Coastal wave refraction in variable currents over a varying bathymetry

TL;DR

This paper develops an analytical approximation for wave refraction caused by variable currents and bathymetry, validated through ray tracing, and clarifies their individual and combined effects on coastal wave propagation.

Contribution

It introduces a linear superposition model for current- and depth-induced wave refraction, enabling separate quantification of their effects under varying conditions.

Findings

The approximation accurately predicts wave ray curvature in complex environments.

Current and depth gradients can either amplify or counteract each other in wave refraction.

The model identifies dominant factors influencing wave propagation in coastal areas.

Abstract

Refraction is the predominant mechanism causing spatially inhomogeneous surface gravity wave fields. However, the complex interplay between depth- and current-induced wave refraction remains poorly understood. Assuming weak currents and slowly varying bathymetry, we derive an analytical approximation to the wave ray curvature, which is validated by an open-source ray tracing framework. The approximation has the form of linear superposition of a current- and depth-induced component, each depending on the gradients in the ambient fields. This separation enables quantification of their individual and combined contributions to refraction. Through analysis of a few limiting cases, we demonstrate how the sign and magnitude of these components influence the wave refraction, and identify conditions where they either amplify or counteract each other. We also identify which of the two plays a dominant role. These findings provide physically resolved insights into the influence of current- and depth-gradients on wave propagation, and are relevant for applications related to remote sensing and coastal wave forecasting services.