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On Extreme Spatial Variations of Surface Slope for a Spilling Breaking Water Wave

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  • 1 Remote Sensing Division, Naval Research Laboratory, Washington, D.C.
  • | 2 Air–Sea Interaction Laboratory, Graduate College of Marine Studies, University of Delaware, Lewes, Delaware
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Abstract

The steep and complex crest structure of a spilling breaking wave was studied in the laboratory by repeated slope measurements at a fixed observation point of a sequence of virtually identical breaking waves. These waves were generated using a repeatable converging wave packet with maximum frequency of 1 Hz. A fixed laser beam was directed vertically downward from the air into the water, and the location of the refracted beam was measured with a photodiode array to provide the water surface slope as the wave passed the laser beam. A maximum slope of 74° was consistently measured just forward of the breaking wave crest with the crest region itself showing less repeatability, which was probably due to parasitic capillary waves. Before reaching its maximum, the slope reveals a two-stage spatial variation. A moderate rate of increase was first observed between 0° and 44°, then the wave slope increased sharply to 74°; the horizontal translation of the crest corresponding to the interval for the slope change from 44° to the observed maximum of 74° was about 4.2 cm. The decrease of surface slope from the maximum to 0° at the crest was subsequently observed over a 3.6-cm translation. The slope variation reported here refines the macroprofile of a spilling breaker suggested by other investigators. Were the laser beam used to illuminate from below, internal reflection would occur for slopes greater than 51.5°, thus eliminating refraction and preventing steeper slopes from being measured.

Corresponding author address: Dr. Shih Tang, Air–Sea Interaction Lab, Hugh R. Sharp Campus, University of Delaware, Lewes, DE 19958-1239. E-mail: stang@udel.edu

Abstract

The steep and complex crest structure of a spilling breaking wave was studied in the laboratory by repeated slope measurements at a fixed observation point of a sequence of virtually identical breaking waves. These waves were generated using a repeatable converging wave packet with maximum frequency of 1 Hz. A fixed laser beam was directed vertically downward from the air into the water, and the location of the refracted beam was measured with a photodiode array to provide the water surface slope as the wave passed the laser beam. A maximum slope of 74° was consistently measured just forward of the breaking wave crest with the crest region itself showing less repeatability, which was probably due to parasitic capillary waves. Before reaching its maximum, the slope reveals a two-stage spatial variation. A moderate rate of increase was first observed between 0° and 44°, then the wave slope increased sharply to 74°; the horizontal translation of the crest corresponding to the interval for the slope change from 44° to the observed maximum of 74° was about 4.2 cm. The decrease of surface slope from the maximum to 0° at the crest was subsequently observed over a 3.6-cm translation. The slope variation reported here refines the macroprofile of a spilling breaker suggested by other investigators. Were the laser beam used to illuminate from below, internal reflection would occur for slopes greater than 51.5°, thus eliminating refraction and preventing steeper slopes from being measured.

Corresponding author address: Dr. Shih Tang, Air–Sea Interaction Lab, Hugh R. Sharp Campus, University of Delaware, Lewes, DE 19958-1239. E-mail: stang@udel.edu

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