Rogue Wave Formation in Adverse Ocean Current Gradients

Abstract

Studies of the nonlinear Schrödinger (NLS) equation indicate that surface gravity waves traveling against currents of increasing strength gain energy and steepness in the process, and this can be a mechanism for rogue wave formation. Likewise, experimental studies have shown that stable wavetrains traveling against adverse currents can give rise to extreme waves. We studied this phenomenon by using computational fluid dynamics (CFD) tools, whereby the non-hydrostatic Euler equations were solved utilizing the finite volume method. Waveforms based on a JONSWAP spectrum were generated in a numerical wave tank and were made to travel against current gradients of known strength, and wave characteristics were monitored in the process. We verified that waves gain energy from the underlying flow field as they travel against current gradients, and the simulated level of energy increase was comparable to that predicted by earlier studies of the NLS equation. The computed significant wave height, H s , increased substantially, and there were strong indications that the current gradients induced nonlinear wave instabilities. The simulations were used to determine a new empirical relationship that correlates changes in the current velocity to changes in the Benjamin⁻Feir Index (BFI). The empirical relationship allows for seafaring entities to predict increased risk of rogue waves ahead, based on wave and current conditions.

Keywords

• rogue wave
• current gradients
• Benjamin–Feir Index
• significant wave height
• extreme waves
• nonlinear Schrödinger (NLS) equation