Time-averaged Suspended Sediment Concentration Research Articles

Study of the wave period effect on the time-averaged suspended sediment concentration distribution under the oscillatory sheet flow condition

ABSTRACT Existing sheet flow experimental data show the measured time-averaged suspended sediment concentration (TSSC) may increase, decrease, or even remain constant if the wave period decreases. With respect to the available sheet flow experimental data, it is confirmed that the TSSC of relatively fine sand undergoes three stages, i.e. first decreases, then increases, and finally decreases again in the case that the wave period decreases from 12 s to 2 s, whereas for the relatively coarse sand, its vertical profile remains almost unchanged. The criterion for identifying the relatively fine or coarse sand was proposed in terms of the nondimensional ratio between the settling velocity and the root-mean-square flow velocity. If this ratio is less than 0.04–0.043, it is deemed as relatively fine sand. Otherwise, it is classified as relatively coarse sand. Applying the classical gradient diffusion model, sediment diffusivity is confirmed to be insensitive to the wave period. Keeping other experimental conditions uniform, TSSCs with different wave periods are proportional to each other and only affected by the reference concentration. Subsequently, a simple quantitative expression considering the wave period effect on the TSSC under the oscillatory sheet flow regime was proposed and verified with the experimental data.

A NUMERICAL MODEL OF CROSS-SHORE BEACH PROFILE EVOLUTION: THEORY, MODEL DEVELOPMENT AND APPLICABILITY

A practical numerical model was developed to simulate cross-shore profile evolution at two coastal sites in Iran. The model consists of three sub-models for calculating wave and current, sediment transport, and bed level changes. Validation and calibration of the model was carried out using the measured field data on the north and south coasts of Iran, where historic measurements of cross-shore beach profiles and wave conditions have been recorded. The model is formulated for calculating cross-shore sediment transports in and outside the surf zone by the product of time-averaged suspended sediment concentration under three different mechanisms and undertow velocity. The comparisons between the model results and field data show reasonable agreement for both coastal sites and will be capable of applying it to other coastal sites with modifications to the free parameters.

Parameterization of Time-Averaged Suspended Sediment Concentration in the Nearshore

To quantify the effect of wave breaking turbulence on sediment transport in the nearshore, the vertical distribution of time-averaged suspended sediment concentration (SSC) in the surf zone was parameterized in terms of the turbulent kinetic energy (TKE) at different cross-shore locations, including the bar crest, bar trough, and inner surf zone. Using data from a large-scale laboratory experiment, a simple relationship was developed between the time-averaged SSC and the time-averaged TKE. The vertical variation of the time-averaged SSC was fitted to an equation analogous to the turbulent dissipation rate term. At the bar crest, the proposed equation was slightly modified to incorporate the effect of near-bed sediment processes and yielded reasonable agreement. This parameterization yielded the best agreement at the bar trough, with a coefficient of determination R2 ≥ 0.72 above the bottom boundary layer. The time-averaged SSC in the inner surf zone showed good agreement near the bed but poor agreement near the water surface, suggesting that there is a different sedimentation mechanism that controls the SSC in the inner surf zone.

Measuring and modeling suspended sediment concentration profiles in the surf zone

Time-averaged suspended sediment concentration profiles across the surf zone were measured in a large-scale three-dimensional movable bed laboratory facility (LSTF: Large-scale Sediment Transport Facility). Sediment suspension under two different types of breaking waves, spilling and plunging breakers, was investigated. The magnitudes and shapes of the concentration profiles varied substantially at different locations across the surf zone, reflecting the different intensities of breaking-induced turbulence. Sediment suspension at the energetic plunging breaker-line was much more active, resulting in nearly homogeneous concentration profiles throughout most of the water column, as compared to the reminder of the surf zone and at the spilling breaker-line. Four suspended sediment concentration models were examined based on the LSTF data, including the mixing turbulence length approach, segment eddy viscosity model, breaking-induced wave-energy dissipation approach, and a combined breaking and turbulence length model developed by this study. Neglecting the breaking-induced turbulence and subsequent sediment mixing, suspended sediment concentration models failed to predict the across-shore variations of the sediment suspension, especially at the plunging breaker-line. Wave-energy dissipation rate provided an accurate method for estimating the intensity of turbulence generated by wave breaking. By incorporating the breaking-induced turbulence, the combined breaking and turbulence length model reproduced the across-shore variation of sediment suspension in the surf zone. The combined model reproduced the measured time-averaged suspended sediment concentration profiles reasonably well across the surf zone.

A Cross-Shore Beach Profile Evolution Model

Developing an accurate and reliable time-averaged beach profile evolution model under storm and nonstorm conditions is a challenging task. Over the last few decades, a number of beach deformation models have been developed under limited experimental conditions and uncertainties, and sometimes they required a long computation time. It is quite evident that a large amount of wave, current, sediment and beach profile data is available today. The present study leads to the development of a simple two-dimensional beach profile evolution model with on-offshore sand bar formation under nonstorm and storm conditions based on the time-averaged suspended sediment concentration models of Jayaratne and Shibayama [Jayaratne, M. P. R. and Shibayama, T. [2007] “Suspended sediment concentration on beaches under three different mechanisms,” Coastal Eng. J., JSCE 49(4), 357–392.] and Jayaratne et al. [Jayaratne, M. P. R., Sritharan, S. and Shibayama, T. [2011] “Examination of the suspended sediment concentration formulae using full-scale rippled bed and sheet flow data,” Coastal Eng. J., JSCE 53(4), 451–489.]. These models were formulated for computing sediment concentration in and outside the surf zone under three different mechanisms: (1) suspension due to turbulent motion over sand ripples, (2) suspension from sheet flow layer and (3) suspension due to turbulent motion under breaking waves. The suspended load is calculated by the product of time-averaged sediment concentration and undertow velocity from edge of the wave boundary layer to wave trough and mass transport velocity from wave trough to crest (bore-like wave region). Sediment transport in wave boundary layer is computed from the modified Watanabe [Watanabe, A. [1982] “Numerical model of nearshore currents and beach deformation model,” Coastal Eng. Jpn., JSCE 25, 147–161.] model. Rattanapitikon and Shibayama [Rattanapitikon, W. and Shibayama, T. [1998] “Energy dissipation model for regular and irregular breaking waves,” Coastal Eng. J., JSCE 40(4), 327–346.] wave model is used to calculate the average rate of energy dissipation due to wave breaking. The beach deformation is calculated from the conservation of sediment mass while the avalanching concept of Larson and Kraus [Larson, M. and Kraus, N. C. [1989] SBEACH: Numerical model for simulating storm induced beach change, Report 1, Technical Report CERC-89-9, US Army Eng. Water. Exp. Station.] is used to re-distribute the sediment mass in neighboring grids for a steady solution. Published field-scale experimental and natural beach profiles from five high-quality data sources from 1983–2009 [Kajima et al., 1983; Kraus and Larson, 1988; Port and Airport Research Institute, Japan, 2005, 2009; Hasan and Takewaka, 2007, 2009; Ruessink et al., 2007] are used to verify the performance of the proposed numerical model. The key feature in this process-based model is that it takes about a couple of minutes to simulate beach profiles of a 2–3 days storm qualitatively at a fairly satisfactory level using a standard personal computer. It is found that the present numerical predictions are not better than the null hypothesis as the model is in a stage of ongoing development. Therefore, it is believed that the final model is often of more value to a practical coastal engineer than a very detailed study of hydrodynamics and sediment transport study, however an incorporation of swash dynamics, more precise evaluation of offshore sand bar formation and continuation to a longer time scale with precise beach deformation are recommended as the next stage of the model.

Using velocimeter signal to noise ratio as a surrogate measure of suspended mud concentration

This study examines the relationship between suspended sediment concentration (SSC) and the signal to noise ratio (SNR) recorded by a 6 MHz Nortek Vector velocimeter in a laboratory water tank using four different synthetic and natural mud mixtures and different combinations of the user-set Vector parameters transmit power level and velocity range. For concentrations less than 1500 mg/l (1.5 g/l), a region of linearity between the logarithm of concentration and time-average SNR was found for all sediment types and transmitter power level settings. Within this concentration range, the experimental data was used to develop calibrated equations of the form, log ( SSC ) = c 1 SNR + c 2 ; R 2 values for all calibrated equations were greater than 0.98, suggesting that properly calibrated relations can yield accurate time-averaged SSC measurements using Vector measured SNR. An analysis of the general calibration equation indicated that the predicted SSC values are sensitive to changes in the coefficient values for c 1 and c 2. Even small (10%) deviations in coefficient values resulted in 20%–65% changes in the predicted SSC. Variation in c 1 and c 2 values among all four mud mixtures were significant enough that the calibrated equations could not be used interchangeably. This was true even among three samples that had similar particle-size distributions. Translation of raw 32 Hz SNR data to 32 Hz SSC time series produced excessively large variation in the SSC time series. Several smoothing and filtering schemes were examined to reduce the magnitude of these fluctuations to more reasonable levels. Of the methods tested, a two-sided moving average functioned best at removing fine-scale variation while retaining larger-scale trends. A 96-point (3 Hz) averaging window brought 98.6% of the Vector estimated SSC time series values to within ±10% of the time-average physical samples. Impacts of turbulent kinetic energy and sampling volume size on instrument recorded SNR were also empirically examined.

TIME-AVERAGED TURBULENT MIXING AND VERTICAL CONCENTRATION DISTRIBUTION OF HIGH-DENSITY SUSPENSIONS FORMED UNDER WAVES

We analyzed oscillating flow data from U-tube experiments by Lamb et al. (2004) and found that the time-averaged turbulent kinetic energy (TKE) near bed decreased exponentially with height above the bed in high-density-suspension (HDS) flows under waves, and that the ratios of TKE distributions in the streamwise, cross-stream, and vertical dimensions were constant. Based on the finite-mixing-length theory, a semi-theoretical time-averaged suspended sediment concentration model for HDS was developed. To avoid the stability problems with the numerical solution, a simplified model was also formulated through combing the apparent Fickian diffusivity and the damping function. The comparison between the calculated results and measurements shows both models consider the effect of the sediment-induced stratification well.

Sediment resuspension on beaches: response to breaking waves

Field data of time-averaged suspended sediment concentration (ssc) are presented from three different UK beaches and a variety of wave conditions. The data are collated into a single analysis to examine the mechanisms associated with sand resuspension in the surf zone. Emphasis is placed upon the relative contribution of bottom and surface generated turbulence in controlling suspended sediment concentration distribution. Inside the surf zone, vortices induced by breaking waves and bores are the main mechanism for sediment resuspension; this process dominates over bottom boundary layer processes. Time-averaged reference concentration, defined as the ssc at 3.5 cm above the bed, does not correlate with bottom-induced shear stress or predicted ripple steepness. Both reference concentration and vertical distribution of sediment are controlled by the breaking wave (plunging, spilling) characteristics. Within the inner surf zone, hydraulic jumps (associated with strong offshore flows) are responsible for sediment resuspension. Vertical distribution of sediment is parameterised using a convective type time-averaged suspended sediment concentration profile. Reference concentration is highly correlated with wave breaking type, as defined by the local breaker parameter. The mixing parameter depends also on the wave breaking type and may be expressed as a fraction of the local water depth.

Field observations and predictions of bed shear stressesand vertical suspended sediment concentration profiles in wave-current conditions

During a study of sediment dynamics at an offshore field site adjacent to Middlekerke Bank, Belgium, high-frequency measurements of turbulence and vertical profiles of the time-averaged suspended sediment concentration, C̄, were obtained in the bottom 1.2 m of the water column above a rippled bed in a water depth of approximately 20 m using the autonomous multisensor instrument STABLE. During the experiment, a combination of large waves and strong currents resulted in the resuspension and transport of bottom sediments. Values for the physical roughness of the sea bed, k s , have been derived. Estimates of the bed shear stress attributable to currents in the presence of waves, τ ̄ c(tke) , and the peak wave-only bed shear stress, τ ̂ w , have been obtained using the turbulent kinetic energy ( tke) method and linear wave theory, respectively, and have been combined to obtain peak, τ ̂ wc , and time-averaged, τ ̄ wc , wave-current ( w– c) bed shear stress values for gain- and ripple-scale roughness using existing models. A new semi-empirical expression giving accurate prediction of measured vertical C̄ profiles for a wide range of w– c conditions has been derived. Using τ ̂ w , τ ̄ wc and k s values as input parameters to the expression, estimates of the dynamic in situ grain settling velocity, wave mixing coefficient and total diffusive bed shear stress that agree well with previous measurements and with theory have been obtained. Results indicate it may now be possible to predict vertical C̄ profiles, and hence suspended sediment transport rates, with knowledge of flow turbulence, wave orbital motion and C̄ measured accurately at only one location near the bed.