 Stationary vorticity mode in linear acoustics

Linearizing inviscid barotropic flow about uniform rest gives ${\partial }_t(\nabla \times u)=0$, not automatically $\nabla \times u=0$. Irrotational linear acoustics therefore requires zero initial vorticity or restriction to the longitudinal acoustic mode. A time-independent divergence-free field, with zero pressure and density perturbations, is a nonacoustic solution of the linearized equations.