19th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 16 – 19, 2018

High-Resolution Planar Two-Component PTV Measurements in a Breaking Wave
Malene H. Vested1,*, F. Gökhan Ergin2, Stefan Carstensen1, Erik D. Christensen1
1: Section of Fluid Mechanics, Coastal and Maritime Engineering, Dep. of Mech. Eng., Technical University of Denmark, Denmark
2: Microfluidics Product Manager, Dantec Dynamics, Denmark* Correspondent author: mlhv@mek.dtu.dk
Keywords: PTV, Dynamic Masking, Two-Phase flow, Interface, Ocean waves, Wave forces

ABSTRACT
Ocean waves and the associated wave forces are of vital importance for marine applications, with offshore windturbines as one example. Since the wave forces are governed by the wave kinematics, detailed studies of wave
kinematics are highly valuable. In this study, wave kinematics of a breaking laboratory wave is investigated using
dynamic masking and Particle Tracking Velocimetry (PTV). First, dynamic masking is used to remove the bubbledroplet layer above the free surface. Second, PTV is used to resolve the kinematics with high spatial resolution
throughout the wave motion from the laboratory bed to the water surface. Instantaneous velocity fields are obtained
at a sample rate of 96Hz, and this provides sufficient temporal resolution for spectrum and acceleration investigations.
The results indicate that, compared to Particle Image Velocimetry (PIV), the current methodology provides a better
understanding for the dynamics of ocean waves, thus leading to more accurate predictions of wave forces.

1. Introduction
The study of ocean waves is essential to multiple marine applications, including offshore windturbines. Offshore wind energy is an expanding industry with wind turbines now planned andinstalled at greater water depths. In order to ensure a low cost of the wind turbine withoutcompromising structural reliability, the wave forces acting on the foundation must be accurately
predicted. When predicting the dynamic wave forces, it is vital to know the wave kinematics, thatis, velocities as well as accelerations. To this end, laboratory measurements of water waves at highspatial and temporal resolution are very important. Measurements of water waves in thelaboratory, however, represent a number of challenges since it is a two-phase flow with a moving
interface. For wake kinematics investigations, both PIV and PTV are well suited, while PTV
provides a better spatial resolution.
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19th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 16 – 19, 2018

Water waves, including breaking events, have already been studied through PIV measurements
by Perli, He & Bernal (1996), Grue et al. (2003), Kimmoun, Branger & Zucchini (2004), Belden &Techet (2011), André & Bardet (2014) among others. One common challenge for PIV investigations
for breaking waves is the contribution of the bubble-droplet layer at the air-water interface in the
cross-correlation function. This is a general problem for PIV in two-phase flows. This is because
the cross-correlation-based PIV algorithms can not distiguish between the two phases, and often,
cross-talk exists close to the phase-boundary due to the finite size of the PIV interrogation window,
Ergin (2017). Ironically, important fluid mechanics phenomena takes place at the phase boundary.
One way of addressing this challenge is to mask out the phase that is not of interest.
Dynamic masking techniques have the advantage of automatically masking the unwanted phasefrom the PIV images, which is convenient for large datasets. The flow around a single bubble risingin a water column was studied by Hassan, Ortiz-Villafuerte & Schmidl (2001), in which theinterface between the bubble and the flow was masked by an edge-tracking technique. Anotheredge-tracking technique was suggested by Guo et al. (2010) to extract bubbles from a flow field.
In a recent study by Dussol et al. (2016), an image masking process is used to investigate the flow
field close to a vessel by using a predefined shape of the vessel. Sanchis & Jensen (2011) suggest a
Radon-transform method to detect the interphase between air and water in a PIV measurement ofan overturning wave. The Radon-transform method detects smaller sections of straight lines andcaptures the particles on the free surface. Subsequently, the smaller sections are fitted to apolynomial to obtain the free surface. This method, however, is less succesful in the case of
breaking waves where the shape is not well represented by a polynomial or any other pre-defined
function. A comprehensive list of dynamic masking references is provided by Ergin (2017).
In this work, a histogram-thresholding-based dynamic masking procedure is applied (Ergin 2017).
Furthermore, we have used a hybrid PIV/PTV technique to obtain the time-resolved flow field
information. The combination of PIV and PTV offers a high spatial resolution, since it combines
the robustness of PIV with the high spatial resolution of PTV, Keane, Adrian & Zhang (1995),
Stotou & Riethmuller (2001). Furthermore, PTV has been found to increase accuracy close toboundaries (Kähler, Scharnowski, and Cierpka 2012).
The objective of this work is to obtain accurate and high resolution – both in time and in space –velocity measurements in a typical ocean wave. The aim is to compute accelerations from the timeresolved velocity data. Accurate studies of the wave kinematics ultimately leads to better wave
force estimates, which can be used in the production of reliable and low cost offshore windturbines.
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19th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 16 – 19, 2018

The paper is structured as follows: The experimental setup is explained in section 2, with adescription of the PTV setup as well as the laboratory flume. In section 3 the image pre-processing
is presented followed by the application of a dynamic masking procedure and in section 4 weshow how detailed velocity information is obtained by the use of PIV / PTV. In section 5 we discuss
on a spectrum analysis of the velocity and the associated acceleration field computed from thevelocity information is presented. Section 6 concludes on the results from the study.
2. Experimental set-up
The experiment was conducted in a wave-current flume at the Hydraulic Laboratory of theTechnical University of Denmark (Fig. 1). It has a length of 28.0m -, width of 0.60m - and a depthof 0.80m. Waves are generated by a piston-type wave paddle positioned at one end of the flume
at a water depth of 0.515m. In order to investigate steep and breaking waves, an inclined, smoothseabed of slope 1/25 is installed in the wave flume. As the waves travel from the wave generator
and up the seabed, the waves steepen and wave breaking occurs at a certain water depth. Here,
we have investigated a wave that breaks at a distance of 19.8m from the wave paddle with abreaking wave height of 0.17 m and wave period of 1.5s . The water surface elevation is measured
at 6 locations in the flume with resistance wave gauges.

Fig. 1 Schematic of the wave-current flume with the wave paddle to the left. The waves travel on a flat bed for 12.7m
before travelling onto a 1/25 slope, which causes the waves to steepen and ultimately break.

The PIV / PTV measurement system is manufactured by Dantec Dynamics. Fig. 2a shows a crosssectional sketch of the flume and the PIV / PTV measurement setup. The sidewall of the wave
flume is made from glass, and furthermore a glass window is incorporated into the inclinedlaboratory bed. Upon reflection from a 45° tilted mirror placed below the inclined bed, the lightsheet illuminates the measurement area vertically from below. The high-frequency PIV laser319th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 16 – 19, 2018

(DualPower 100-100) is a dual-cavity, ND:YAG laser emitting 532nm light. Each cavity can
produce 100mJ pulse energy at a rate of 100Hz with a pulse length of 12ns. The thickness of thelaser sheet ranges from 2 mm to 2.8 mm in the measurement area. The particle images are captured

(a)

(b)

Fig. 2 (a) Cross-sectional view of the wave flume at the PIV / PTV measurement area. The horizontal laser sheet reflects
on a 45°-tilted mirror at the bottom of the wave flume and propagates vertically through a window in the inclined,smooth laboratory bed. (b) Field of view of the PIV / PTV measurement area.

using a 4Mpix, SpeedSense1040 4MP camera with a 50mm lens and the pixel resolution is
2320×1726 pixels. The flow is seeded with silver-coated hollow glass spheres with a buoyancy of
1 g/cc and a mean diameter of 10 µm. The seeding particles ensure a high reflection thanks to thesilver coating. Double-images are sampled at 96 Hz with an interframe time of 5ms. The PIV / PTV
measurement area covers 0.30×0.22 m and the water depth at the measurement location is 205mm.
Fig. 2b shows the field-of-view of the PIV / PTV measurement area, with a snapshot of the raw
image inserted.
3. Image Pre-processing and Dynamic Masking
During image pre-processing, the following image pre-processing steps were performed;
background subtraction, application of a Gaussian difference filter and a histogram-thresholdbased dynamic masking. Before the velocity calculation, it was necessary to perform image preprocessing on the raw particle images. The particle image is shown in Fig. 3, which depicts thewave as it is overturning. Note that the vertical line thought the center of the image is the wave
gauge measuring the surface elevation. First, a background image pair was computed based on
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19th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 16 – 19, 2018

the temporal minimum pixel value of all the aquired raw images. The background image was thensubtracted from the raw images in the ensemble. In Fig. 4a the inverted particle image is shown
after the background subtraction. Subsequently, the particle images were enhanced using a

Fig. 3 Particle image at t=0.646s. The vertical line seen in the center is a wave gauge.

difference of Gaussian (DoG) filter (Ergin et al. 2014). Briefly, the DoG filter is the difference
between an image filtered by 7×7 Gaussian filter and the same image filtered by a 3×3 Gaussian
filter. The resulting particle image, shown in Fig 4b, is filtered from noise caused by the
background disturbance, wave gauge and the air-water mixture above the water surface during
the breaking event. The last step before the actual dynamic masking is the application of asequence of opening and closing filters, in this case a combination of 10 opening filters followed
by 15 closing filters (Fig. 4c). As a final step, a histogram-treshold based dynamic masking isapplied on the DoG filtered images in order to clean out intermittent laser reflections and a few
bright pixels above the water surface in Fig. 4b.

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19th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 16 – 19, 2018

(a)

(b)

(c)

Fig. 4 (a) Inverted raw particle image after background subtraction. (b) After application of Difference of Gaussian
filter (c) Pre-processed image used for histogram-threshold based dynamic masking. All at t=0.646s.

4. PIV / PTV Results
After the dynamic masking process, the velocities are computed through a three-step procedure.
First, a preliminary Particle Image Velocimetry (PIV) analysis is performed, see Fig. 5a. The PIV
algorithm is an adaptive PIV with an initial interrogation area of 64x64 pixel and final
interrogation area of 32×32, using a grid step size of 16×16 pixels (50% overlap). The interrogation
area size was adapted to the particle density with a minimum of five particles as the limit. A
universal outlier detection (UOD) was applied and outliers were substituted by the local median.
The PIV result is used as input for the subsequent PTV analysis. Second, the PTV was computed
through a 2-pass particle-matching scheme. A total of 28,697 particles were matched at the time
instant where the wave is at its highest point. A separate new UOD scheme was used after the
PTV analysis. The velocity field computed by PIV and PTV are shown in Fig. 5a and 5b,
respectively. Comparing these subfigures we notice that many of the spurious vectors calculated
close to the free surface are eliminated using the PTV technique. Furthermore, some of the velocity
vectors smoothened during the PIV analysis were re-captured in the PTV analysis. (Observe e.g.
one red velocity vector in a zone of yellow velocity vectors in Fig. 5b in the middle to the left).
Finally, the PTV results are interpolated back onto a Cartesian grid using a spline interpolation
scheme (Fig. 6) in order to perform subsequent vector post processing.

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19th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 16 – 19, 2018

(a)

(b)

Fig. 5 (a) Preliminary PIV analysis used as input for subsequent PTV analysis. Color bar is velocity [m/s] (b) PTV
results. Color bar is velocity [m/s]. Both at t=0.646s.

Fig. 6 PTV-result interpolated back onto Cartesian grid at t=0.646s. Color bar is velocity [m/s]

The PTV analysis serves three purposes here: Firstly, it acts as an outlier detector for the PIV result.
In particular, the spurious vectors in the areas close to the water surface and in the less-illuminatedcorners are removed (Fig. 5a). Secondly, the spatial resolution is improved compared to PIV, since7

19th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 16 – 19, 2018the spatial smoothing is reduced. Thirdly, the accuracy of the computed velocity is improved,since PTV allows for greater local variation of velocity, due to the reduced smoothing. Thus,
applying PTV provides improved results for wave kinematics throughout the flow field.
4. Spectrum and acceleration measurements
Once the PTV results with high spatial and temporal resolution are obtained, further postprocessing steps such as spectrum and acceleration calculations can be performed. First, thevelocity time series, u(t) and v(t), at a single point, indiacted by the black circle in Fig. 6, areshown in Fig. 7. Comparing the horizontal and vertical velocity time series, it is seen that thehorizontal velocity displays a larger amplitude with peak velocity 70% larger than peak
amplitude of the verticxal velocity. It is seen that the horizontal velocity increases rapidly as thewave approaches breaking around t=0.65s, while the vertical velocity peaks just before breaking
around t=0.5s. A small-amplitude fluctuation can be observed in the v(t) which is not seen foru(t).

Fig. 7 Velocity time series in the horizontal, u(t), and in the vertical, v(t), obtained at the black circle in Fig. 6.

A spectrum analyis of the velocities is presented in Fig. 8. The spectrum of v(t) indicates that themeasured fluctuation frequency is at 19.2 Hz (Fig. 8). At this point, the reason for this fluctuation
is not clear, and this will be the subject of future investigations.
819th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 16 – 19, 2018

(a)

(b)

Fig. 8 Spectrum analysis, (a) horizontal velocity u(t), (b) vertical velocity v(t).

Second, the acceleration is computed by a right-sided first order finite difference scheme:
𝑑𝑑𝑑𝑑
𝑢𝑢 −𝑢𝑢≅ 𝑖𝑖+1∆𝑡𝑡 𝑖𝑖 , and the acceleration field at t=0.646s is shown in Fig. 9. The acceleration results
𝑑𝑑𝑑𝑑𝑖𝑖

indicate that the rightwards-propogating wave has rightward acceleration on the right andleftward acceleration on the left. This is expected due to the breaking occuring around this time
instant.

Fig. 9 Acceleration field at t=0.646s. Vectors represent the total acceleration magnitude and direction, where colors
represent acceleration only in the horizontal direction (warmer colors towards left and colder colors toward right).

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19th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics・LISBON | PORTUGAL ・JULY 16 – 19, 2018

5. Conclusions
We present here a high-resolution PTV study of a breaking wave. We have demonstrated that
careful image pre-processing and histogram-thresholding based dynamic masking is successful inmasking the air phase and the bubble-droplet mixture on the free surface and therefore very
suitable in wave kinematics investigations. Furthermore, we found that the applied PTV algorithm
improves the data in three points: 1) The PTV algorithm acts as an outlier detector for PIV, 2) PTV
provides improved spatial resolution compared to PIV, due to the reduced spatial smoothing and3) PTV provides more accurate velocities. The velocity information obtained from PTV wassuccesfully used to compute the associated acceleration field. The detailed kinematics uncoveredby these measurements are of great importance in marine applications including the offshore windenergy industry, for which wave dynamics and wave forces on the substructures play an essentialrole. Future work will include force estimates based on the obtained kinematics for wave loads on
a monopile.
Acknowledgements
The study was partly supported by the DeRisk project funded by Innovation Fund Denmark, grant
number 4106-00038B and partly by DHI.
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