The properties of a standard hydraulic jump depend critically on a Froude number F r defined as the ratio of the flow velocity to the gravity waves speed. In the case of a horizontal circular jump, the question of the Froude number is not well documented. Our experiments show that F r measured just after the jump is locked on a constant value that does not depend on flow rate Q, kinematic viscosity ν and surface tension γ. Combining this result to a lubrication description of the outer flow yields, under appropriate conditions, a new and simple law ruling the jump radius R J :in excellent agreement with our experimental data. This unexpected result asks an unsolved question to all available models. PACS numbers: 47.55.N-, Interfacial flows, 47.55.nb, Capillary and thermocapillary flows.

The displacement of water molecules associated with the flow of water inside a nonconsolidated packing of 800 μm OD glass spheres has been measured by a pulsed gradient NMR technique. Using a stimulated spin-echo sequence, mean displacements of up to 300 μm corresponding to measurement times of up to 200 ms can be analyzed. The measurement can be quantitatively calibrated using the pure molecular self-diffusion of water at zero flow conditions. For molecular displacements much smaller than the pore size, the distribution of the flow velocity component along the mean flow direction is determined at Reynolds numbers high enough so that longitudinal molecular diffusion is negligible. An exponential decay of the probability distribution of the displacements is observed at large distances. The results are very similar to those obtained by numerical solution of the Stokes equation in random sphere packings. At longer displacement distances, a secondary peak of the displacement distribution is observed: It is interpreted as the first step toward the transition toward classical dispersion at displacements much larger than the pore size. The influence of molecular diffusion and of the heterogeneities of the magnetic permeability also are discussed.

We report experiments on liquid curtains falling between two vertical wires. The flow is mainly driven by gravity, so that the Weber number (We) (ratio of momentum flux to twice the surface tension) is close to zero at the top of the curtain and increases downstream, with the possible existence of a location where We equals 1 (which turns out to be a singular point in the sheet, in terms of waves propagation). In the present paper, we focus on the curtain response to localized perturbations, i.e., formation of either surface waves or free edges behind a thin needle touching the curtain, with a special emphasis to what happens near the break-up limit. We extract and compare the shapes of two kind of “wakes” left behind the obstacle: classical triangular wake of standing sinuous waves and stationary hole involving two free edges pinned on the needle. It is found that these two wakes are very similar for high enough We, but behave very differently when We reaches 1 from above; the sinuous wake disappears, while the “hole wake” still exists, and its shape becomes rounded. Below We=1, the hole can either stay stable, oscillate or expand and break the curtain. We provide exact analytical expressions for stationary free-edges that compare very well with experiments.