Arrays of coupled unstable water jets

Abstract

We consider the interaction of oscillators with a noninstantaneous coupling ensured by slow traveling waves. Actually, this particular type of coupling is observed in an experimental system which consists of a bidimensional network of vertical water jets in the presence of a water–air interface: jets rotate and their motions are coupled together through surface waves. Depending on the free jet rotation frequency and of the geometry of the array, this system exhibits various collective modes where the jets synchronise themselves to form phase patterns, rendered sometimes complex by the fact that each jet can rotate clockwise or anticlockwise. A model is proposed which explains many features of the experiment. The dynamics of jets is described by amplitude equations with retarded interaction terms. An interesting point is that the dispersion relation of the surface waves renders the interaction term non linear in a subtle way since its effect depends on the frequency of the limit cycle of the array. This model allows one to determine the possible phase patterns and provides a criterion for the selection process.