ИСТИНА

Parametric generation of low-frequency sound in nonlinear sound beams of high-amplitude and high-frequency pump waves has been a subject of intensive research in the past. There is continuing interest in this phenomenon caused by modern applications in underwater acoustics, aeroacoustics, and in medical ultrasound. Parametrically generated beam of a difference-frequency wave is advantageously characterized by high directivity, low side lobes, and broad frequency bandwidth. However, low efficiency is the main factor precluding widespread use of such technology. In theory, higher efficiency is expected for interactions of strongly nonlinear pump waves, when shock fronts are developed in acoustic pressure waveform. Numerical modeling of nonlinear propagation of strongly distorted waves becomes extremely difficult due to the presence of a large number of spectral components, being harmonics of the difference frequency. In this study a new efficient numerical algorithm is developed for fully nonlinear three-dimensional (3D) simulation of a difference-frequency acoustic beam resulting from interactions in initially biharmonic pump waves. Finite-difference frequency domain algorithm is based on the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation, where spectrum filtering method is adopted to sufficiently reduce the number of harmonics by discarding those that weakly contribute to generation of the difference-frequency wave. As a result of filtering, only dozens of spectral components are retained in the algorithm instead of thousands, and 3D simulations become feasible. As an example, the acoustic field generated by an underwater multi-element ellipsoidal array is simulated in free space and in a shallow-water waveguide. The efficiency and pressure distributions of the difference-frequency wave at increasing excitation levels are analyzed and compared with existing simplified analytical solutions. It is shown that the percentage of the total acoustic power converted to the difference-frequency wave from pump waves increases at high power outputs without saturation.