Interfacial waves from pressure forcing: revisiting classical theories from an IVP perspective
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.
Cite
@article{arxiv.2605.12254,
title = {Interfacial waves from pressure forcing: revisiting classical theories from an IVP perspective},
author = {Vinod Kumar Kadari and Nikhil Yewale and Palas Kumar Farsoiya and Y. S. Mayya and Ratul Dasgupta},
journal= {arXiv preprint arXiv:2605.12254},
year = {2026}
}