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Researchers investigated the wave patterns created when localized pressure moving faster than a critical speed acts on the interface between two fluid layers of different densities. Using mathematical modeling, they found that the interface develops short capillary waves ahead of the pressure source and long gravity waves behind it, with this asymmetric pattern resulting from time-dependent transient effects that decay over time. This initial-value problem approach provides a more complete solution than classical steady-state methods, which require arbitrary additional conditions to determine a unique answer.
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This work advances our fundamental understanding of wave generation at fluid interfaces, with potential applications in predicting wave patterns behind ships, understanding atmospheric pressure disturbances over water surfaces, and designing systems involving moving loads on stratified fluids.
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⚠️ Preprint – Noch nicht peer-reviewed
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Abstract: A localised overpressure translating at a uniform speed greater than a critical value acts at the interface between two deep fluid layers with different densities. We analyse the resulting wave patterns using an initial-value problem formulation within the linearised, inviscid, potential flow framework. The steady-state interface exhibits short capillary waves ahead of the forcing and long gravity waves behind it, arising from an asymmetric cancellation of Fourier components in the far field. The time-dependent part of the solution, decaying algebraically with time, plays a crucial role in this mechanism. This contrasts with classical steady approaches, which require additional conditions to select a unique solution. We extend this approach to a two-fluid interface and validate the predictions against nonlinear simulations.
Source: Interfacial waves from pressure forcing: role of the transients