The function of a healthy ureter is analyzed in terms of a fluid-mechanical model. To the extent that the Reynolds number is of the order of one, the fundamental equations are shown to reduce to those of the theory of lubrication. It is found that from the point of view of the pressure variation with time (the urometrogram) the important part of the peristaltic wave is the constricting part. For this reason this part of the wave is represented with an algebraic expression of the form h ∼ xn making it possible to find closed form solutions. Using Fourier analysis in defining the complete wave shape of the ureter it was also possible to obtain numerical solutions. For both cases it is shown that there is good agreement between the theoretical and experimental pressure distributions, this not being the case for sinusoidal wave shapes. An approximate equation for the flux is developed and a universal relation is presented connecting the maximum pressure, flux and kinematic behaviour of the ureter.

The persistence of the large vortices formed at the origin of wakes and mixing layers constitutes a kind of memory of initial conditions by the turbulence. In order to study the fading of this turbulence memory, and its effect on the rate of approach to the fully developed state, two wakes with different initial conditions have been examined experimentally. The wake of a sphere was compared with the wake of a porous disk which had the same drag, but did not exhibit vortex shedding. Measurements were made of the mean and fluctuating velocities, the anisotropy of the turbulence, and the intermittency. It was found that the wake of the sphere developed self-preserving behaviour more rapidly than the wake of the disk, and that even after both wakes became self-preserving there were differences between them in the structure of the turbulence and the scale of the mean flow. From this it is concluded that the behaviour of self-preserving wakes does not depend on the drag alone, but also on the structure of the dominant eddies. Generalizing these results, it is suggested that reported differences in the value of the entrainment constant of jets, wakes, and mixing layers are due to differences in the structure of the dominant eddies, rather than differences in the type of flow.

Turbulence measurements under the influence of a transverse magnetic field have been made at Purdue University's Magneto-Fluid-Mechanic Laboratory in a high aspect ratio channel. The Reynolds number range covered was 25000 ≤ Re 282000; the geometry and experimental conditions were such that the experiment approximated turbulent Hartmann flow. The aspect ratio of the channel was 5·8:1, its walls were electrically insulated and the working fluid was mercury. Measurements in the presence of a magnetic field were made of the skin friction coefficient, the mean velocity profiles, the turbulence intensity profiles (both u’ and v’) and the Reynolds stress profiles.A sudden change in the damping of the Reynolds stresses was manifested by a ‘hump’ in the curves of Cf versus M/Re taken with the Reynolds number held constant. This ‘hump’ occurs as a gentle rise and sudden drop to the Hartmann laminar line of the Cf data. Close examination of the $\overline{u^{\prime}v^{\prime}}$ data near the wall confirms this behaviour, indicating that the turbulent contribution to the shear stress is the controlling factor in this behaviour of Cf. The Reynolds stresses were completely suppressed to zero at high values of the magnetic field, though the turbulence intensities of u’ and v’ were not. The Reynolds stress data are fundamental in revealing the mechanisms which are at work during the suppression of turbulence by a magnetic field.It was also found that at high magnetic fields, when most of the turbulence was damped, the skin friction coefficient fell below the values predicted by Hartmann's (1937) laminar solution for high values of M/Re. This result was linked to the presence of ‘M-shaped’ velocity profiles in the direction perpendicular to both the magnetic field and the mean velocity vector. The presence of ‘M-shaped’ profiles has not previously been linked to a reduction in Cf.

An experimental investigation was conducted in a circular pipe to examine the influence of a transverse magnetic field on the structure of turbulent shear flow of a conducting fluid (mercury). In the present paper, part 1, mean velocity profiles, turbulence intensity profiles, velocity fluctuation spectra, axial pressure drop profiles, and skin friction data are presented which quantitatively exhibit the Hartmann effect and damping of the velocity fluctuations over a broad range of Reynolds numbers and magnetic fields. The results of heat transfer experiments will be reported by the authors in the following paper, part 2.

A semi-empirical theoretical analysis is presented describing the fully established turbulent channel flow of an electrically conducting fluid in the presence of a transverse and uniform magnetic field. The channel is assumed to be electrically insulated and of such geometry that two-dimensional flow prevails. The magnetic Reynolds number is assumed to be small so that the distortion of the externally imposed magnetic field is negligible. The paper establishes that a straightforward generalization of Prandtl's mixing length concept providing for the damping of the turbulent fluctuation is sufficient in predicting skin friction coefficients and velocity profiles over the whole range of Reynolds and Hartmann numbers for which experimental data are available.