New exact relations for steady irrotational two-dimensional gravity and capillary surface waves.

Steady two-dimensional surface capillary-gravity waves in irrotational motion are considered on constant depth. By exploiting the holomorphic properties in the physical plane and introducing some transformations of the boundary conditions at the free surface, new exact relations and equations for the free surface only are derived. In particular, a physical plane counterpart of the Babenko equation is obtained.

Observation of star-shaped surface gravity waves.

We report a new type of standing gravity wave of large amplitude, having alternatively the shape of a star and of a polygon. This wave is observed by means of a laboratory experiment by vertically vibrating a tank. The symmetry of the star (i.

Note on the velocity and related fields of steady irrotational two-dimensional surface gravity waves.

The velocity and other fields of steady two-dimensional surface gravity waves in irrotational motion are investigated numerically. Only symmetric waves with one crest per wavelength are considered, i.e.

New standing solitary waves in water.

By means of the parametric excitation of water waves in a Hele-Shaw cell, we report the existence of two new types of highly localized, standing surface waves of large amplitude. They are, respectively, of odd and even symmetry. Both standing waves oscillate subharmonically with the forcing frequency.

Response of a noncohesive packing of grains to a localized force: deviation from continuum elasticity.

In order to characterize the mechanical behavior of grain piles, we investigate the response of a noncohesive two-dimensional packing of cylinders submitted to a localized force. By means of image processing, we obtain an accurate measurement of the individual grain displacements in the reversible regime of deformation. The measured displacement field deviates unambiguously from the predictions of linear elasticity and of other theoretical descriptions commonly used to model the behavior of cohesionless soils in civil engineering or in soil mechanics.