Acoustic streaming

Acoustic streaming is a steady flow in a fluid driven by the absorption of high amplitude acoustic oscillations. This phenomenon can be observed near sound emitters, or in the standing waves within a Kundt's tube. Acoustic streaming was explained first by Lord Rayleigh in 1884.
It is the less-known opposite of sound generation by a flow.
There are two situations where sound is absorbed in its medium of propagation:
Origin: a body force due to acoustic absorption in the fluid.
Acoustic streaming is a non-linear effect. 
We can decompose the velocity field in a vibration part and a steady part formula_5.
The vibration part formula_6 is due to sound, while the steady part is the acoustic streaming velocity (average velocity).
The Navier–Stokes equations implies for the acoustic streaming velocity:
The steady streaming originates from a steady body force formula_8 that appears on the right hand side. This force is a function of what is known as the Reynolds stresses in turbulence formula_9. The Reynolds stress depends on the amplitude of sound vibrations, and the body force reflects diminutions in this sound amplitude.
We see that this stress is non-linear (quadratic) in the velocity amplitude. It is non-vanishing only where the velocity amplitude varies. 
If the velocity of the fluid oscillates because of sound as formula_10, the quadratic non-linearity generates a steady force proportional to 
formula_11.
Order of magnitude of acoustic streaming velocities.
Even if viscosity is responsible for acoustic streaming, the value of viscosity disappears from the resulting streaming velocities in the case of near-boundary acoustic steaming.
The order of magnitude of streaming velocities are:
with formula_13 the sound vibration velocity and formula_14 along the wall boundary. The flow is directed towards decreasing sound vibrations (vibration nodes).