Nonlinear Acoustic Wave Dynamics

Nonlinear acoustic wave dynamics explores the behaviour of pressure waves in media where the wave amplitude influences propagation speed and waveform. Unlike linear acoustics, where small perturbations are assumed and superposition holds, nonlinear regimes give rise to phenomena such as harmonic generation, shock formation and solitary wave propagation. These effects emerge when acoustic amplitudes approach levels that induce finite material deformation or when propagation distances amplify weak nonlinearities. Theoretical modelling employs a hierarchy of equations—from the quasilinear Kuznetsov equation, incorporating viscous and thermal effects, through simplified Westervelt and Khokhlov–Zabolotskaya–Kuznetsov forms used in focused beam applications, to the higher-order Jordan–Moore–Gibson–Thompson framework, which accounts for intrinsic relaxation processes. Analysis of these models involves examining dispersion, attenuation and memory effects, often requiring novel mathematical techniques to establish existence, stability and long-time behaviour of solutions. Advances in computational methods have enabled detailed simulations of high-intensity focused ultrasound for medical therapy, acoustic metamaterial design for sound manipulation, and subsurface imaging in geophysics. The interplay between theory, numerics and experiment continues to refine our understanding of wave steepening, energy transfer across scales and control strategies for nonlinear acoustic fields.

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Nonlinear Acoustic Wave Dynamics publication trend

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Technical terms

Nonlinear acoustic wave: A pressure wave whose amplitude alters propagation speed, leading to non-superposable behaviour.

Shock wave: A steep pressure front characterised by discontinuous changes in flow properties due to nonlinear steepening.

Harmonic generation: The production of integer multiples of a fundamental frequency as a result of waveform distortion.

Paraxial approximation: A simplification assuming small angular deviations, reducing wave equations to directional parabolic forms.

Memory kernel: A function representing time-dependent material response, introducing hereditary damping into wave dynamics.

Jordan–Moore–Gibson–Thompson equation: A third-order-in-time wave model accounting for both thermal and molecular relaxation effects.

References

1. Poroacoustic front propagation under the linearized Eringen–Cattaneo–Christov–Straughan model. Journal of Non-Equilibrium Thermodynamics (2024).
2. Models of nonlinear acoustics viewed as approximations of the Kuznetsov equation. Discrete and Continuous Dynamical Systems (2020).
3. On the Jordan–Moore–Gibson–Thompson Wave Equation in Hereditary Fluids with Quadratic Gradient Nonlinearity. Journal of Mathematical Fluid Mechanics (2020).