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. 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:

Acoustic streaming is a non-linear effect. We can decompose the velocity field in a vibration part and a steady part ${\displaystyle {u}=v+{\overline {u}}}$. The vibration part ${\displaystyle v}$ 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 ${\displaystyle f_{i}=-{\partial }({\overline {\rho v_{i}v_{j}}})/{\partial x_{j}}}$ that appears on the right hand side. This force is a function of what is known as the Reynolds stresses in turbulence ${\displaystyle -{\overline {\rho v_{i}v_{j}}}}$. The Reynolds stress depends on the amplitude of sound vibrations, and the body force reflects diminutions in this sound amplitude.

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