Why do some pressure fluctuations in fluids move at the speed of sound or faster and others do not? If we consider classical pressure waves, whose amplitude is small compared to the ambient pressure, they propagate ~ at the speed of sound. If strong pressure peaks occur, the shock waves can also propagate at supersonic speed. The reason is that the propagation speed increases with the pressure, which is also the reason for the steepening of the waves during propagation. The waves are quite non-linear.
Question: If you look at a wind turbine or a propeller under water, vortices etc. occur, which can lead to considerable pressure changes in the fluid over time and space, but propagate at subsonic speed. Why? On what variables does this depend?
 A: Short Answer:  Rotational flows.
Longer Answer:
Ignoring viscosity and assuming adiabatic processes in a homogeneous medium, linear fluid motion (small amplitudes) is fully described by the continuity and dynamic equations, given respectively by
\begin{gather}
  \nabla\cdot\vec v + \frac{1}{\rho c^2}\frac{\partial p}{\partial t} = 0, \\
  \nabla p + \rho\frac{\partial\vec v}{\partial t} = 0,
\end{gather}
where $\rho$ is the equilibrium mass density, $\vec v$ is the particle velocity, $c$ is the wave speed, and $p$ is the acoustic pressure, and the position vector and time are given by $\vec x$ and $t$.  Both of these equations are needed to obtain the wave equation (usually by cancelling the particle velocity to give an equation for the pressure).  However, it is important to note that the only spatial derivative of the particle velocity that is used is the divergence.  The divergence operator causes rotational flows to go to zero, and so these are not accounted for in the wave motion.
If the flow were purely rotational, then the continuity equation would lead to $p$ being independent of time, and so the dynamic equation can be integrated with respect to time to yield
$$ \vec v = \vec v_0(\vec x) - \frac{t}{\rho}\nabla p. $$
Thus, the particle velocity flow maintains its original pattern but may also advect with an external pressure gradient.
As I mentioned above, I assumed away nonlinear effects which are important when considering rotational flows.  I did not intend for this post to accurately describe rotational flow, but only to showcase how there can be fluid flows that are not affected by the wave equation.
