Near-Shore Sediment Transport Under Cnoidal Waves Using Particle Image Velocimetry by Jenna Katrina A thesis submitted to the College of Engineering and Science of Florida Institute of Technology in partial fulfillment of the requirements for the degree of Master of Science in Ocean Engineering Melbourne, Florida July, 2021 We the undersigned committee hereby approve the attached thesis, “Near-Shore Sediment Transport Under Cnoidal Waves Using Particle Image Velocimetry.” by Jenna Rose Katrina _________________________________________________ Robert J. Weaver, Ph.D. Associate Professor Ocean Engineering and Marine Sciences Major Advisor _________________________________________________ Stephen Wood, Ph.D. Professor Ocean Engineering and Marine Sciences Committee Member _________________________________________________ Michael Splitt, M.S. Assistant Professor College of Aeronautics Committee Member _________________________________________________ Richard Aronson Ph.D. Professor and Department Head Ocean Engineering and Marine Sciences Abstract Title: Near-Shore Sediment Transport Under Cnoidal Waves Using Particle Image Velocimetry Author: Jenna Katrina Advisor: Robert J. Weaver, Ph.D. With future trends showing a higher percentage of the human population living along the coast, coastal resilience is a significant topic of concern for many researchers. The purpose of this research was to analyze near-shore sediment transport under different wave parameters using the technique of Particle Image Velocimetry (PIV) and laboratory studies for linear and nonlinear cnoidal waves. At the deeper extent of the nearshore profile, waves will tend to be linear, having an Ursell number less than 40, with little or no net sediment transport due to orbital velocities. The velocities are the same under the crest and trough and will be dominated by undertow for linear waves. It is hypothesized that as the wave propagates shoreward, the wave transforms into a nonlinear cnoidal wave and the skewness of a cnoidal wave profile, having an Ursell number greater than 40, will drive nearshore sediment transport onshore. The project goal was to quantify the volumetric sediment transport rates based on these dimensionless parameters and analyze how the linearity of waves affect the sediment transport onshore and offshore. To accomplish this goal, a sandy bed with a sediment distribution mimicking that found on East Coast beaches, was constructed in the Florida Tech wave channel. A range of waves were generated at three different water depths and three different frequencies over a flat and rippled bed. The velocity near the bed was analyzed in the laboratory using a PIV system consisting of a laser to illuminate the sediment particles and a high-frame rate camera to record videos, which were analyzed in the Matlab PIV toolbox, PIVlab. Through image analysis, a relationship was developed between wave characteristics and dimensionless parameters, the Ursell number and Shields parameter, wave linearity, and sediment movement. Furthermore, time- iii lapse videography of the sediment movement was recorded and analyzed to determine accretion/erosion rates caused by these conditions. The time-lapse video, paired with the results from the PIV toolbox, was used to quantify sediment movement. The results from this study elucidated the relationship between water depth, wave height, wave period, and wavelength to the linearity of the wave, the velocity of the sediment being transported and the corresponding Ursell and Shields parameter. The results will aid in the development of improved models for predicting bed morphology, which will lead to a better understanding of coastal resilience in the future. iv Table of Contents Abstract ................................................................................................................................ iii List of Figures ...................................................................................................................... vii List of Tables ........................................................................................................................ ix Acknowledgement ................................................................................................................. x Chapter 1 Introduction ........................................................................................................... 1 Sediment Movement.......................................................................................................... 1 Wave Non-linearity ........................................................................................................... 8 Particle Image Velocimetry ............................................................................................. 16 Chapter 2 Methodology ....................................................................................................... 20 Research Questions ......................................................................................................... 20 Experimental Setup ......................................................................................................... 20 Sonic Wave Sensors ........................................................................................................ 22 PIV Laboratory Setup ...................................................................................................... 22 Sediment Analysis and Beach Profile ............................................................................. 24 Camera ............................................................................................................................ 26 PIVLab ............................................................................................................................ 29 Testing ............................................................................................................................. 31 Ripple Testing Analysis .................................................................................................. 32 Time-lapse Video Analysis ............................................................................................. 35 Chapter 3 Results ................................................................................................................. 36 Chapter 4 Discussion ........................................................................................................... 57 Chapter 5 Conclusion .......................................................................................................... 67 References ........................................................................................................................... 68 v Appendix A .......................................................................................................................... 74 List of Variables .............................................................................................................. 74 Appendix B .......................................................................................................................... 77 Matlab Codes ................................................................................................................... 77 Code to find m parameter............................................................................................ 77 Code to calculate cnoidal parameters .......................................................................... 78 Code for plots .............................................................................................................. 79 Appendix C .......................................................................................................................... 85 vi List of Figures Figure 1: Stoss and lee side of a ripple (Brock University, 2017) ......................................... 6 Figure 2: Ripple parameters (Nielsen, 1981) ......................................................................... 7 Figure 3: Validity of wave theories (Hedges, 1995) ............................................................ 10 Figure 4: Cnoidal shapes based on different values of elliptical modulus, m, and Ursell Number, Ur (Hinis, 2003) .................................................................................................... 11 Figure 5: Florida Tech wave channel .................................................................................. 21 Figure 6: Stroke adjustment for wave paddle ...................................................................... 21 Figure 7: Laser and camera mount for testing ..................................................................... 23 Figure 8: Sediment distribution ........................................................................................... 25 Figure 9: PIV laser illuminating sediment bed .................................................................... 31 Figure 10: Wave channel panels .......................................................................................... 35 Figure 11: Rippled bed for 0.25 meters and period of 1.5 seconds ..................................... 40 Figure 12: Rippled bed for 0.25 meters and period of 3 seconds ........................................ 40 Figure 13: Rippled bed for 0.46 meters and 6 second period .............................................. 40 Figure 14: Velocity area for 0.25 meters with 3 second period, from PIVLab ................... 42 Figure 15: Velocity area for 0.25 meters with 1.5 second period, from