Léo Touzo (U. Chicago)

Wave turbulence in odd fluids and odd solids

Weakly non-linear physical systems which support the propagation of waves may exhibit a phenomenon called wave turbulence (by analogy with the well-known hydrodynamic turbulence), characterized by a flux across scales of one or more conserved quantities (such as the energy). These so-called turbulent cascades are by definition out of equilibrium phenomena, which require forcing and dissipation at separated scales. They may arise in systems as diverse as water surfaces, the atmosphere, plasmas, elastic plates, or Bose-Einstein condensates. In this talk, I will consider situations in which such a turbulent cascade develops on top of a driven-dissipative steady-state, which is already out of equilibrium in the absence of forcing. I will focus on chiral active media, in which waves arise as a consequence of non-reciprocal responses known as odd viscosity and odd elasticity. Using a combination of analytical and numerical results, I will demonstrate how odd viscous fluids and odd elastic solids may both exhibit wave turbulent cascades with unique properties. In the case of the odd solid, this occurs despite the energy not being conserved by the medium, the cascading quantity being instead a new emergent conserved quantity of the system.