Bernard Molin

Experimental study of the wave propagation and decay in a channel through a rigid ice-sheet

Abstract Experiments are carried out in a wave flume, to study wave propagation in a narrow channel along a barge-like structure, attached to one of the side-walls. By geometric symmetry this is equivalent to a channel through a rigid ice-sheet, in a tank twice as wide. When both the draft and width of the channel are small, the wavelength increases dramatically as the waves enter into it. It is checked that this modification of the wavelength is in agreement with the theory given by Molin [J. Fluid Mech. 430 (2001) 27]. The slow decrease in amplitude of the waves, as they propagate along the channel, is related to losses of energy due to flow separation at the lower edges of the channel. These effects are expressed via some kind of drag force, involving a drag coefficient which is determined from amplitude measurements along the channel. Results are given for different values of the amplitude over width ratio. The present results have some relevance for the design of new offshore barge concepts, with large rectangular moonpools.

The role of tertiary wave interactions in wave-body problems

Results from experiments on wave interaction with a rigid plate are reported. The plate is projected from one of the sidewalls of the basin. The sidewall acts as a plane of symmetry, thereby doubling the widths of the plate and of the basin. The tests are carried out in regular waves of varying periods and steepnesses. At wavelengths comparable with the width of the plate, strong run-ups are observed at the plate-wall intersection, increasing with the wave steepness. These run-ups take many wave cycles to develop, with no steady state being reached in some cases. It is advocated that these phenomena result from third-order interactions between the incident and reflected wave fields, over a wide area on the weather side of the plate. A theoretical model is proposed, based on tertiary wave interaction. A parabolic equation is derived that describes the transformation of the incoming waves through their interaction with the reflected wave field. A steady-state solution is obtained through iterations. Results from the theoretical model are compared with the experimental data, with good agreement.

On viscous forces on non-circular cylinders in low KC oscillatory flows

Abstract This note provides a reanalysis of a result given by Bearman, Downie, Graham and Obasaju in 1985. It deals with viscous forces on fixed two-dimensional bodies in oscillatory flow, in the asymptotic case of low Keulegan–Carpenter number ( KC ) and high Stokes parameter ( β ). The flow is assumed to be laminar and attached (sharp corners are excluded). Bearman et al. show that, whatever the body shape, skin friction and pressure forces contribute equally to the viscous force, generalizing the result given earlier by Stokes in 1851 (see also Wang, 1968) for circular cylinders. Here we show that their conclusion is ill-founded and that, presumably, it is only in the case of particular geometries that both components are equal.