Cover Image

HARDBACK
$198.00



View/Hide Left Panel

the vorticity seen in the crest roller. After a series of analyses, he shows that due to surface curvature, there exists a Stokes layer δ=(2v/γ)2, where v is the kinematic viscosity, and γ is the radian frequency of the wave, within which vorticity is generated, and beyond which vorticity escapes and is ω≈2(aκ)2γ, where a is the wave amplitude, κ is the wave number, and describes the wave steepness. After detailed observations, Lin and Rockwell (10, 11) conclude that the sharp surface curvature serves as a source of vorticity, thereby giving rise to a separated mixing layer. They also observe that the region between the free surface and the mixing layer contains vorticity levels which are small compared with the mixing layer itself. Lastly, Hornung, et. al. (13) suggest that the substantial vorticity seen downstream of a hydraulic jump is due to the entrainment of bubbles during breaking. This was further explained by suggesting that the circulation around a loop, drawn directly beneath the free surface on oneside and stretching into the fluid bulk on all other sides such that the loop incorporates a bubble, is non-zero. Furthermore, they also suggest that the entrainment of vorticity is also connected to how the circulation loop is drawn.

It is therefore the purpose of this paper to shed some light on the origins of the source of vorticity seen within a spilling breaking wave. Specifically, the questions that will be answered are a) What is the source of the vorticity seen beneath and downstream of the breaker? b) Do capillary waves contribute to the vorticity? c) Do we need large breaking and therefore air entrainment in order to generate vorticity?

2.
EXPERIMENTAL SET-UP
2.1
The test facility

In order to answer these questions, a series of spilling wave breaking experiments were performed in a closed-loop water tunnel facility at CALTECH. The water tunnel has a contraction ratio of 4:1, with a 15.2× 15.2×61 cm3 test section. Previous approaches for generating spilling breaking waves have been to situate a hydrofoil located at some distance below the water level in a water tunnel. This caused the fluid above the

Figure 2. Image acquisition set-up.

hydrofoil to accelerate, and therefore generate spilling breaking waves. For the present experiments, an original technique was devised to generate spilling breaking waves. A 15.2×15.2×2.54 cm3 honeycomb section with a screen is placed at the beginning of the test section, where the honeycomb straws are 2.3 mm in diameter, and the wire screen is 50 mesh/inch stainless steel (see figure 1). Due to the pressure drop across the honeycomb/screen section, the fluid is accelerated to a maximum velocity, while dropping in height, and thereby generating spilling breaking waves.

Figure 1. Wave breaking experimental set-up (not to scale).

2.2
The DPIV set-up and acquisition system

Figure 2 shows a schematic for the experimental setup for data acquisition. The flow is seeded with 14 +/– 5 micrometer silver-coated hollow glass spheres with a specific gravity of 1.4 g/cm3. Through a series of optics and mirrors, a laser light sheet with a maximum thickness of 1 millimeter is generated. This light sheet is then set parallel to the flow direction allowing the wave to be viewed before, during, and after breaking. The Dantec Flowgrabber DPIV system is used to record images onto a laser disk, which are subsequently digitized onto the hard disk. The Dantec Flowgrabber DPIV system is based on the cross-correlation technique. Therefore, images are exposed only once and are recorded at 30 frames per second. For analysis, a small

Figure 2. Image acquisition set-up.

interrogation window uniformly steps through the same locations within sequential pairs of images, performing a cross-correlation analysis at each location. Finally, a guassian curve-fit is used to obtain sub-pixel accuracy of the cross-correlation peak. Once this is done at all locations within the image pairs, a displacement field in pixel values is obtained. By calibrating the pixels to spatial values, and knowing the time difference between exposures, the velocity field can be obtained. A more detailed description of the cross-correlation technique used here can be found in Willert and Gharib (14). Unfortunately, previous cross-correlating hardware limited the technique to slow flows, since each image



The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement