Clapotis

Clapotis

Incoming wave (red) reflected at the wall produces the outgoing wave (blue), both being overlaid resulting in the clapotis (black).

In hydrodynamics, the clapotis (from French: "lapping of water") is a non-breaking standing wave pattern, caused for example, by the reflection of a traveling surface wave train from a near vertical shoreline like a breakwater, seawall or steep cliff.[1][2][3][4] The resulting clapotic[5] wave does not travel horizontally, but has a fixed pattern of nodes and antinodes.[6] These waves promote erosion at the toe of the wall,[7] and can cause severe damage to shore structures.[8] The term was coined in 1877 by French mathematician and physicist Joseph Valentin Boussinesq who called these waves ‘le clapotis’ meaning ‘standing waves’.[9][10]

In the idealized case of "full clapotis" where a purely monotonic incoming wave is completely reflected normal to a solid vertical wall,[11][12] the standing wave height is twice the height of the incoming waves at a distance of one half wavelength from the wall.[13] In this case, the circular orbits of the water particles in the deep-water wave are converted to purely linear motion, with vertical velocities at the antinodes, and horizontal velocities at the nodes.[14] The standing waves alternately rise and fall in a mirror image pattern, as kinetic energy is converted to potential energy, and vice versa.[15] In his 1907 text, Naval Architecture, Cecil Peabody described this phenomenon:

Related phenomena

True clapotis is very rare, because the depth of the water or the precipitousness of the shore are unlikely to completely satisfy the idealized requirements.[15] In the more realistic case of partial clapotis, where some of the incoming wave energy is dissipated at the shore,[17] the incident wave is less than 100% reflected,[11] and only a partial standing wave is formed where the water particle motions are elliptical.[18] This may also occur at sea between two different wave trains of near equal wavelength moving in opposite directions, but with unequal amplitudes.[19] In partial clapotis the wave envelope contains some vertical motion at the nodes.[19]

When a wave train strikes a wall at an oblique angle, the reflected wave train departs at the supplementary angle causing a cross-hatched wave interference pattern known as the clapotis gaufré ("waffled clapotis").[8] In this situation, the individual crests formed at the intersection of the incident and reflected wave train crests move parallel to the structure. This wave motion, when combined with the resultant vortices, can erode material from the seabed and transport it along the wall, undermining the structure until it fails.[8]

Clapotic waves on the sea surface also radiate infrasonic microbaroms into the atmosphere, and seismic signals called microseisms coupled through the ocean floor to the solid Earth.[20]

References

  1. ^ "clapotis". Glossary of Meteorology.  
  2. ^ "clapotis". Glossary of Scientific Terms.  
  3. ^ Eid, B. M.; Zemell, S. H. (1983). "Dynamic analysis of a suspended pump in a vertical well connected to the ocean". Canadian Journal of Civil Engineering 10 (3): 481–491.  
  4. ^ prepared by the Task Committee on Hydrology Handbook of Management Group D of the American Society of Civil Engineers. (1996). Hydrology handbook. New York: ASCE.  
  5. ^ Carter, Bill (1989). Coastal environments: an introduction to the physical, ecological, and cultural systems of coastlines. Boston: Academic Press. p. 50.  
  6. ^ Matzner, Richard A. (2001). Dictionary of geophysics, astrophysics, and astronomy. Boca Raton: CRC Press. p. 81.  
  7. ^ Beer, Tom (1997). Environmental oceanography. Boca Raton: CRC Press. p. 44.  
  8. ^ a b c Fleming, Christopher; Reeve, Dominic; Chadwick, Andrew (2004). Coastal engineering: processes, theory and design practice. London: Spon Press. p. 47.  
  9. ^ Iooss, G. (2007). "J. Boussinesq and the standing water waves problem". C. R. Mecanique 335 (9–10): 584–589.  
  10. ^ Iooss, G.; Plotnikov, P. I.; Toland, J. F. (2005). "Standing Waves on an Infinitely Deep Perfect Fluid Under Gravity". Archive for Rational Mechanics and Analysis 177 (3): 367–478.  
  11. ^ a b "D.4.14 Glossary". Guidelines and Specifications for Flood Hazard Mapping Partners (pdf).  
  12. ^ Mai, S.; Paesler, C. and Zimmermann, C. (2004). "Wellen und Seegang an Küsten und Küstenbauwerken mit Seegangsatlas der Deutschen Nordseeküste : 2. Seegangstransformation (Waves and Sea State on Coasts and Coastal Structures with Sea State Atlas of the German North Sea Coast : 2. Sea State Transformation)" (PDF).  
  13. ^ Jr, Ben H. Nunnally (2007). Construction of Marine and Offshore Structures, Third Edition. Boca Raton, FL: CRC Press. p. 31.  
  14. ^ van Os, Magchiel (2002). "4.2 Pressures due to Non-Breaking Waves". Breaker Model for Coastal Structures : Probability of Wave Impacts on Vertical Walls.  
  15. ^ a b Woodroffe, C. D. (2003). Coasts: form, process, and evolution. Cambridge, UK: Cambridge University Press. p. 174.  
  16. ^  
  17. ^ Hirayama, K. (2001). "Numerical Simulation of Nonlinear Partial Standing Waves using the Boussinesq Model with New Reflection Boundary". Report ff the Port and Airport Research Institute 40 (4): 3–48. The waves in front of actual seawalls and harbor breakwaters, however, are rather partial standing waves such that some incident wave energy is dissipated… 
  18. ^ Leo H. Holthuijsen (2007). Waves in Oceanic and Coastal Waters. Cambridge, UK: Cambridge University Press. p. 224.  
  19. ^ a b Silvester, Richard (1997). Coastal Stabilization. World Scientific Publishing Company.  
  20. ^ Tabulevich, V. N.; Ponomarev, E. A.; Sorokin, A. G.; Drennova, N. N. (2001). "Standing Sea Waves, Microseisms, and Infrasound". Izv. Akad. Nauk, Fiz. Atmos. Okeana 37: 235–244. Retrieved 2007-11-28. In this process, the interference of differently directed waves occurs, which forms standing water waves, or the so-called clapotis.…To examine and locate these waves, it is proposed to use their inherent properties to exert (“pump”) a varying pressure on the ocean bottom, which generates microseismic vibrations, and to radiate infrasound into the atmosphere. 

Further reading

  • Boussinesq, J. (1872). "Théorie des ondes liquides périodiques". Mémoires présentés par divers savants à l'Académie des Sciences (Paris) 20: 509–616. 
  • Boussinesq, J. (1877). "Essai sur la théorie des eaux courantes". Mémoires présentés par divers savants à l'Académie des Sciences (Paris) 23 (1): 1–660. 
  • Hires, G. (1960). "Étude du clapotis". La Houille Blanche 15: 153–63. 
  • Leméhauté, B.; Collins, J. I. (1961). Clapotis and Wave Reflection: With an Application to Vertical Breakwater Design. Civil Engineering Dept., Queen's University at Kingston, Ontario.