Nonlinear ultrasound wave propagation in thermoviscous fluids

Traditional ultrasound theory is based on linear theory, however, for strongly focused sound beams, the pressure levels are sufficiently high to generate nonlinear waves. In thermoviscous fluids nonlinearity arises as a result of a nonlinear equation of state together with nonlinear advection. Furthermore, dissipation and dispersion is included in a combined third order term in the velocity potential.

We shall report on solitary pulse propagation with generation of higher harmonics of the emitted carrier wave frequency. The envelopes of the carrier wave and its first higher harmonics satisfy two coupled nonlinear partial differential equations, which resembles those of optical chi-2 materials. We think this result makes a remarkable link between nonlinear acoustics and nonlinear optics.

Finally our analysis reveal an exact kink solution to the nonlinear acoustic problem. This kink solution is interpreted as a shock wave formation, similar in nature to those of the simple Burgers equation. The results are relevant for medical ultrasound imaging.