An evaluation of the effectiveness of the VITA, Quadrant, TPAV, U -level, Positive slope, and VITA with slope burst-detection algorithms has been done by making direct comparisons with flow visualization. Measurements were made in a water channel using an X-type hot-film probe located in the near-wall region. Individual ejections from bursts which contacted the probe were identified using dye flow visualization. The effectiveness of each of the detection algorithms was found to be highly dependent on the operational parameters, i.e. threshold levels and averaging or window times. These parameters were adjusted so that the number of events detected by each of the algorithms corresponded to the number of ejections identified by flow visualization, while the probability of a false detection was minimized. Comparing the detection algorithm using these optimum parameter settings, the Quadrant technique was found to have the greatest reliability with a high probability of detecting the ejections and a low probability of false detections. Furthermore, it was found that the ejections detected by the Quadrant technique could be grouped into bursts by analysing the probability distribution of the time between ejections.

This paper presents a detailed quantitative model of osmotic fine structure for both permeable and semi-permeable membranes in dilute bathing solutions. The analysis differs from all previous studies in that it treats for the first time, albeit in an approximate manner, the detailed three-dimensional hydrodynamic interaction of the particles in the entrance and exit regions and the coupling of the convective—diffusive effects in these regions with those in the interior of the pore. Reasonable interpolations between various asymptotic formulas are used to derive the tensorial components of the particle diffusivity and the slip between the fluid and particle phases as functions of position throughout the entire flow field. The solutions show that the entrance and exit regions in the case of permeable membranes can have a significant effect on the osmotic solvent flux q for small particles in short pores although changes in the overall reflection coefficient are small. This is due to the nonlinear sweeping effect of convection at the higher osmotic-flow rates. For semi-permeable membranes the predictions of the model support the hypothesis of Mauro (1957) and Ray (1960) that there is a region of near-discontinuity in pressure and concentration at the plane of the pore entrance and the sweeping effects of convection on the concentration profile are very minor for the dilute solutions studied herein. In contrast, the solutions for the permeable membrane clearly show the existence of three-dimensional unstirred regions which extend two-to-three pore radii from the pore openings. These solutions form the ubstructure of the much thicker one-dimensional unstirred layer described by Dainty (1963) and Pedley et al. (1978). It is shown that when the porosity is low (such as in most biological membranes), the wall concentration in Pedley's solution is the far-field concentration for the entrance/exit solutions presented herein.

A series of large-eddy simulations of plane Poiseuille flow are discussed. The subgrid-scale motions are represented by an eddy viscosity related to the flow deformation — the ‘Smagorinsky’ model. The resolution of the computational mesh is varied independently of the value of the coefficient Cs which determines the magnitude of this subgrid eddy viscosity. To ensure that results are from a statistically steady state unrealistic initial conditions are used and sufficient time is allowed for the flow to become independent of the initial conditions. In keeping with previous work it is found that for large Cs the resolved-scale motions are damped out; however, this critical value of Cs is found to depend on the mesh resolution. Only with a fine mesh does the value of Cs previously found to be appropriate for homogeneous turbulence (≈ 0.2) give simulations with sustained resolved-scale motions. The ratio l0/δ of the channel width 2δ to the scale of the ‘Smagorinsky’ mixing length, l0 = CsΔ where Δ is a typical mesh spacing), is found to be the key parameter determining the ‘turbulent’ eddy-viscosity ‘Reynolds number’ of the resolved-scale motions. A fixed value of 10 is regarded as determining the separation of scales into resolved and subgrid. The value of l0 is regarded as a measure of numerical resolution and values of Cs less than about 0.2 correspond to inadequate resolution.

An investigation has been conducted of the three-dimensional flow associated with the inlet-vortex phenomenon. Quantitative measurements were made of inlet– and trailing-vortex circulation and position. Flow visualization was used to obtain information on the overall structure of the vorticity field. It is shown that the inlet vortex and the trailing vortex have essentially equal and opposite circulation. In addition, the production of vorticity, due to vortex stretching, is the mechanism by which both of these are maintained. A limited parametric study was also conducted to define the circulation and position (in the inlet) of the inlet vortex, for parameters of practical engineering interest.

A compact (streamwise scale small compared with characteristic length) pressure distribution, which models a ship and is equivalent to a compact bottom deformation of cross-sectional area A,exerts a net vertical force ρgA on, and advances with speed U over, the free surface of a shallow canal of upstream depth H. The hypotheses of weak dispersion, weak nonlinearity and steady, two-dimensional flow in the reference frame of the force yield, through a generalization of Rayleigh's (1876) formulation of the (free) solitary-wave problem, a cnoidal wave downstream of the force matched to a null solution on the upstream side if $|A|/H^2 < \frac{2}{9}(1-{\mathbb F}^2)^{\frac{3}{2}}\ll 1 $ (Cole 1980) or a cusped solitary wave if $|A|/H^2 < \frac{4}{9}({\mathbb F}^2-1)^{\frac{3}{2}}\ll 1 $, where ${\mathbb F}\equiv U/(gH)^{\frac{1}{2}}$ is the Froude number. The hypothesis of steady flow presumably fails in the transcritical range $1 - (9A/2H^2)^{\frac{2}{3}} < {\mathbb F}^2 < 1 + (9A/4H^2)^{\frac{2}{3}}$, at least under the restrictions of weak dispersion and weak nonlinearity. Comparisons with experiment and numerical solutions of the nonlinear initial-value problem provide some confirmation of the cusped solitary wave but suggest that the cnoidal wave may be unstable in the absence of dissipation.