Observation and measurement of the bottom boundary layer flow in the prebreaking zone of shoaling waves

doi:10.1016/S0029-8018(01)00094-4

Ocean Engineering

Volume 29, Issue 12, September 2002, Pages 1479-1502

https://doi.org/10.1016/S0029-8018(01)00094-4 Get rights and content

Abstract

In this paper, the characteristics of the bottom boundary layer flow induced by nonlinear, asymmetric shoaling waves, propagating over a smooth bed of 1/15 uniform slope, is experimentally investigated. Flow visualization technique with thin-layered fluorescent dye was first used to observe the variation of the flow structure, and a laser Doppler velocimeter was then employed to measure the horizontal velocity, U.

The bottom boundary layer flow is found to be laminar except within a small region near the breaking point. The vertical distribution of the phase-averaged velocity 〈U〉 at each phase is non-uniform, which is directly affected by the mean velocity, $U ̄$ . The magnitude of $U ̄$ increases from zero at the bottom to a local positive maximum at about z/δ≅2.0∼2.5 (where z is the height above the sloping bottom and δ is the Stokes layer thickness), then decreases gradually to zero at z/δ≅6.0∼7.0 approximately, and finally becomes negative as z/δ increases further. Moreover, as waves propagate towards shallower water, the rate of increase in the maximum onshore oscillating velocity component $U ̃^{+}$ is greater than that of the offshore counterpart $U ̃^{−}$ except near the breaking point. The free stream velocities in the profiles of the maximum onshore and offshore oscillating velocity components, $U ̃^{+}_{∞}$ and $U ̃^{−}_{∞}$ are found to appear at z/δ≥6.0. This implies that, if the Stokes layer thickness is used as a length scale, the non-dimensionalized boundary layer thickness remains constant in the pre-breaking zone. Although $U ̃^{+}_{∞}$ is greater than $U ̃^{−}_{∞}$ and the asymmetry of the maximum free stream velocities (i.e. $| U ̃^{+}_{∞} / U ̃^{−}_{∞} |$ ) increases with decrease of water depth, a universal similar profile can be established by plotting z/δ versus ( $| U ̃^{+} / U ̃^{+}_{∞} |$ ) or ( $| U ̃^{−} / U ̃^{−}_{∞} |$ ). The final non-dimensional profile is symmetric and unique for the distributions of the maximum onshore and offshore oscillating velocity components within the bottom boundary layer, which are induced by nonlinear, asymmetric shoaling waves crossing the pre-breaking zone.

Introduction

Gravity waves propagating from deep to shallow water exhibit continuous transformation in wave profile due to shoaling accompanied by nonlinearity, thus leading to steepening of the wave crest and flattening of the wave trough. Eventually, the profile becomes unstable, leading to breaking waves. Since the hydrodynamic characteristics of shoaling waves are closely related to onshore/offshore sediment transport, vertical distribution of suspended loads, and pollutant dispersion in coastal waters; it is of paramount importance to investigate the flow field of shoaling waves, with special emphasis on the velocity distribution within the bottom boundary layer.

Although numerous investigations for the wave shoaling have been carried out in the past (e.g. Koh and LeM'ehout'e, 1966, Adeyemo, 1970, Iwagaki et al., 1974, Flick et al., 1981, Hedges and Kirkgöz, 1981, Kirkgöz, 1986, Nadaoka, 1986, Hwung and Lin, 1990, Voropayev et al., 2001), the study for the bottom boundary layer structure of shoaling waves propagating on a sloping bottom is still rather limited. Recently, considerable efforts have been devoted to the phenomenon of wave propagating over horizontal bottom. For example, Horikawa and Watanabe (1968) and Sleath (1970) used hydrogen bubbles and tension wire, respectively, to measure velocity distributions near smooth and rough beds. Jonsson and Carlsen (1976), utilizing a micropropeller flow-meter, measured the velocity profiles of turbulent boundary layer flow over rough beds in an oscillating water tunnel. Employing a laser Doppler velocimeter (LDV), Van Doorn (1981), Kemp and Simons (1982), Asano and Iwagaki (1984) and Belorgey et al. (1989) performed non-intrusive measurements of the near-bottom velocities in water waves with or without a current.

Teleki and Anderson (1970) may have been the first research to investigate the near-bottom water-particle velocity on a (smooth) slope with a Preston tube. However, their measurements were only made at the instants of wave-crest and wave-trough by alternatively orienting the L-shaped probe upslope and downslope, which interfered with flow field and thus led to measurement error. Recently, Hwung and Lin, 1989, Hwung and Lin, 1990 and Kirkgöz (1989) utilized LDV to measure the horizontal velocity profiles in the bottom boundary layer of shoaling waves propagating on 1/15 and 1/12 uniform slopes, respectively. Hwung and Lin, 1989, Hwung and Lin, 1990 investigated the vertical distributions of the mean velocity in the pre-breaking zone for different breaking waves. Kirkgöz (1989) examined the vertical distributions of the horizontal velocity under the wave-crest and wave-trough in the transformation zone of plunging breakers. In Kirkgöz (1989), the discrepancy between the measured and predicted velocity distributions was considered to be attributable to the turbulent effect in the near wall region. However, no clear evidence of turbulence was demonstrated, nor was the influence of mass transport on the measured velocity distribution (which might result in such inconsistency) discussed in his investigation.

The aim of this study is to elucidate the flow characteristics within the bottom boundary layer induced by nonlinear, asymmetric shoaling waves, propagating on an 1/15 sloping beach. A flow visualization technique with thin-layered fluorescent dye was first used to observe the flow structure of the bottom boundary layer. Then, a one-component LDV was employed to measure the horizontal (water-particle) velocity in the bottom boundary layer across the pre-breaking zone. Finally, some important features of the bottom boundary layer structure are examined and discussed.

Section snippets

Experimental set-up and method

Experiments were conducted in a glass-walled wave flume located at Tainan Hydraulic Laboratory, National Cheng Kung University. The wave flume is 9.5 m long, 0.3 m wide and 0.7 m deep. The first 3.77 m section had a fixed horizontal smooth bottom starting from the end where a flap-type wave maker was installed. The remaining 5.73 m of the flume had an adjustable sloping smooth bed made of polished stainless plate. A fixed slope of 1/15 was used in this study. Monochromatic waves could be generated

Data analysis

Hussain and Reynolds (1970) proposed a phase average method that, for a steady turbulent shear flow coexisting with a periodic motion, any physical quantity Q could be decomposed into a time mean $Q ̄$ , a (periodically) oscillating component $Q ̃$ , and a turbulent fluctuation component Q′. The relation can be expressed as $Q(r ̄, t)= Q ̄ (r →)+ Q ̃ (r →, t)+Q′(r →, t),$ in which $r →$ and t are position vector and time variable, respectively. The time mean of Q is in the form of $Q ̄ (r →)= 1 T_{s} ∫^{T_{s}}_{0} Q(r →, t) d t,$ where T_s is the

Flow visualization results

It has been widely recognized that the boundary layer developed over natural sea bottom is a turbulent flow. However, it is not clear if turbulence could occur in the case of laboratory wave. It should be examined in the first stage of this investigation.

Figures 3(a, b) show the visualized results of the dye layer flow on the sloping bottom within the pre-breaking zone of case 1 (see Table 1). They were photographed at different times by a camera with different viewing angles when the wave

Concluding remarks

Experimental work was conducted in a wave flume to investigate the characteristics of the bottom boundary layer flow induced by nonlinear, asymmetric shoaling waves, propagating over a smooth bed with an 1/15 uniform slope. A flow visualization technique with thin-layered of fluorescent dye and a laser Doppler velocimeter were both employed. Based on the observation and measurement results depicted above, the following conclusions can be drawn.

1.
From the time history of all the horizontal

Acknowledgements

The authors are grateful for the support of the National Science Council, Taiwan, Republic of China, under Grant No. NSC 89-2611-E-005-005.

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Observation and measurement of the bottom boundary layer flow in the prebreaking zone of shoaling waves

Abstract

Introduction

Section snippets

Experimental set-up and method

Data analysis

Flow visualization results

Concluding remarks

Acknowledgements

Coastal Eng.

Coastal Eng.

Coastal Eng.

Ocean Eng.

Velocity fields in the wave breaker zone

Proc. 12th Int. Conf. Coastal Eng., ASCE

Bottom turbulent boundary layer in wave-current co-existing systems

Proc. 19th Int. Conf. Coastal Eng., ASCE

Mass transport in gravity waves on a sloping bottom

Proc. 14th Int. Conf. Coastal Eng., ASCE

The transition to turbulence in the wake of a circular cylinder

J. Fluid Mech.

Elevation and velocity measurements of laboratory shoaling waves

J. Geophys. Res.

Laboratory study on oscillatory boundary layer flow

Proc. 11th Int. Conf. Coastal Eng., ASCE

The mechanics of an organized wave in turbulent shear flow

J. Fluid Mech.

The characteristics of internal flow field and bottom boundary layer of waves propagating on sloping bottoms

Bulletin No. 16

The mass transport of waves propagating on a sloping bottom

Proc. 22nd Int. Conf. Coastal Eng., ASCE

Relationship between vertical distribution of water particle velocity and type of breakers on beaches

Coastal Eng. Jap.