On the Estimation of the Surface Elevation of Regular and Irregular Waves Using the Velocity Field of Bubbles

Diana Vargas,Edgar Mendoza,Rodolfo Silva,Ravindra Jayaratne

doi:10.3390/jmse8020088

Abstract

This paper describes a new set of experiments focused on estimating time series of the free surface elevation of water (FSEW) from velocities recorded by submerged air bubbles under regular and irregular waves using a low-cost non-intrusive technique. The main purpose is to compute wave heights and periods using time series of velocities recorded at any depth. The velocities were taken from the tracking of a bubble curtain with only one high-speed digital video camera and a bubble generator. These experiments eliminate the need of intrusive instruments while the methodology can also be applied if the free surface is not visible or even if only part of the depth can be recorded. The estimation of the FSEW was successful for regular waves and reasonably accurate for irregular waves. Moreover, the algorithm to reconstruct the FSEW showed better results for larger wave amplitudes.

Highlights

The kinematic study of the free surface elevation of water (FSEW) is the main data source to estimate the wave velocities and forces acting on maritime infrastructure
The technique employed to estimate the FSEW through the velocity field of the air bubbles gave good results compared to traditional measuring methods
The horizontal motion of the bubbles can serve as a proxy to the motion of the water particles in coastal waves

Summary

Introduction

The kinematic study of the free surface elevation of water (FSEW) is the main data source to estimate the wave velocities and forces acting on maritime infrastructure. The authors of [1] presented a comparison between mathematical and laboratory measurements of velocities below the FSEW with a laser Doppler velocimeter (LDV) to compute the wave forces on submarine pipelines. The same set of experiments was replicated with inductive- and impeller-type probes instead of an LDV to confirm the theories with the prediction of velocities and pressures by [2,3]. These authors estimated the FSEW using pressure data. Later, [5] compared the theory and measurements of water particle velocities in solitary waves, while [6] carried out the same experiments under monochromatic waves

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