Francis C. K. Ting

Observation of undertow and turbulence in a laboratory surf zone

Abstract Undertow and turbulence in the surf zone have been studied in a wave flume for a spilling breaker and a plunging breaker. Fluid velocities across a 1 on 35 sloped false bottom were measured using a fiber-optic laser-Doppler anemometer, and wave decay and set-up were measured using a capacitance wave gage. The characteristics of mean flow and turbulence in spilling versus plunging breakers were studied. The mean flow is the organized wave-induced flow defined as the phase average of the instantaneous velocity, while the turbulence is taken as the deviations from the phase average. It was found that under the plunging breaker turbulence levels are much higher and vertical variations of undertow and turbulence intensity are much smaller in comparison with the spilling breaker. It was also found that turbulent kinetic energy is transported seaward under the spilling breaker and landward under the plunging breaker by the mean flow. The study indicates that there are fundamental differences in the dynamics of turbulence between spilling and plunging breakers, which can be related to the processes of wave breaking and turbulence production. It is suggested that the types of beach profile produced by storm and swell waves may be the results of different relationships between mean flow and turbulence in these waves.

Dynamics of surf-zone turbulence in a spilling breaker

The structure of turbulence in a spilling breaker has been studied experimentally based on the transport equation for turbulent kinetic energy (the k-equation). We study turbulence transport in the evolving flow from the breaking point to the inner surf zone in the region below trough level and above the bottom boundary layer. The study shows that turbulence transport processes are similar in the outer and inner surf zones. It is found that diffusive transport plays the most important role in the distribution of turbulence, while advection is important mainly near the surface. It is also found that although turbulence production below trough level amounts to only a small portion of the wave energy loss, the production term is not small compared to the dissipation term and the major terms in the k-equation and thus it cannot be neglected. The mixing length is estimated based on the measured rates of vertical advance of the turbulent front, and comparisons of turbulence production and energy dissipation. The results are similar to those found in previous studies. It is shown that the length scale and velocity scale of the large eddies are subject to turbulence transport processes, therefore their distributions cannot be prescribed in an easy way. The relative values of the components of the Reynolds stress tensor are examined. The results of analysis supports the notion that surf-zone turbulence created by spilling and plunging breakers differ primarily in the method of energy transfer from organized wave-induced motion to turbulent motion, and the constraints imposed by the mean flow and the solid bottom on the large-scale turbulence.

Dynamics of surf-zone turbulence in a strong plunging breaker

Abstract The characteristics of turbulence created by a plunging breaker on a 1 on 35 plane slope have been studied experimentally in a two-dimensional wave tank. The experiments involved detailed measurements of fluid velocities below trough level and water surface elevations in the surf zone using a fibre-optic laser-Doppler anemometer and a capacitance wave gage. The dynamical role of turbulence is examined making use of the transport equation for turbulent kinetic energy (the k-equation). The results show that turbulence under a plunging breaker is dominated by large-scale motions and has certain unique features that are associated with its wave condition. It was found that the nature of turbulence transport in the inner surf zone depends on a particular wave condition and it is not similar for different types of breakers. Turbulent kinetic energy is transported landward under a plunging breaker and dissipated within one wave cycle. This is different from spilling breakers where turbulent kinetic energy is transported seaward and the dissipation rate is much slower. The analysis of the k-equation shows that advective and diffusive transport of turbulence play a major role in the distribution of turbulence under a plunging breaker, while production and dissipation are not in local equilibrium but are of the same order of magnitude. Based on certain approximate analytical approaches and experimental measurements it is shown that turbulence production and viscous dissipation below trough level amount to only a small portion of the wave energy loss caused by wave breaking. It is suggested that the onshore sediment transport produced by swell waves may be tied in a direct way to the unique characteristics of turbulent flows in these waves.

Vortex generation in water waves propagating over a submerged obstacle

Abstract Laboratory experiments have been conducted to investigate flow separation effects induced by time-periodic water waves travelling over a submerged rectangular obstacle. Water surface elevations and fluid velocities were obtained for a range of non-breaking wave conditions. From these measurements, the kinematics and dynamics of eddy motions were studied. The measured velocities were compared to the theoretical predictions of a linear inviscid model. It was found that the formation and growth of separation region respond directly to the wave transformation above the submerged obstacle, leading to a variety of different eddy geometries. The interaction of the separated flow with the wave field significantly modifies the transmission process but has little effect on the reflection process. The most important consequence of flow separation is energy dissipation at the expense of the transmitted waves. The observed data indicate that separation loss is the results of viscous shear in the formation of eddies and the subsequent dissipation of energy as the eddies decay. When the obstacle is slightly submerged the presence of separation modifies the effective boundary of the flow above the obstacle. The complex nature of this problem suggests that it would be very difficult to determine flow separation effects unambiguously without solving the viscous flow equations in the near field.

Laboratory study of wave and turbulence velocities in a broad-banded irregular wave surf zone

Abstract The characteristics of wave and turbulence velocities created by a broad-banded irregular wave train breaking on a 1:35 slope were studied in a laboratory wave flume. Water particle velocities were measured simultaneously with wave elevations at three cross-shore locations inside the surf zone. The measured data were separated into low-frequency and high-frequency time series using a Fourier filter. The measured velocities were further separated into organized wave-induced velocities and turbulent velocity fluctuations by ensemble averaging. The broad-banded irregular waves created a wide surf zone that was dominated by spilling type breakers. A wave-by-wave analysis was carried out to obtain the probability distributions of individual wave heights, wave periods, peak wave velocities, and wave-averaged turbulent kinetic energies and Reynolds stresses. The results showed that there was a consistent increase in the kurtosis of the vertical velocity distribution from the surface to the bottom. The abnormally large downward velocities were produced by plunging breakers that occurred from time to time. It was found that the mean of the highest one-third wave-averaged turbulent kinetic energy values in the irregular waves was about the same as the time-averaged turbulent kinetic energy in a regular wave with similar deep-water wave height to wavelength ratio. It was also found that the correlation coefficient of the Reynolds stress varied strongly with turbulence intensity. Good correlation between u′ and w′ was obtained when the turbulence intensity was high; the correlation coefficient was about 0.3–0.5. The Reynolds stress correlation coefficient decreased over a wave cycle, and with distance from the water surface. Under the irregular breaking waves, turbulent kinetic energy was transported downward and landward by turbulent velocity fluctuations and wave velocities, and upward and seaward by the undertow. The undertow in the irregular waves was similar in vertical structure but lower in magnitude than in regular waves, and the horizontal velocity profiles under the low-frequency waves were approximately uniform.

Laboratory study of wave and turbulence characteristics in narrow-band irregular breaking waves

Abstract Wave elevations and water particle velocities were measured in a laboratory surf zone created by the breaking of a narrow-band irregular wave train on a 1/35 plane slope. The incident waves form wave groups that are strongly modulated. It is found that the waves that break close to the shoreline generally have larger wave-height-to-water-depth ratios before breaking than the waves that break farther offshore. After breaking, the wave-height-to-water-depth ratio for the individual waves approaches a constant value in the inner surf zone, while the standard deviation of the wave period increases as the still water depth decreases. In the outer surf zone, the distribution of the period-averaged turbulent kinetic energy is closely correlated to the initial wave heights, and has a wider variation for narrow-band waves than for broad-band waves. In the inner surf zone, the distribution of the period-averaged turbulent kinetic energy is similar for narrow-band waves and broad-band waves. It is found that the wave elevation and turbulent kinetic energy time histories for the individual waves in a wave group are qualitatively similar to those found in a spilling regular wave. The time-averaged transport of turbulent kinetic energy by the ensemble-averaged velocity and turbulence velocity under the irregular breaking waves are also consistent with the measurements obtained in regular breaking waves. The experimental results indicate that the shape of the incident wave spectrum has a significant effect on the temporal and spatial variability of wave breaking and the distribution of turbulent kinetic energy in the outer surf zone. In the inner surf zone, however, the distribution of turbulent kinetic energy is relatively insensitive to the shape of the incident wave spectrum, and the important parameters are the significant wave height and period of the incident waves, and the beach slope.

A numerical investigation of wave‐breaking‐induced turbulent coherent structure under a solitary wave

To better understand the effect of wave-breaking-induced turbulence on the bed, we report a 3-D large-eddy simulation (LES) study of a breaking solitary wave in spilling condition. Using a turbulence-resolving approach, we study the generation and the fate of wave-breaking-induced turbulent coherent structures, commonly known as obliquely descending eddies (ODEs). Specifically, we focus on how these eddies may impinge onto bed. The numerical model is implemented using an open-source CFD library of solvers, called OpenFOAM, where the incompressible 3-D filtered Navier-Stokes equations for the water and the air phases are solved with a finite volume scheme. The evolution of the water-air interfaces is approximated with a volume of fluid method. Using the dynamic Smagorinsky closure, the numerical model has been validated with wave flume experiments of solitary wave breaking over a 1/50 sloping beach. Simulation results show that during the initial overturning of the breaking wave, 2-D horizontal rollers are generated, accelerated, and further evolve into a couple of 3-D hairpin vortices. Some of these vortices are sufficiently intense to impinge onto the bed. These hairpin vortices possess counter-rotating and downburst features, which are key characteristics of ODEs observed by earlier laboratory studies using Particle Image Velocimetry. Model results also suggest that those ODEs that impinge onto bed can induce strong near-bed turbulence and bottom stress. The intensity and locations of these near-bed turbulent events could not be parameterized by near-surface (or depth integrated) turbulence unless in very shallow depth.

Flow Velocity and Pier Scour Prediction in a Compound Channel: Big Sioux River Bridge at Flandreau, South Dakota

The two-dimensional (2D) depth-averaged river model Finite-Element Surface-Water Modeling System (FESWMS) was used to predict flow distribution at the bend of a compound channel. The site studied was the Highway 13 bridge over the Big Sioux River in Flandreau, South Dakota. The Flandreau site has complex channel and floodplain geometry that produces unique flow conditions at the bridge crossing. The 2D model was calibrated using flow measurements obtained during two floods in 1993. The calibrated model was used to examine the hydraulic and geomorphic factors that affect the main channel and floodplain flows and the flow interactions between the two portions. A one-dimensional (1D) flow model of the bridge site was also created in Hydrologic Engineering Centers River Analysis System (HEC-RAS) for comparison. Soil samples were collected from the bridge site and tested in an erosion function apparatus (EFA) to determine the critical shear stress and erosion rate constant. The results of EFA testing and 2D flow modeling were used as inputs to the Scour Rate in Cohesive Soils (SRICOS) method to predict local scour at the northern and southernmost piers. The sensitivity of predicted scour depth to the hydraulic and soil parameters was examined. The predicted scour depth was very sensitive to the approach-flow velocity and critical shear stress. Overall, this study has provided a better understanding of 2D flow effects in compound channels and an overall assessment of the SRICOS method for prediction of bridge pier scour.

On forced internal waves in a rectangular trench

The generation of internal waves in a submarine rectangular trench by normally incident surface waves has been investigated through laboratory experiments and theory. A linear model was developed for small-amplitude, simple harmonic wave motions. In this model, the fluid outside the trench is homogeneous, and the fluid in the trench is composed of two homogeneous layers of different densities separated by a transition region of linear density variation; viscous dissipation is treated based on the assumption of a laminar boundary layer. In the experiments, the stratification in the trench was created using fresh water and salt water, and a scanning laser beam and detector system was used to measure the amplitude of internal waves. The study shows that, when the frequency of the surface waves corresponds to the natural frequency of internal waves, the amplitude of internal waves becomes large compared to the amplitude of surface waves. The natural frequency of oscillation of internal waves decreases as the thickness of the density interface increases and the depth of the lower fluid decreases. Two distinct classes of internal waves were observed, namely, standing internal waves when the lower fluid was deep, and travelling internal waves when the lower fluid was shallow. The linear model predicted the response curve for internal waves quite well in all the cases investigated. It was also found that the internal waves were strongly damped when the depth of the lower fluid was small compared to the wavelength of internal waves.

Dynamic response of fluid mud in a submarine trench to water waves

Abstract The dynamic response of fluid mud in a submarine rectangular trench to time-periodic surface waves propagating over the trench has been studied experimentally and theoretically. It was shown that for a particular trench geometry relative to the characteristic length scale of the surface waves, the fluid mud in the trench may be excited in a mode of resonant oscillation. Resonance within the trench resulted in large strain rates in the fluid mud compared to off resonance conditions, and thus reduced scale effects in the experiments. Detailed experiments were conducted to study the dynamics of fluid mud under wave action and its relationship with the fluid mud properties. A mathematical model was developed to predict the wave-induced motion of the fluid mud in the trench. The model employed small amplitude wave theory and treated the viscosity of fluid mud as a function of strain rate. The objective of the study was to determine how motions of sediment-laden fluids under water waves differ from that of a clear-water fluid, knowledge of which is important for description of near bottom kinematics in waters with “ill-defined” bottoms. It was found that the Carreau model described the viscosity of fluid mud well and shear rate and time of shearing had only minor effects on the fluid mud viscosity at small strain rates. Experimental measurements showed that the fluid mud in the trench was gradually eroded by wave action, but changes in density distribution were confined to a layer near the clear-water/fluid-mud interface. The theoretical model predicted the movement of fluid mud in the trench qualitatively. The results of this study indicated that fluid mud would behave as a Newtonian fluid at small strain rates.