Topographical Measurements of Water Waves at a Matrix of Measuring Points

Projektarbeit von Peter Vennemann

Abstract:

The measurement of the shape of a water wave is important for the study of a wide range of questions like the understanding of wave motions, the wave shapes dependence an the quality of the ground, the water depth or the surface tension which might be altered by pollution. The mixing of substances or gases at the surface of the sea is dependent an the waves shapes. The shape of a water wave is also interesting for understanding the transport mechanisms and the energy of waves. Knowledge about water wave shapes is essential for the design of an effective shore protection which is going to be more and more important when the sea level is rising. Furthermore offshore designers require knowledge about the shape of a wave during its interaction with installations for optimising the shape of offshore structures and for calculating the loading. This is a key requisite for the design and the construction of cost effective and save structures of any kind like buoys, lifeboats, ships, oil rigs or other offshore platforms. Measurements of wave shapes for example can help to understand the interference or upwelling caused by the legs of typical offffshore platform geometries which can enhance the wave amplitude and possible wave impact with the underside of the platform.

The probably simplest way of measuring the surface of a wave is to put a certain number of water depth gauges into the water, taking a photo of the wave when it is passing the gauges and then reading every single measure from the photograph. The wave shape can be reconstructed by interpolating the waves surface between the measuring points. The considerable distortion of the measuring object by the measuring instruments is disadvantageous.

An array of pressure sensors in a plain below the water surface can be used instead of the gauges to avoid the distortions. The pressure at every single sensor is a measure for the water height above the sensor. The disadvantage of this method is the sensitivity of the pressure sensors for the dynamic pressure of water flows caused by turbulences, in particular in shallow water, underneath breaking waves or close to constructions. Also disadvantageous is the necessity of mounting a part of the measuring system under the water.

To avoid this problems, photographic methods for the recording of surface waves have been developed:

At the beginning of the 20th century the first attempts have been made to collect elevation data of ocean waves by stereo photography. Referring to Holthuijsen the principle of stereo-photography is taking two pictures of the same object from different viewpoints. Afterwards unique points are identified an both pictures. From the two dimensional coordinates in the photographs the three dimensional coordinates of these points can be calculated in a reference coordinate system.

The water surface need to be marked with dots or identifiable structures for using stereo photography. A difficulty is to determine which points an the two pictures correspond to the same point an the object. Shemdin explains accurate and cost effective, automatic digital stereo-correlation techniques.

Grant et al. describe an apparatus which tackles the problem of correlating the pictures by using a bundle of laser beams to produce a matrix of highlights an a water wave surface. Grant uses one film camera together with a split screen viewing system which permits to photograph the highlights simultaneously from different viewpoints.

Another measurement method is based an the Moire-effect. Grant et al. describe a method in which light is projected through a grating onto a water wave surface. The pattern an the water is viewed by a camera through a similar grating. The result is a fringe pattern photograph which can be interpreted as a discrete level-map of the surface. Unfortunately the calibration and tracking of the fringes are complex operations. The water has to be dyed in order to get sufficient contrast.

Further methods use the projection of a regular pattern onto the surface. From the recorded, disturbed pattern the surface of the wave can be calculated.

Other approaches use the effect of light refraction at the water surface. The disadvantage is, that it is usually necessary to mount components like the light source or the camera under water.

Table of Contents:

1.	Introduction	5
1.1	Necessity of Measuring the Shape of a Water Wave	5
1.2	Measuring Methods	5
1.3	Objectives of the Present Study	8
2.	Experimental Set-up	9
2.1	Idea	9
2.2	Components	12
3.	Evaluation	16
3.1	Calibration Procedure	16
3.1.1	Definition of Coordinate Systems	16
3.1.2	Camera Adjustment	17
3.1.3	Calculating the Camera Position	19
3.1.4	Transformation Matrixes between the Coordinate Systems	22
3.2	Calculation of the Wave Shape	24
3.2.1	Convention of Symbols	24
3.2.2	Calculation	25
3.2.3	Error Estimation	29
4.	Outlook	30
5.	Bibliography	31
A.	Calibration	32
B.	Calculation of Water Heights	34
C.	Graphs of the Results	38