Breaking time reversal symmetry with coriolis mean flow systems

Abstract

One way to break time reversal symmetry is to have a moving wave propagation medium. If the acoustic wave vector and the moving fluid velocity are collinear, such as the one created by Fluery et al. (Science, 343, 2014) we can use the wave vector shift caused by the fluid flow to break reciprocity. An alternative approach we have taken is to use a fluid velocity field which enters the differential equation of the system as a cross product term with the wave vector. A circular field in which the fluid velocity increases radially has a Coriolis acceleration term. In this system, the acoustic wave enters from the central wall and exits from the perimeter wall. Equations of conservation of mass and momentum, after linearization can be simplified to: (∂/∂t+V.▽)P+ρC2▽.(u+V) = 0, ρ∂/∂t(u+V)+ρ(V.▽)u+ρ(u.▽)V+ρ(V.▽)V+▽P = 0, in which u is the particle acoustic velocity and V = rωeθis the fluid velocity due to the rotational velocity field. It can be shown that the third term in the second equation can be simplified as:ρωek×u. This term Coriolis acceleration induces nonreciprocity. In this work, we solved the differential equation numerically and investigated the effect of fluid velocity on the nonreciprocity factor.