Stationary vorticity mode in linear acoustics
= 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.