A top-rated journal The Journal of the Acoustical Society of America (SJR Q1, IF 2.1) has published our article "Fully nonlinear three-dimensional modeling of parametric interactions in the field of a dual-frequency acoustic array" based on the results of our joint research with Gubkin Russian State University of Oil and Gas.

When two intense high-frequency waves with close frequencies propagate in a nonlinear medium, a set of higher harmonics and combinational frequencies is generated but only a difference-frequency wave (with the lowest frequency) can propagate at a sufficient distance from the transducer as all high-frequency waves dissipate rapidly.

Therefore, generation of a difference-frequency wave (the accepted terminology is parametric generation) is actively used in various applications:

• highly directional audible sound in the air (contactless audio guides in the libraries and museums, active noise control systems);
• highly directional signal that propagates over long distances in the water (profiling sea-bottom structures and long-range ocean research);
• medical applications (ultrasound difference-frequency imaging, contrast elastography), etc.

However, numerical modelling of parametric interactions is extremely cumbersome in terms of required time and memory computer costs. Therefore, the existing numerical algorithms solve quasi-linear problems and/or in 2D (and even 1D) formulation.

In our published paper, a new numerical algorithm optimized by filtering the spectrum has been developed. The algorithm allows for solving 3D parametric problems for arbitrary shape transducers in the modes when nonlinear effects are strongly manifested. Using the new algorithm, specific features of parametric generation of a difference-frequency wave have been studied.

As a result, it is shown that:

• quasi-linear approximation is improper at high pressures on the transducer (the pressure amplitude and divergence of the difference-frequency wave are quantitatively incorrect);
• the efficiency of difference-frequency wave generation increases with an increase in the initial power of the pump waves;
• but this is accompanied by an additional divergence of the difference-frequency beam.

Thus, numerical 3D nonlinear modelling serves as a tool for determining optimal parameters of the pump wave radiation in order to increase the difference-frequency output power while maintaining the desired directivity of the beam.

For more details – see the text of the paper.