Obtaining Reflection Coefficients from a Single Point Velocity Measurement

Rachael Mckee,Björn Elsäßer,Pál Schmitt

doi:10.3390/jmse6020072

Abstract

The quantification of the reflection of water waves is of paramount importance in coastal and marine engineering. Reflected waves are produced as a result of an incident wave meeting a reflective boundary e.g., in a wave basin. While reflection can be seen as an undesirable disturbance, for example in experimental tests performed in confined tanks, it can also have a useful purpose such as being directed towards wave energy converters (WECs). Whether useful or not, reflection needs to be accurately quantified. For cases effected by directional spreading such as WECs, the wave height of a reflected wave will be spatially variable. The majority of quantification methods are based on frequency domain analysis of surface elevation data at more than one discrete location over approximately one wavelength. Thus, a method which requires a single point measurement is desirable. This paper presents a novel method derived from Linear Wave theory to quantify reflection coefficients using orbital velocity measurements at one discrete location. An additional advantage of this method is it only requires data over a single wave cycle and thus will be particularly suitable for numerical simulations. In the present form the method is only applicable to monochromatic waves. The theoretical background of the method is explained in detail. An application is demonstrated through a comparison to reflections quantified using surface elevation measurements in Computational Fluid Dynamics (CFD) numerical simulations. It is found that the results of the new proposed method compare to surface elevation methods within the levels of experimental accuracy.

Highlights

Reflection of gravity surface waves in wave tanks occurs when an incident wave is intercepted by more den of gravity surface waves in wave tanks occurs when an incident wave is intercepted by more dense material or changing bed slopes creating a reflective boundary
While reflection can be seen as an undesirable disturbance, for example in experimental tests performed in confined tanks, it can have a useful purpose such as being directed towards wave energy converters (WECs)
An application is demonstrated through a comparison to reflections quantified using surface elevation measurements in Computational Fluid Dynamics (CFD) numerical simulations

Summary

Introduction

Reflection of gravity surface waves in wave tanks occurs when an incident wave is intercepted by more den of gravity surface waves in wave tanks occurs when an incident wave is intercepted by more dense material or changing bed slopes creating a reflective boundary. The majority of published methods to quantify reflections involve the analysis of surface elevation data. Thorten [3] and Goda and Suzuki [4] determined two dimensional (2D) reflection using two independent surface elevation measurements spaced at reasonably short distances from each other in line with the wave propagation direction. Mansard and Funke [5] presented a slightly different method which requires three independent in-line surface elevation measurements in order to separate the incident and reflected spectra in irregular waves. Viviano [7] presented a modification of the Mansard and Funke method For all the aforementioned methods, the wave frequency in question is limited by the separation distance(s) between the probes. Isaacson [8] conducted a review on various reflection analysis techniques and concluded that the three probe method, known hereafter as the Mansard and Funke method , was the most accurate

Results

Discussion

Conclusion