference across the interface, the velocity of propagation of the ring normal to the interface and the diameter of the ring is less than unity. It is found that the depth of maximum penetration of the ring, and the diameter of the region of contact between the ring and the interface, are functions of the Froude number. A simple model of the ring-interface interaction which accounts for the observed motion is proposed. This model is then used to calculate the volume rate of entrainment produced by the vortex rings. It is found that this rate of entrainment is proportional to the cube of the Froude number, a result which agrees with measurements of entrainment across density interfaces caused by grid-generated turbulence (Turner 1968) and by a plume incident on the interface (Baines 1973). Thus the vortex ring would appear to be a good approximation to a turbulent eddy in these situations. The main feature of the model is that it identifies the way in which the kinetic energy of the turbulence is converted into potential energy by entraining fluid across the interface. In particular, it indicates that the essential force balance is inertial, and that it is possible to discuss entrainment across a sharp density interface without explicitly invoking either viscosity or molecular diffusion.

Additional experimental studies of the structure of Reynolds stress which supplement our previous work (Willmarth & Lu 1971) are reported. The velocity at the edge of the viscous sublayer is again used as a detector signal for bursts and sweeps. The signal uv obtained from an X-wire probe at various locations is conditionally sampled and sorted into four quadrants of the u, v plane. Using this method it is found that, when the velocity uw at the edge of the viscous sublayer becomes low and decreasing, a burst occurs. On the other hand, a sweep occurs when uw becomes large and increasing. The convection speeds of the bursts and the sweeps are found to be equal and are about 0·8 times the local mean velocity and 0·425 times the free-stream velocity at a distance y ≈ 0·15δ* from the wall (δ* is the displacement thickness). Throughout the turbulent boundary layer, the bursts are the largest contributors to $\overline{uv}$ with the sweeps the second largest. On average, the bursts account for 77% of $\overline{uv} $, while the sweeps provide 55%; the excess percentage over 100% is due to the other small negative contributions.

Characteristic mean time intervals are obtained for both bursts and sweeps from certain unique features of the measurements of fractional contributions to $\overline{uv}$ from different events. Both mean time intervals are approximately equal and constant for most of the turbulent boundary layer. The scaling of the mean time interval between bursts with outer flow variables is confirmed. It is suggested that many of the features of the fluctuating flow revealed by the measurements may be explained by convection past the measuring station of an evolving deterministic flow pattern such as the hairpin vorticity model of Willmarth & Tu (1967).

A mathematical model is proposed for steady two-dimensional flow around a submerged screen. The general problem analysed is the flow in a parallel-sided channel partially spanned by a screen, and the fluid is considered to be inviscid except at the screen, where the flow has the required pressure drop. The model is constructed by first replacing the screen with a distribution of sources and then manipulating the stream function for this flow so that the mass and momentum balances across the screen are satisfied. Consequently the model predicts a flow field which is realistic except for the expected discontinuity in velocity between the wake and external flow. In general, the governing equations must be solved numerically, but for the important case of a plane screen oriented normal or roughly normal to the approaching flow, an approximate analytical solution is possible. The accuracy of the model was ascertained by conducting wind-tunnel tests on screens of various solidities and orientations, and comparing the measured downstream velocity distributions with those predicted by the numerical and analytical solutions of the model. Overall, the theoretical results agree well with the experimental data, showing that the model is valid for screens of low and high solidity, in fact, for pressure drop coefficients up to 10. Comparisons with the work of others show that the proposed model is also accurate for the special cases of a screen submerged in an infinite flow field and of a screen spanning the full width of the channel.

The transition to turbulence in the convective flow of air between horizontal plates in a circular convection chamber has been investigated. Measurements of the heat flux and the instantaneous spatial temperature field were made simultaneously for a range of Rayleigh number Ra between 3 × 103 and 5 × 104. Ra could be varied by changing the vertical separation or the temperature difference between the plates. The temperature field was measured with either a horizontal or a vertical array of resistance wires mounted so that the flow field could be traversed at velocities much greater than flow velocities characteristic of thermal convection. Slope transitions in the heat flux were found at Ra = 9600 and Ra = 26000. Many measurements of the instantaneous horizontal distribution of temperature for Ra > RaT2 indicate a growth in amplitude of fluctuations with non-dimensional cyclical wavenumbers of 0·4 and greater. The probability of observing these high wavenumber fluctuations also increases as Ra becomes greater than RaT2. The horizontal wavelengths of the different types of temperature fluctuations are compared with the observations of others.

The spin-up of a thermally stratified Boussinesq fluid in a circular cylinder with insulated side walls is analysed under the conditions of strong stratification (Brunt-Väisälä frequency N [Gt ] rotation frequency Ω) and small Prandtl number. An earlier paper (Sakurai, Clark & Clark 1971) showed that complete spin-up is achieved in the Eddington-Sweet time. The present work considers in detail the spin-up transients corresponding to shorter time scales.

The analysis reveals a complicated system of merging and bifurcating horizontal layers in the interior flow. Following the spin-up of the cylindrical container, a rotational shear layer, of the kind discovered by Holton (1965), forms near each horizontal boundary. At the same time, a thermal boundary layer begins diffusing outward from each boundary. When the thermal layer reaches the shear layer, the two merge and form a higher order layer, which diffuses at a rate proportional to t¼. At a later time, the layer splits into a steady layer and another diffusing layer, this time following a t½ law. One important conclusion from the analysis is that the lifetime of the rotational shear layer is not great: it is of order (Ω/N)2 (R2/χ), where R is the radius of the cylinder and χ is the thermal diffusivity.

The problem of computing the angular velocity from the poorly converging series is dealt with in some detail, and graphs are given of representative values. The results show that, for spin-up, there are appreciable adverse gradients of angular momentum near the side wall, and thus there is some question about the stability of the spin-up configuration.

Finally, a discussion is given of continuous spin-up of the container and the results are applied qualitatively to the solar spin-down problem. The principal conclusion is that the Ekman time scale is unimportant in the solar case.

A Poiseuille-flow problem in a cylindrical capillary in the whole range of Knudsen numbers with incomplete tangential momentum accommodation of molecules incident on the wall has been worked out. The linear non-homogeneous integral equation for the macroscopic gas velocity flow has been solved by the Bubnov-Galerkin method. For a limited range of Knudsen numbers, generally known results have been obtained.

An experimental investigation of the rare gases helium, neon and argon in the range of Knudsen numbers 103−10−3 has been made on packets consisting of 10 and 100 glass capillaries with molten walls. Comparison of theoretical and experimental data enables us to define both slip constants and tangential momentum accommodation coefficients. In the free-molecule flow regime the accommodation coefficients are 0·935, 0·929 and 0·975 for helium, neon and argon, respectively. In the viscous slip-flow regime these coefficients are equal to 0·895, 0·865 and 0·919, respectively. This difference in the tangential momentum accommodation coefficients is, most probably, due to the variable density of adsorbed molecules coating the capillary wall. Gas viscosity coefficients which coincide with those of Kestin within 0.5% have also been calculated. Argon was used as the calibrating gas.

An analytic expression is found for an infinite subset of the coefficients of the perturbation expansion. They are the coefficients of the terms most rapidly varying at each order, which are also the first terms in the expansion of each Fourier coefficient. The sum of these terms gives a nonlinear approximation to the solution. At greatest height this approximation has a profile with a 90° corner.

An asymptotic description is proposed for supersonic laminar flow over a wedge or a backward-facing step, for large Reynolds number and for a base or step height which is small compared with the boundary-layer length. The analysis is carried out for adiabatic wall conditions and a viscosity coefficient proportional to temperature. In a particular limit corresponding to a very thick boundary layer, a similarity law is obtained for the base pressure $\overline{p}_b$. For a thinner boundary layer an asymptotic form for $\overline{p}_b$ is obtained which shows the dependence on the parameters explicitly and which permits good agreement with experiment. This latter result is based on an inviscid-flow approximation for the corner expansion and for reattachment, with viscous forces important primarily in a thin sublayer about the dividing streamline. A prediction of the pressure distribution at reattachment is given and the result is compared with experimental pressure distributions.