Propagation of bichromatic-bidirectional waves

Mario Grüne De Souza E Silva,Claudio Freitas Neves,Paulo Cesar Colonna Rosman

doi:10.1590/2318-0331.241920180095

Mario Grüne De Souza E Silva, Claudio Freitas Neves + Show 1 more

Open Access

https://doi.org/10.1590/2318-0331.241920180095

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Journal: RBRH	Publication Date: Jan 1, 2019
License type: CC BY 4.0

Affiliation: Universidade Federal do Rio de Janeiro

Abstract

ABSTRACT This study aims to investigate the transformations experienced by the mean water level and radiation stress tensor during the propagation of Bichromatic-Bidirectional (Bi-Bi) waves on a slope of 1:22 and water depth varying from 55 cm to 26 cm, simulating laboratory conditions. A computer program written in Python was used to compute those quantities at different combinations of wave angles and periods. The setup and setdown of the mean water level are strongly dependent on the combination of periods and direction of the primary waves, as they propagate along the slope, modifying the bound infragravity wave. Mohr’s circles for the radiation stress tensor showed significant changes of diameter and center at different points along the basin. The radiation stress components for the Bi-Bi waves are the sum of the stresses associated with each primary wave and a nonlinear term which results from the interference between primary waves. Disregarding these nonlinear terms may significantly affect the nearshore hydrodynamics prediction.

Highlights

Infragravity waves are long surface waves with frequencies ranging from 0.004 Hz to 0.04 Hz, and amplitudes of O(100 - 101 cm)
Inside a wave group, where a slow periodical change of the individual wave heights exists, there will be a variation of the radiation stress, which will be compensated by the gradient of the mean water level from the terms of the expressions of momentum flux and dynamic free surface boundary condition
The results showed that for angle differences of 0° and 180°, and an equal initial phase, the calculated mean water level was identical to traditional formulas and that it varies through all possible angle combinations as a continuous and smooth curve

Summary

Introduction

Infragravity waves are long surface waves with frequencies ranging from 0.004 Hz to 0.04 Hz, and amplitudes of O(100 - 101 cm). According to Bertin et al (2018), infragravity waves are widely accepted as responsible for significant impacts on the hydrodynamics and morphodynamics of coastal areas like sandy beaches, tidal inlets, coral reefs and harbors. These long period oscillations can drive rip currents (DALRYMPLE et al, 2011), can propagate into aquifers on sandy coasts and cause underground water fluxes through barrier islands, between sea and lagoons (GENG; BOUFADEL, 2015; LI; BARRY, 2000; LONGUET‐HIGGINS, 1983), can intensify wave run-up and overtopping over dunes, structures and fringing coral reefs (CHERITON; STORLAZZI; ROSENBERGER, 2016) and can eventually dominate the net sediment transport in the surf zone (AAGAARD; GREENWOOD, 2008). Infragravity waves have been associated with microseisms (LONGUET-HIGGINS, 1950), can cause vibrations in coastal cliffs, leading to their instability and erosion (YOUNG et al, 2011), and are related to seismic waves in the solid Earth, a phenomenon known as “the hum” (ARDHUIN; GUALTIERI; STUTZMANN, 2015)

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