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\begin{document}

\title{Numerical investigation of the refractive properties of near-horizontal
shore platforms and their effects on harmonic and stationary wave
patterns}



\author[1]{Raphael Krier-Mariani}%
\author[1]{Stephenson Wayne}%
\author[2]{Sarah Wakes}%
\author[3]{Mark E. Dickson}%
\affil[1]{University of Otago}%
\affil[2]{Department of Mathematics and Statistics, University of Otago}%
\affil[3]{University of Auckland}%


\vspace{-1em}



  
  \date{June 15, 2024}


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\begin{abstract}
Near-horizontal shore platforms display highly irregular plan shapes,
but little is known about the way in which these irregularities
influence the significant wave height (Hs) on the platforms and the
frequency components of the nearshore wave field. We use a nonlinear
Boussinesq wave model to conduct harmonic and bispectral mode
decomposition analyses, studying the control of concave and convex
platform edges over wind (WW: 0.125 - 0.33 Hz), swell (SW: 0.05 - 0.125
Hz) and infragravity (IG: 0.008 - 0.05 Hz) frequencies. For breaking and
non-breaking waves, increasing the platform edge concavity intensified
wave divergence and subsequent attenuation of SW and IG across the outer
platforms, reducing by up to 25\%. Increasing the platform edge
convexity intensified focusing and amplification of SW and WW over the
outer platforms, increasing by up to 18\% and 55\% for breaking and
non-breaking waves. In the presence of breaking, IG amplification
depended on the generation of wave divergence across the inner platform,
a condition determined by a critical convex curvature threshold (\selectlanguage{greek}Κ\selectlanguage{english}=1.8)
balancing wave focusing from refraction and defocusing from breaking. We
find that convex curvature can determine the relative dominance of WW,
SW and IG across platforms. Alongshore, coherent wave interactions
governed IG stationary patterns defined by a node near the platform
centreline and two antinodes on either side of concave edges. A node was
generated at the platform centreline, and two antinodes were observed on
either side of the convex edges for \selectlanguage{greek}Κ\selectlanguage{english}\textgreater{}1.8, with the
opposite pattern observed for \selectlanguage{greek}Κ\selectlanguage{english}\textless{}1.8.%
\end{abstract}%



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