Consider a gas flow with a uniform velocity field  and having a pressure , density , entropy  and sound speed . Now we  add small perturbations to these variables, which are denoted with a symbol . The perturbed variables being small quatities satisfy linearized form of the Euler equations, which is given by
where in the continuity equation, we have used the relation  (since  and ) and the used the entropy equation to simplify it. Taking perturbations to be of the plane-wave form , the linearised equations can be reduced to algebraic equations
The last equation shows that either , which corresponds to sound waves in which entropy does not change or . The later condition indicating that perturbations are carried by the gas corresponds to the entropy-vortex wave. In this case, we have
where  is the vorticity perturbation. As we can see, the entropy perturbation  and the vorticity perturbation  are independent meaning that one can have entropy waves without vorticity waves or vorticity waves with entropy waves or both entropy and vorticity waves.
In non-reacting mutlicomponent gas, we can also have compositional perturbations since in this case, , where  is the mass fraction of ith specices of total  chemical species. In the entropy-vorticity wave, we have then