Enhancement of the Benjamin-Feir instability with dissipation

Thomas Bridges (1) , Frédéric Dias (2)

1 Department of Mathematics
2 CMLA - Centre de Mathématiques et de Leurs Applications

It is shown that there is an overlooked mechanism whereby some kinds of dissipation can enhance the Benjamin-Feir instability of water waves. This observation is new, and although it is counterintuitive, it is due to the fact that the Benjamin-Feir instability involves the collision of modes with opposite energy sign (relative to the carrier wave), and it is the negative energy perturbations which are enhanced.

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Equations aux dérivées partielles [math.AP]; Physique Atmosphérique et Océanique [physics.ao-ph]

Thomas Bridges, Frédéric Dias. Enhancement of the Benjamin-Feir instability with dissipation. Physics of Fluids, 2007, ⟨10.1063/1.2780793⟩. ⟨hal-00170699⟩