Shock waves have been observed travelling in a closed gas-filled tube when the gas is excited by a piston operating at half the fundamental frequency of the tube. Linear theory predicts a continuous periodic solution, while its first correction in a regular expansion is unbounded at such a quadratic resonant frequency. To take account of the intrinsic nonlinearity of travelling waves, a finite-rate theory of resonance is necessary. The periodic motion is then calculated from discontinuous solutions of a functional equation. Two of the three weak-shock conditions and the entropy condition are inherent in the functional equation, and hence the addition of the equal-area rule to fit shocks ensures uniqueness of the solutions.

This paper complements an earlier paper by Bentwich & Miloh in which the matched asymptotic expansion type of solution is presented for an unsteady low-Reynolds-number flow past a sphere when a constant rectilinear velocity is suddenly imparted to the sphere. It is shown that the matching procedure proposed in the earlier paper is incomplete. The present paper represents a complete procedure for successful matching; the drag of the sphere is calculated up to the term of O(Re2 In Re) using the new procedure.

The wave motion created by a small obstacle placed in a viscous liquid curtain which falls steadily between two vertical guide wires is studied experimentally. The disturbances introduced by the obstacle propagate in the curtain to form two distinctive stationary lines of constant phase; one corresponds to the sinuous mode and the other to the varicose mode. The observed wave motion compares very well with that predicted by the theory of Lin (1980). The observed angle between the tangent at any point on the line of constant phase and the vertical are used to infer the dynamic surface tension of a rapidly moving surface. A considerable difference between the dynamic surface tension and the usual static surface tension is found for a liquid solution. However, no measurable difference is found for a pure liquid at the flow rates used in our experiments.

The head of an intrusive flow advancing along the interface between two fluids is studied experimentally when the two layers are of equal depth and the density of the intrusion is the mean of the two densities. The dependence of the flow on the interface thickness and the depth of the intrusion is determined. When the interface is very thin the flow is similar to the nominally inviscid gravity currents observed by Britter & Simpson (1978).

The stability of pipe flow to axisymmetric disturbances is studied by direct numerical simulation of the incompressible Navier-Stokes equations. There is no evidence of finite-amplitude equilibria at any of the wavenumber/Reynolds number combinations investigated, with all perturbations decaying on a time scale much shorter than the diffusive (viscous) time scale. In particular, decay is obtained where amplitude-expansion perturbation techniques predict equilibria, indicating that these methods are not valid away from the neutral curve of linear stability theory.

The thermal response of hot-film anemometers to fluid velocity fluctuations is investigated for low-Prandtl-number fluids. A quartz-coated hot-film probe with a diameter of 0[sdot ]002 inches and an aspect ratio of 20 was oscillated in a horizontal plane while immersed in a steadily rotating tank of mercury. The probe was oscillated sinusoidally from 2 to 1200 Hz with a vibrator. The amplitude of velocity fluctuation was regulated to about 20 % of the mean flow within a Peclet-number range of 0[sdot ]1–1[sdot ]0.

The findings concur with the theoretical results obtained numerically and published earlier by Malcolm & Verma (1973) and compare well with some results of other researchers. The results confirm that the sensitivity of the hot-film probes is inhibited at low Peclet numbers, even at quite low frequencies in liquid metals owing to their very low Prandtl numbers.

Two important effects are noticed: (a)The amplitude of fluctuation is attenuated and the degree of attenuation depends upon a non-dimentional quantity αf/$\macr{U}$2, for the range of Peclet numbers considered, whereL α is the thermal diffusivity, f is the frequency of the fluctuations and $\macr{U}$ is the free-stream velocity, in compatible units. The amplitude is attenuated by 10 % and 90 % at αf/$\macr{U}$2 values of 0[sdot ]02 and 4[sdot ]0 respectively. (b)There is a phase lag in the hot-film probe signal with respect to the true velocity of the fluctuation which is somewhat the same as that in potential flow at low frequencies, but is considerably higher than that in potential flow at higher frequencies. The measured lag does not level off asympotically at high frequencies as noted in the numerically obtained results for potential flow.

Corrections may be made to unsteady velocity measurements in low Prandtl number fluids to account for the above effects with some confidence depending upon the value of the αf/$\macr{U}$2 quantity. The results of the investigation are of more general interest, in that the hot-film sensor can be considered as a model of a long circular cylinder in a flow at low to moderate Peclet numbers.

This paper is a summary of the Third Beer-Sheva Seminar on magnetohydrodynamic (MHD) flows and turbulence, held in Israel in March 1981 with 67 participants from 9 countries. Reviews and research papers were presented on fundamental MHD and turbulence studies, both theoretical and experimental, including two-phase phenomena, and on applications of MHD to electrical generation (especially in two-phase systems), electromagnetic pumps, flow-couplers and flowmeters, thermonuclear fusion and a range of metallurgical problems, many involving free surfaces.