Experimental investigation of the vorticity generation within a spilling water wave

Abstract

Sources of vorticity are examined for a laboratory-generated spilling breaking wave. Two cases are studied. For the first case, based on the breaker height, the Reynolds and Froude numbers are 7370 and 2.04, respectively. The breaker is preceded by 1 mm wavelength capillary waves, with the largest amplitude-to-wavelength ratio equal to 0.18. For this case, it is found that the dominant source of vorticity flux is a viscous process, due to the deceleration of a thin layer of the surface fluid. For the second case, the Reynolds and Froude numbers based on the wave height are 1050 and 1.62, respectively. No breaking is observed for this case; rather a capillary–gravity wave is observed with 4 mm wavelength capillaries preceding the gravity wave. The largest amplitude-to-wavelength ratio of these capillaries is 0.28. This case shows that capillary waves do not contribute to the vorticity flux; rather the only dominant source of the vorticity flux into the flow is the free-surface fluid deceleration.

Lastly, a thin free-surface jet that is relatively vorticity-free is found to precede the spilling breaker. Analyses suggest that our wave-breaking phenomena can be modelled by a hydraulic jump phenomenon where the Froude number is based on the thickness of the free-surface jet, and on the velocity of the free-surface jet just prior to breaking. We believe this to be a more physically descriptive value of the Froude number. For the high-speed case, the Froude number based on the thickness of the free-surface jet is 4.78, while for the lower-speed case it is 2.14.