Acoustic second harmonic generation from rough surfaces under shear excitation in liquids.

Emission of compressional acoustic waves at the second harmonic frequency (second harmonic generation, SHG) is possible from rough surfaces undergoing oscillatory shear in liquids. This nonlinear response is a consequence of the inertial term in the Navier-Stokes equation. On a corrugated surface, the streamlines of the sheared liquid are not strictly parallel to the surface, leading to variation of pressure along the streamlines and a concomitant Bernoulli pressure. Being quadratic in speed, the Bernoulli pressure contains a static term and a term at the second harmonic frequency, 2omega. Pressure fluctuations at 2omega generate compressional waves.