Numerical modeling of finite-amplitude sound beams: Shock formation in the near field of a cw plane piston source
Bibliographic record
Abstract
Two theoretical models and the corresponding numerical codes for the description of nonlinear acoustic beams radiated from intense cw sources in water are presented. In the first model, diffraction effects are included using the Rayleigh integral, whereas nonlinearity and thermoviscous absorption are accounted for in a quasi-plane approximation. The simulations are performed in the time domain using the code previously developed for single-pulse propagation in medium having arbitrary frequency-dependent absorption. The second model is based on the Khokhlov–Zabolotskaya–Kuznetsov equation, which, contrary to the first model, accounts for diffraction in the parabolic approximation. The simulations are performed in the frequency domain using a novel algorithm that has been developed. A variable number of harmonics, which follows the nonlinear broadening of the wave spectrum are employed in the algorithm to speed up calculations. In order to prove the validity and the accuracy of the two codes developed, the simulation of diffraction and nonlinear effects in the near field of an intense ultrasound circular piston source in water is performed. The results of modeling obtained by both codes are compared with each other and with known experimental data, and are found to be in a good agreement. Frequency-domain code is then used for detailed study of the strongly nonlinear regime of propagation, when shocks are developed in the waveform close to the source. It is demonstrated that diffraction plays a major role in shock formation. Development of two shocks in each cycle and their further collision is predicted. It is also shown that nonlinear propagation and shock formation result at some distance in the two times excess of peak positive pressure in comparison with the maximum value obtained in the case of linear propagation. The beam total power decay due to formation of shocks as a function of the propagation distance is compared with the intensity in a plane wave propagation without diffraction. It is shown that nonlinear energy decay starts earlier for the beam, but decreases slower over longer distances.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".