Estimating superharmonic bound waves with the variable wavenumber approximation

Conference item

1. We introduce the Variable Wavenumber Approximation (VWA), an FFT-based framework for computing superharmonic bound waves, providing both η⁽ⁿⁿ⁾ and the free-surface potential ϕs⁽ⁿⁿ⁾ to arbitrary order.

2. For second-order superharmonics, VWA matches established interaction theory in deep-water unidirectional waves and is further validated against fully nonlinear potential-flow simulations across bandwidth and depth.

3. The formulation extends naturally to higher-order harmonics and directionally spread wave groups, while delivering orders-of-magnitude reductions in runtime (typically thousands-fold speedup relative to exact interaction evaluation).

Authors: Liu, X; Tang, T; Taylor, PH; Mostert, W; Adcock, TAA

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: International Workshop on Water Waves and Floating Bodies
• Publication date: 2026-04-26
• Acceptance date: 2026-02-01
• Event title: 41st International Workshop on Water Waves and Floating Bodies (IWWWFB 2026)
• Event location: Plitvice, Croatia
• Event website: http://www.iwwwfb.org/Workshops/41.htm
• Event start date: 2026-04-26
• Event end date: 2026-04-29
• Language: English