Arrays of coupled unstable water jets

We consider the interaction of oscillators with a noninstantaneous coupling ensured by slow traveling waves. Actually, this particular type of couplin g is observed in an experimental system which consists of a bidimensional n etwork of vertical water jets in the presence of a water-air interface: jet s rotate and their motions are coupled together through surface waves. Depe nding on the free jet rotation frequency and of the geometry of the array, this system exhibits various collective modes where the jets synchronise th emselves to form phase patterns, rendered sometimes complex by the fact tha t each jet can rotate clockwise or anticlockwise. A model is proposed which explains many features of the experiment. The dynamics of jets is describe d by amplitude equations with retarded interaction terms. An interesting po int is that the dispersion relation of the surface waves renders the intera ction term non Linear in a subtle way since its effect depends on the frequ ency of the limit cycle of the array. This model allows one to determine th e possible phase patterns and provides a criterion for the selection proces s. (C)2000 Elsevier Science B.V. All rights reserved.