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Research Papers: Multiphase Flows

# Wave Height and Wave Velocity Measurements in the Vicinity of the Break Point in Laboratory Plunging Waves

[+] Author and Article Information
R. Mukaro

College of Agriculture, Engineering, and Science,
School of Chemistry and Physics,
University of KwaZulu-Natal,
Private Bag X54001,
Durban 4000, South Africa
e-mail: mukaror@ukzn.ac.za

K. Govender

Honorary Research Fellow
Centre for Instrumentation Research,
Department of Electrical Engineering,
Cape Peninsula University of Technology,
P.O. Box 652,
Cape Town 8000, South Africa;
College of Agriculture, Engineering and Science,
School of Chemistry and Physics,
University of KwaZulu-Natal,
Private Bag X54001,
Durban 4000, South Africa
e-mail: kessie.gov@gmail.com

College of Agriculture, Engineering, and Science,
School of Chemistry and Physics,
University of KwaZulu-Natal,
Private Bag X54001,
Durban 4000,South Africa

1Corresponding author.

Manuscript received February 29, 2012; final manuscript received January 31, 2013; published online April 12, 2013. Assoc. Editor: Mark R. Duignan.

J. Fluids Eng 135(6), 061303 (Apr 12, 2013) (13 pages) Paper No: FE-12-1097; doi: 10.1115/1.4023659 History: Received February 29, 2012; Revised January 31, 2013

## Abstract

Results are presented of laboratory experiments undertaken to study the dynamics of wave propagation and transformation within the surf zone. The study involved measuring the external flow characteristics of regular plunging waves propagating along a 20 m long flume fitted with a 1:20 plane slope. To achieve this, monochromatic waves of frequency 0.4 Hz and a deep water wave height of 12 cm were generated by a servo-controlled piston-type wave maker. A set of calibrated parallel-wire capacitive wave gauges were employed to measure statistics of the free surface elevation along the slope in order to get an insight into the wave breaking behavior. To characterize the wave field, free surface elevation measurements were made in the vicinity of the break point. The measured time series data were analyzed at each flume position to obtain statistics of the mean water level, wave height, and wave velocity along the flume. Results show that as the wave propagates from deep water towards shallow water, there is an increase in the wave height, reaching a maximum height of about 21.5 cm at the break point, and then decreases sharply thereafter. Wave phase velocity calculations at different flume positions were made from the measured time series. Cross correlation techniques were used to determine the phase difference between the reference wave near the generator and the wave at various points along the flume. The local wave velocity was obtained by taking the phase difference between two points spaced 0.2 m apart. A comparison was made between the measured wave phase velocity, its linear shallow water ($(gh)$) approximation and the roller model concept wave velocity ($1.3(gh)$), at various points along the flume. The measured wave velocity c was found to lie in the range $(gh) for most of the positions except near the break point. After the break point, the measured wave velocity is up to 38% higher than the theoretical value predicted using the roller model concept. Also noted is the variability of the phase speed in the breaking region. The present experiments of quantifying the mean macroscopic properties of breaking waves are a necessary prerequisite for more detailed experiments involving internal fluid velocity measurements that will follow.

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Topics: Waves , Water , Gages , Flumes

## Figures

Fig. 1

Sketch defining coordinate axes and wave parameters for a wave propagating in the positive x direction. The still water line (swl) is at z = 0.

Fig. 2

Aerial view of the laboratory flume where measurements were performed. Waves generated near the bottom left corner propagate along the flume towards the top right corner.

Fig. 3

Schematic of the flow geometry (not drawn to scale) showing the side view of the wave flume structure, dimensions and the reference frame used. Initial positions of the wave gauges labeled G1, G2, and G3 are shown. Free surface elevation measurements were made over the experimental range as gauges G2 and G3 were sequentially moved in steps of 10 cm towards the generator. The still water line (swl) mark is at x = 0, and vertical elevations are measured relative to z = 0, which is at the swl.

Fig. 4

Parallel-wire capacitor wave gauges used for free surface elevation measurements in the flume, looking towards the wave generator

Fig. 5

Facilities for wave generation, capacitive wave gauge signal conditioning and data acquisition equipment (a) picture, and (b) block diagram schematic

Fig. 6

Time series of water displacement over a 20 s record measured by three wave gauges (a) G1-near wave generator at (x = −14.0 m), (b) G2-before the breaking point at (x = −4.0 m), and (c) G3-after the break point at (x = −1.5 m)

Fig. 7

Signals used for determining wave height (a) instantaneous free surface elevation time series, (b) gating signal, and (c) sync function, used for locating a full wave cycle in the sampled data

Fig. 8

Cross-shore variation of wave height measurements from the still water line mark on the beach. Breaking occurs at a point x = −4.0 m from the still water line mark and is marked by the inscription B.P. uncertainty bars were estimated from the standard deviations and show variations in the wave heights at each point.

Fig. 9

Variation of wave height and mean water levels along the flume. The gray vertical line at x = −4.0 m marks the break point.

Fig. 10

Time series showing phase at that point relative to wave gauge G1 for positions (a) −3.1 m, (b) −2.7 m, (c) −2.3 m, and (d) −1.7 m from the still water line mark

Fig. 11

Variation of the measured wave phase along the flume for points 0.1 m apart. These were measured relative to the time series of wave gauge G1.

Fig. 12

Variation of the measured average wave velocity along the flume and the theoretical estimates calculated using linear and nonlinear wave theories

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