# Bichromatic synthetic schlieren applied to surface wave measurements

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## Abstract

The present paper provides an introduction to bichromatic synthetic schlieren (BiCSS) for surface measurements, a novel extension of the free surface synthetic schlieren (FS-SS) by Moisy et al. (Exp Fluids 46:1021–1036, 2009). The new technique is based on the fact that light diffraction through a medium varies with wavelength. Therefore, one may apply light at two different wavelengths to measure the change in density gradient in a medium. This paper explores the use of the difference between blue visual and near-infrared light, but the choice of wavelengths will typically depend on the application. Calibration was performed using stationary targets of plexiglass and the results show that the new BiCSS technique improves accuracy for large surface gradients, compared to the traditional FS-SS technique. In order to test the applicability of the technique in the laboratory, two sets of experiments were performed. Firstly, an experiment using phase-locked regular waves was conducted for comparing BiCSS with FS-SS, analyze the properties and give an estimation of the error. Secondly, to investigate the applicability for more complex surface patterns, a study on a vertical surface-piercing cylinder exposed to a focused wave was conducted, obtaining the complex surface characteristics. The new technique clearly reveals nonlinear wave diffraction, in addition to cross waves and parasitic capillary waves.

## Notes

### Acknowledgements

The study has been carried out with financial support from Stiftelsen Det Norske Veritas, DNV GL and The Research Council of Norway through grant number 231491: Developments in Optical Measurement Technologies (DOMT). Technical assistance during the experimental work by Head Engineer Olav Gundersen is gratefully acknowledged.

## References

- Aureli F, Dazzi S, Maranzoni A, Mignosa P (2014) A combined colour-infrared imaging technique for measuring water surface over non-horizontal bottom. Exp Fluids 55:1–14CrossRefGoogle Scholar
- Benetazzo A, Barbariol F, Bergamasco F, Torsello A, Carniel S, Sclavo M (2016) Stereo wave imaging from moving vessels: practical use and applications. Coast Eng 109:114–127CrossRefGoogle Scholar
- Chaplin JR, Rainey RCT, Yemm RW (1997) Ringing of a vertical cylinder in waves. J Fluid Mech 350:119–147MathSciNetCrossRefGoogle Scholar
- Chen LF, Zang J, Hillis AJ, Morgan GCJ, Plummer AR (2014) Numerical investigation of wave-structure interaction using openfoam. Ocean Eng 88:91–109CrossRefGoogle Scholar
- Ciddor PE (1996) Refractive index of air: new equations for the visible and near infrared. Appl opt 35:1566–1573CrossRefGoogle Scholar
- Daimon M, Masumura A (2007) Measurement of the refractive index of distilled water from the near-infrared region to the ultraviolet region. Appl Opt 46:3811–3820CrossRefGoogle Scholar
- Dalziel S, Hughes GO, Sutherland BR (2000) Whole-field density measurements by ’synthetic schlieren’. Exp Fluids 28:322–335CrossRefGoogle Scholar
- D’Errico J (2006) Inverse (integrated) gradient for Matlab. http://www.mathworks.com/matlabcentral/.File9734
- Fedorov AV, Melville WK (1998) Nonlinear gravity-capillary waves with forcing and dissipation. J Fluid Mech 354:1–42MathSciNetCrossRefMATHGoogle Scholar
- Goda Y, Suzuki Y (1977) Estimation of incident and reflected waves in random wave experiments. Coast Eng 1976:828–845CrossRefGoogle Scholar
- Gomit G, Chatellier L, Calluaud D, David L (2013) Free surface measurement by stereo-refraction. Exp Fluids 54:1–11CrossRefGoogle Scholar
- Jähne B (1990) Two-dimensional wave nulllber spectra of small-scale water surface waves. J Geophys Res 95:11–531CrossRefGoogle Scholar
- Jähne B, Schmidt M, Rocholz R (2005) Combined optical slope/height measurements of short wind waves: principle and calibration. Meas Sci Technol 16:1937CrossRefGoogle Scholar
- Kiefhaber D, Reith S, Rocholz R, Jähne B (2014) High-speed imaging of short wind waves by shape from refraction. J Eur Opt Soc. https://doi.org/10.2971/jeos.2014.14015 Google Scholar
- Kolaas J (2016) Getting started with HydrolabPIV v1.0. Preprint series. Research Report in MechanicsGoogle Scholar
- Kolaas J, Smith L, Sveen JK, Jensen A (2016) Bichromatic synthetic schlieren for surface measurement. In: Proceedings of the 18th international symposium on the application of laser and imaging techniques to fluid mechanicsGoogle Scholar
- Kristiansen T, Faltinsen OM (2017) Higher harmonic wave loads on a vertical cylinder in finite water depth. J Fluid Mech 833:773–805CrossRefGoogle Scholar
- Longuet-Higgins MS (1992) Capillary rollers and bores. J Fluid Mech 240:659–679MathSciNetCrossRefMATHGoogle Scholar
- Meier G (2002) Computerized background-oriented schlieren. Exp Fluids 33:181–187CrossRefGoogle Scholar
- Moisy F, Rabaud M, Salsac K (2009) A synthetic schlieren method for the measurement of the topography of a liquid interface. Exp Fluids 46:1021–1036CrossRefGoogle Scholar
- Paquier A, Moisy F, Rabaud M (2015) Surface deformations and wave generation by wind blowing over a viscous liquid. Phys Fluids 27:122103CrossRefGoogle Scholar
- Paulsen BT, Bredmose H, Bingham HB (2014a) An efficient domain decomposition strategy for wave loads on surface piercing circular cylinders. Coast Eng 86:57–76CrossRefGoogle Scholar
- Paulsen BT, Bredmose H, Bingham HB, Jacobsen NG (2014b) Forcing of a bottom-mounted circular cylinder by steep regular water waves at finite depth. J Fluid Mech 755:1–34MathSciNetCrossRefGoogle Scholar
- Rainey RCT (2007) Weak or strong nonlinearity: the vital issue. J Eng Math 58:229–249MathSciNetCrossRefMATHGoogle Scholar
- Schäffer HA (1996) Second-order wavemaker theory for irregular waves. Ocean Eng 23:47–88CrossRefGoogle Scholar
- Sheikh R, Swan C (2005) The interaction between steep waves and a vertical, surface-piercing column. J Offshore Mech Arct 127:31–38CrossRefGoogle Scholar
- Sultanova N, Kasarova S, Nikolov I (2009) Dispersion proper ties of optical polymers. Acta Phys Polonica Ser A 19:585CrossRefGoogle Scholar
- Sutherland BR, Dalziel SB, Hughes GO, Linden P (1999) Visualization and measurement of internal waves by ’synthetic schlieren’. part 1. vertically oscillating cylinder. J Fluid Mech 390:93–126CrossRefMATHGoogle Scholar
- Swan C, Sheikh R (2015) The interaction between steep waves and a surface-piercing column. Phil Trans R Soc A 373:20140114CrossRefGoogle Scholar
- Toffoli A, Gramstad O, Trulsen K, Monbaliu J, Bitner-Gregersen E, Onorato M (2010) Evolution of weakly nonlinear random directional waves: laboratory experiments and numerical simulations. J Fluid Mech 664:313–336MathSciNetCrossRefMATHGoogle Scholar
- Zappa CJ, Banner ML, Schultz H, Corrada-Emmanuel A, Wolff LB, Yalcin J (2008) Retrieval of short ocean wave slope using polarimetric imaging. Meas Sci Technol 19:055503CrossRefGoogle Scholar