## 1pPA13. Modeling of nonlinear shock wave propagation in dispersive media with nearly linear frequency dependence of attenuation.

### Session: Monday Afternoon, December 2

### Time: 5:00

**Author: Vera A. Khokhlova**

**Location: Dept. of Acoust., Phys. Faculty, Moscow State Univ., Moscow 119899, Russia**

**Author: Oleg A. Sapozhnikov**

**Location: Dept. of Acoust., Phys. Faculty, Moscow State Univ., Moscow 119899, Russia**

**Author: Michalakis A. Averkiou**

**Location: Univ. of Washington, Seattle, WA 98105**

**Author: Mark F. Hamilton**

**Location: Univ. of Texas, Austin, TX 78712-1063**

**Abstract:**

Acoustic wave propagation is generally weakly dispersive, and thus
frequency dependence of the sound speed is usually considered negligible.
However, if absorption does not have a quadratic frequency dependence,
dispersion will be important. For broadband signals such as shock waves,
dispersion may influence the waveform distortion and the corresponding nonlinear
attenuation. These effects are important for the case of biological media which
have absorption laws obeying a nearly linear frequency dependence over a wide
frequency range. The sound-speed dispersion can be reconstructed from a given
attenuation law by the use of the Kramers--Kronig relations. Because attenuation
is typically specified over only a restricted frequency range, it is not
possible to uniquely reconstruct the dispersion law, and thus an appropriate
approximation of the absorption coefficient at high frequencies is required. The
effective dispersion law is reconstructed for various absorption models:
multiple relaxation, piecewise linear, and power-law absorption. Theoretical
modeling of nonlinear wave propagation is performed using a modified spectral
approach. The propagation of both shock pulses and periodic sawtoothlike waves
is investigated. The results show that it is important to account for dispersion
when modeling propagation of broadband finite-amplitude waves. [Work supported
by NATO CRG, FIRCA, and RFBR.]

ASA 132nd meeting - Hawaii, December 1996