Acoustic Streaming - Origin: A Body Force Due To Acoustic Absorption in The Fluid

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 . The vibration part 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:

\overline{\rho}{\partial_{t} \overline{u}_i}+\overline{\rho} \overline{u}_j {\partial_{j} \overline{u}_i}=-{\partial \overline{p}_{i}}+\eta {\partial^2_{jj} \overline{u}_i}-{\partial_j}(\overline{\rho v_i v_j} ).

The steady streaming originates from a steady body force that appears on the right hand side. This force is a function of what is known as the Reynolds stresses in turbulence . 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, the quadratic non-linearity generates a steady force proportional to .

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