Turbulent Velocity Variances Research Articles

Investigation of Hydrostatic Imbalance with Field Observations

Abstract The hydrostatic equilibrium addresses the approximate balance between the positive force of the vertical pressure gradient and the negative gravity force and has been widely assumed for atmospheric applications. The hydrostatic imbalance of the mean atmospheric state for the acceleration of vertical motions in the vertical momentum balance is investigated using tower, the global positioning system radiosonde, and Doppler lidar and radar observations throughout the diurnally varying atmospheric boundary layer (ABL) under clear-sky conditions. Because of the negligibly small mean vertical velocity, the acceleration of vertical motions is dominated by vertical variations of vertical turbulent velocity variances. The imbalance is found to be mainly due to the vertical turbulent transport of changing air density as a result of thermal expansion/contraction in response to air temperature changes following surface temperature changes. In contrast, any pressure change associated with air temperature changes is small, and the positive vertical pressure-gradient force is strongly influenced by its background value. The vertical variation of the turbulent velocity variance from its vertical increase in the lower convective boundary layer (CBL) to its vertical decrease in the upper CBL is observed to be associated with the sign change of the imbalance from positive to negative due to the vertical decrease of the positive vertical pressure-gradient force and the relative increase of the negative gravity force as a result of the decreasing upward transport of the low-density air. The imbalance is reduced significantly at night but does not steadily approach zero. Understanding the development of hydrostatic imbalance has important implications for understanding large-scale atmosphere, especially for cloud development. Significance Statement It is well known that the hydrostatic imbalance between the positive pressure-gradient force due to the vertical decrease of atmospheric pressure and the negative gravity forces in the vertical momentum balance equation has important impacts on the vertical acceleration of atmospheric vertical motions. Vertical motions for mass, momentum, and energy transfers contribute significantly to changing atmospheric dynamics and thermodynamics. This study investigates the often-assumed hydrostatic equilibrium and investigate how the hydrostatic imbalance is developed using field observations in the atmospheric boundary layer under clear-sky conditions. The results reveal that hydrostatic imbalance can develop from the large-eddy turbulent transfer of changing air density in response to the surface diabatic heating/cooling. The overwhelming turbulence in response to large-scale thermal forcing and mechanical work of the vast Earth surface contributes to the hydrostatic imbalance on large spatial and temporal scales in numerical weather forecast and climate models.

Wind Turbulence Statistics of the Atmospheric Inertial Sublayer under Near-Neutral Conditions

The inertial sublayer comprises a considerable and critical portion of the turbulent atmospheric boundary layer. The mean windward velocity profile is described comprehensively by the Monin–Obukhov similarity theory, which is equivalent to the logarithmic law of the wall in the wind tunnel boundary layer. Similar logarithmic relations have been recently proposed to correlate turbulent velocity variances with height based on Townsend’s attached-eddy theory. The theory is particularly valid for high Reynolds-number flows, for example, atmospheric flow. However, the correlations have not been thoroughly examined, and a well-established model cannot be reached for all turbulent variances similar to the law of the wall of the mean-velocity. Moreover, the effect of atmospheric thermal condition on Townsend’s model has not been determined. In this research, we examined a dataset of free wind flow under a near-neutral range of atmospheric stability conditions. The results of the mean velocity reproduce the law of the wall with a slope of 2.45 and intercept of −13.5. The turbulent velocity variances were fitted by logarithmic profiles consistent with those in the literature. The windward and crosswind velocity variances obtained the average slopes of −1.3 and −1.7, respectively. The slopes and intercepts generally increased away from the neutral state. Meanwhile, the vertical velocity and temperature variances reached the ground-level values of 1.6 and 7.8, respectively, under the neutral condition. The authors expect this article to be a groundwork for a general model on the vertical profiles of turbulent statistics under all atmospheric stability conditions.

Methane emissions from a waste treatment site: Numerical analysis of aircraft-based data

Methane (CH4) is an important greenhouse gas. Emissions from landfills and waste treatment sites are regarded as the third largest anthropogenic source in the world. Precise estimates of CH4 emissions depend on a well-designed sampling procedure and detailed analyses. This study estimates CH4 emissions from a waste treatment site by analyzing the data from a flight, which was carried out in Eastern Ontario, Canada, on May 6, 2011. The CH4 dispersion plume at about 140 m above ground level downwind of the source is analyzed with data from 14 flight tracks. The observation period of about 72 min is characterized by unstable boundary layer conditions, strong wind, and shifting wind direction. To replicate the boundary layer turbulence and the CH4 dispersion during the measurement period, a combined large-eddy simulation (LES) and Lagrangian stochastic (LS) particle dispersion modeling method is used. A preliminary simulation run with mean meteorological variables during the experiment's duration is carried out. The results reproduced the shifts in wind direction well, in addition to the dispersion plume, but in a smaller magnitude in comparison to the measured data. Therefore, two sets of LES runs are carried out to represent the boundary layer turbulence before and after the wind shift. Another deficiency in the LES runs is that the simulated turbulent velocity variances are systematically smaller than the observed counterparts. In response to this discrepancy, additional terms are incorporated into the LS dispersion model so as to represent the turbulence dispersion process better. With these treatments, the LES-LS modeling results replicated the dispersion plume both in lateral width and in concentration distribution shape. Then, by using the simulated relationship between source and concentrations/vertical fluxes in space, the CH4 emission rate of the site is estimated as 2393 (kg CH4 hr−1) / 2088 (kg CH4 hr−1) respectively.

The evaluation of mixing methods in HYSPLIT using measurements from controlled tracer experiments

The HYSPLIT dispersion model has different options to estimate the turbulent mixing depending on the availability of stability and turbulent parameters in the meteorological data. Dispersion simulations using different mixing options were conducted to simulate two controlled tracer experiments – the Project Sagebrush phase 1 (PSB1) for the sub-kilometer transport and the Cross Appalachian Tracer Experiment (CAPTEX) for the long-range transport. Through the comparisons of velocity variance and the evaluations of tracer concentrations, we evaluated different estimations of the turbulent velocity variance affecting the dispersion results. The mixing options in HYSPLIT are the Belijaars-Holtslag (BH) method, the Kantha-Clayson (KC) method, the turbulent kinetic energy (TKED) option, and the turbulent exchange coefficient (EXCH) option. The KC and EXCH method produced a larger maximum of the vertical velocity variance and at a higher altitude than other mixing options did. The vertical velocity variance profile of the BH scheme had a sharp increase from the surface to the height of the maximum values. The TKED option generated a flat profile with the smallest variation in its value with height. The plumes generated by the BH and TKED method (weaker mixing) had higher concentrations near the surface than those driven by the KC and EXCH option (stronger mixing). The statistical rank for the dispersion result using the TKED option was slightly better than others while the BH mixing generated results with a roughly worse rank. No mixing option always outperformed the other options. HYSPLIT users can select a mixing option according to the scenario and availability of meteorological fields, and use different options to generate dispersion ensembles.

The Universality of the Normalized Vertical Velocity Variance in Contrast to the Horizontal Velocity Variance in the Convective Boundary Layer

AbstractThe vertical turbulent velocity variance normalized by the convective velocity squared as a function of the boundary layer depth–normalized height [i.e., ] in the convective boundary layer (CBL) over a homogeneous surface exhibits a near-universal profile, as demonstrated by field observations, laboratory experiments, and numerical simulations. The profile holds over a wide CBL stability range set by the friction velocity, CBL depth, and surface heating. In contrast, the normalized horizontal turbulent velocity variance increases monotonically with decreasing stability. This study investigates the independence of the profile to changes in CBL stability, or more precisely, wind shear. Large-eddy simulations of several convective and neutral cases are performed by varying surface heating and geostrophic winds. Analysis of the turbulent kinetic energy budgets reveals that the conversion term between and depends almost entirely on buoyancy. This explains why does not vary with shear, which is a source to only. Further analysis through rotational and divergent decomposition suggests that the near-universal profile of is fundamentally related to the dynamics and interactions of local and nonlocal CBL turbulence. Specifically, the preferential interactions between local wavenumbers and the downscale energy cascade of CBL turbulence offer plausible explanations to the universal profile of .

Scale interactions and anisotropy in stable boundary layers

Regimes of interactions between motions on different time‐scales are investigated in the FLOSSII dataset for nocturnal near‐surface stable boundary layer turbulence. The non‐stationary response of turbulent vertical velocity variance to non‐turbulent, submeso‐scale wind velocity variability is analysed using the bounded variation, finite element, vector autoregressive factor models (FEM‐BV‐VARX) clustering method. Several locally stationary flow regimes are identified with different influences of submeso wind velocity on the turbulent vertical velocity variance. In each flow regime, we analyse multiple scale interactions and quantify the amount of turbulent variability which can be statistically explained by external forcing by the submeso wind velocity. The state of anisotropy of the Reynolds stress tensor in the different flow regimes is shown to relate to these different signatures of scale interactions. In flow regimes under considerable influence of the submeso‐scale wind variability, the Reynolds stresses show a clear preference for strongly anisotropic, one‐component states. These periods additionally show stronger persistence in their dynamics, compared to periods of more isotropic stresses. The analyses give insights on how the different topologies relate to non‐stationary turbulence triggering by submeso‐scale motions.

Observed Features of Langmuir Turbulence Forced by Misaligned Wind and Waves under Destabilizing Buoyancy Flux

AbstractSeveral features of Langmuir turbulence remain unquantified despite its potentially large impacts on ocean surface mixing. For example, its vertical velocity variance, expected to be proportional to based on numerical simulations, was proportional to in recent field observations, where is the friction velocity and is surface Stokes velocity. To investigate unquantified features of Langmuir turbulence, we conducted a field experiment around a marine observation tower in a shallow sea off the southern coast of Japan in early winter when winds and waves (often swells) were often misaligned. Coherent structures similar to Langmuir cells were successfully identified in the horizontal and vertical structures of turbulent flows measured with upward- and horizontally looking acoustic Doppler current profilers (ADCPs). ADCPs and several anemometers attached at the tower showed that turbulent vertical velocity variance was large when the Langmuir number and Hoenikker number (; where B is surface buoyancy flux and H is the water depth) were both small and that the orientation of the cells was generally aligned in the direction of Lagrangian current shear. These results agree well with the previous numerical results. As in the previous observations, however, the vertical velocity variance appeared to be proportional to . In our experiment, this curious feature was explained by compensatory effects between waves and convection. Misaligned wind with waves also seems to characterize the observed Langmuir turbulence, though further quantitative analysis is required to confirm this result.

Gravity Wave Dynamics in a Mesospheric Inversion Layer: 2. Instabilities, Turbulence, Fluxes, and Mixing

AbstractA companion paper by Fritts, Laughman, et al. (2017) employed an anelastic numerical model to explore the dynamics of gravity waves (GWs) encountering a mesospheric inversion layer (MIL) having a moderate static stability enhancement and a layer of weaker static stability above. That study revealed that MIL responses, including GW transmission, reflection, and instabilities, are sensitive functions of GW parameters. This paper expands on two of the Fritts, Laughman, et al. (2017) simulations to examine GW instability dynamics and turbulence in the MIL; forcing of the mean wind and stability environments by GW, instability, and turbulence fluxes; and associated heat and momentum transports. These direct numerical simulations resolve turbulence inertial‐range scales and yield the following results: GW breaking and turbulence in the MIL occur below where they would otherwise, due to enhancements of GW amplitudes and shears in the MIL. 2‐D GW and instability heat and momentum fluxes are ~20–30 times larger than 3‐D instability and turbulence fluxes. Mean fields are driven largely by 2‐D GW and instability dynamics rather than 3‐D instabilities and turbulence. 2‐D and 3‐D heat fluxes in regions of strong turbulence yield small departures from initial T(z) and N2(z) profiles, hence do not yield nearly adiabatic “mixed” layers. Our MIL results are consistent with the relation between the turbulent vertical velocity variance and energy dissipation rate proposed by Weinstock (1981) for the limited intervals evaluated.

A Linearized $$k-\epsilon $$ k - ϵ Model of Forest Canopies and Clearings

A linearized analysis of the Reynolds-averaged Navier–Stokes (RANS) equations is proposed where the $$k-\epsilon $$ turbulence model is used. The flow near the forest is obtained as the superposition of the undisturbed incoming boundary layer plus a velocity perturbation due to the forest presence, similar to the approach proposed by Belcher et al. (J Fluid Mech 488:369–398, 2003). The linearized model has been compared against several non-linear RANS simulations with many leaf-area index values and large-eddy simulations using two different values of leaf-area index. All the simulations have been performed for a homogeneous forest and for four different clearing configurations. Despite the model approximations, the mean velocity and the Reynolds stress $$\overline{u'w'}$$ have been reasonably reproduced by the first-order model, providing insight about how the clearing perturbs the boundary layer over forested areas. However, significant departures from the linear predictions are observed in the turbulent kinetic energy and velocity variances. A second-order correction, which partly accounts for some non-linearities, is therefore proposed to improve the estimate of the turbulent kinetic energy and velocity variances. The results suggest that only a region close to the canopy top is significantly affected by the forest drag and dominated by the non-linearities, while above three canopy heights from the ground only small effects are visible and both the linearized model and the simulations have the same trends there.

Mean-velocity profile of smooth channel flow explained by a cospectral budget model with wall-blockage

A series of recent studies has shown that a model of the turbulent vertical velocity variance spectrum (Fvv) combined with a simplified cospectral budget can reproduce many macroscopic flow properties of turbulent wall-bounded flows, including various features of the mean-velocity profile (MVP), i.e., the “law of the wall”. While the approach reasonably models the MVP’s logarithmic layer, the buffer layer displays insufficient curvature compared to measurements. The assumptions are re-examined here using a direct numerical simulation (DNS) dataset at moderate Reynolds number that includes all the requisite spectral and co-spectral information. Starting with several hypotheses for the cause of the “missing” curvature in the buffer layer, it is shown that the curvature deficit is mainly due to mismatches between (i) the modelled and DNS-observed pressure-strain terms in the cospectral budget and (ii) the DNS-observed Fvv and the idealized form used in previous models. By replacing the current parameterization for the pressure-strain term with an expansive version that directly accounts for wall-blocking effects, the modelled and DNS reported pressure-strain profiles match each other in the buffer and logarithmic layers. Forcing the new model with DNS-reported Fvv rather than the idealized form previously used reproduces the missing buffer layer curvature to high fidelity thereby confirming the “spectral link” between Fvv and the MVP across the full profile. A broad implication of this work is that much of the macroscopic properties of the flow (such as the MVP) may be derived from the energy distribution in turbulent eddies (i.e., Fvv) representing the microstate of the flow, provided the link between them accounts for wall-blocking.

A Spectral Budget Model for the Longitudinal Turbulent Velocity in the Stable Atmospheric Surface Layer

Abstract A spectral budget model is developed to describe the scaling behavior of the longitudinal turbulent velocity variance with the stability parameter and the normalized height in an idealized stably stratified atmospheric surface layer (ASL), where z is the height from the surface, L is the Obukhov length, and δ is the boundary layer height. The proposed framework employs Kolmogorov’s hypothesis for describing the shape of the longitudinal velocity spectra in the inertial subrange, Heisenberg’s eddy viscosity as a closure for the pressure redistribution and turbulent transfer terms, and the Monin–Obukhov similarity theory (MOST) scaling for linking the mean longitudinal velocity and temperature profiles to ζ. At a given friction velocity , reduces with increasing ζ as expected. The model is consistent with the disputed z-less stratification when the stability correction function for momentum increases with increasing ζ linearly or as a power law with the exponent exceeding unity. For the Businger–Dyer stability correction function for momentum, which varies linearly with ζ, the limit of the z-less onset is . The proposed framework explains why does not follow MOST scaling even when the mean velocity and temperature profiles may follow MOST in the ASL. It also explains how δ ceases to be a scaling variable in more strongly stable (although well-developed turbulent) ranges.

Derivation of the Turbulent Time Scales and Velocity Variances from LES Spectral Data: Application in a Lagrangian Stochastic Dispersion Model

Turbulent time scales and velocity variances for a convective boundary layer are derived from large eddy simulation spectral data. Spectral peak frequencies obtained from LES data are used directly in expressions that allow establishing such times scales and velocity variances. These turbulent parameters were compared with those provided by experimental turbulence data. The comparison employing a stochastic dispersion model and observed concentration data shows that both parameterizations reproduce adequately the contaminant dispersion process in a convective boundary layer.

Optimization of ADV sampling strategies using DNS of turbulent flow

ABSTRACTThis work presents an investigation on the effects of spatial and temporal averaging processes (filtering) implemented in an Acoustic Doppler Velocimeter (ADV) on the computations of the turbulent kinetic energy, velocity variances, and Reynolds shear stresses. The averaging processes are implemented in the ADV technology in order to reduce the noise level inherent in acoustic measurements. A conceptual model, simulating the ADV operation and the turbulent flow field, is developed to assess the filtering effects on the turbulence parameter estimates of sampling volume heights, recording frequencies, and distances from the sampling volume to the channel bottom. The results of the conceptual model are compared with experimental data. The findings provide a criterion to examine the capability of ADV to characterize turbulent flows using different sampling configurations.

UMA NOVA EXPRESSÃO PARA A VARIÂNCIA DA VELOCIDADE TURBULENTA CONVECTIVA DERIVADA DE UM MODELO LES

The aim of this study is to derive a new expression for the vertical turbulent velocity variance using LES data in a convective boundary layer.

Comparing Lagrangian and Eulerian models for CO<sub>2</sub> transport – a step towards Bayesian inverse modeling using WRF/STILT-VPRM

Abstract. We present simulations of atmospheric CO2 concentrations provided by two modeling systems, run at high spatial resolution: the Eulerian-based Weather Research Forecasting (WRF) model and the Lagrangian-based Stochastic Time-Inverted Lagrangian Transport (STILT) model, both of which are coupled to a diagnostic biospheric model, the Vegetation Photosynthesis and Respiration Model (VPRM). The consistency of the simulations is assessed with special attention paid to the details of horizontal as well as vertical transport and mixing of CO2 concentrations in the atmosphere. The dependence of model mismatch (Eulerian vs. Lagrangian) on models' spatial resolution is further investigated. A case study using airborne measurements during which two models showed large deviations from each other is analyzed in detail as an extreme case. Using aircraft observations and pulse release simulations, we identified differences in the representation of details in the interaction between turbulent mixing and advection through wind shear as the main cause of discrepancies between WRF and STILT transport at a spatial resolution such as 2 and 6 km. Based on observations and inter-model comparisons of atmospheric CO2 concentrations, we show that a refinement of the parameterization of turbulent velocity variance and Lagrangian time-scale in STILT is needed to achieve a better match between the Eulerian and the Lagrangian transport at such a high spatial resolution (e.g. 2 and 6 km). Nevertheless, the inter-model differences in simulated CO2 time series for a tall tower observatory at Ochsenkopf in Germany are about a factor of two smaller than the model-data mismatch and about a factor of three smaller than the mismatch between the current global model simulations and the data.

Algebraic Formulation for the Dispersion Parameters in an Unstable Planetary Boundary Layer: Application in the Air Pollution Gaussian Model

An alternative formulation for the dispersion parameters in a convective boundary layer is presented. The development consists of a simple algebraic relation for the dispersion parameters, originated from the fitting of experimental data, in which the turbulent velocity variances and the Lagrangian decorrelation time scales are derived from the turbulent kinetic energy convective spectra. Assuming homogeneous turbulence for elevated regions in an unstable planetary boundary layer (PBL), the present approach, which provides the dispersion parameters, has been compared to the observational data as well as to results obtained by classical complex integral formulations. From this comparison yields that the vertical and lateral dispersion parameters obtained from the simple algebraic formulas reproduce, in an adequate manner, the spread of contaminants released by elevated continuous source in an unstable PBL. Therefore, the agreement with dispersion parameters available by an integral formulation indicates that the hypothesis of using an algebraic formulation as a surrogate for dispersion parameters in the turbulent convective boundary layer is valid. In addition, the algebraic vertical and lateral dispersion parameters were introduced into an air pollution Gaussian diffusion model and validated with the concentration data of Copenhagen experiments. The results of such Gaussian model, incorporating the algebraic dispersion parameters, are shown to agree with the measurements of Copenhagen.

Measurements of Boundary Layer Profiles with In Situ Sensors and Doppler Lidar

AbstractA new in situ measurement system and lidar processing algorithms were developed for improved measurements of boundary layer profiles. The first comparisons of simultaneous Doppler lidar–derived profiles of the key turbulence statistics of the two orthogonal horizontal velocity components (longitudinal and transverse) are presented. The instrument requirements for accurate observations of stably stratified turbulence were determined. A region of stably stratified low turbulence with constant gradients of temperature and velocity was observed above the nocturnal boundary layer using high-rate sensors. The important turbulence parameters were estimated, and turbulence spectra were consistent with new theoretical descriptions of stratified turbulence. The impact of removing the larger-scale velocity features in Doppler lidar estimates of turbulent velocity variance and length scales was investigated. The Doppler lidar–derived estimates of energy dissipation rate ε were found to be insensitive to spatial filtering of the large-scale atmospheric processes. The in situ and lidar-derived profiles were compared for the stable boundary layer in a suburban environment.

Turbulent statistical characteristics associated to the north wind phenomenon in southern Brazil with application to turbulent diffusion

A parameterization for the transport processes in a shear driven planetary boundary layer (PBL) has been established employing turbulent statistical quantities measured during the north wind phenomenon in southern Brazil. Therefore, observed one-dimensional turbulent energy spectra are compared with a spectral model based on the Kolmogorov arguments. The good agreement obtained from this comparison leads to well defined formulations for the turbulent velocity variance, local decorrelation time scale and eddy diffusivity. Furthermore, for vertical regions in which the wind shear forcing is relevant, the eddy diffusivity derived from the north wind data presents a similar profile to those obtained from the non-extensive statistical mechanics theory. Finally, a validation for the present parameterization has been accomplished, using a Lagrangian stochastic dispersion model. The Prairie Grass data set, which presents high mean wind speed, is simulated. The analysis developed in this study shows that the turbulence parameterization constructed from wind data for north wind flow cases is able to describe the diffusion in a high wind speed, shear-dominated PBL.

Langmuir turbulence in shallow water. Part 1. Observations

During extended deployment at an ocean observatory off the coast of New Jersey, a bottom-mounted five-beam acoustic Doppler current profiler measured large-scale velocity structures that we interpret as Langmuir circulations filling the entire water column. These circulations are the large-eddy structures of wind-wave-driven turbulent flows that occur episodically when a shallow water column experiences prolonged strong wind forcing. Many observational characteristics agree with former descriptions of Langmuir circulations in deep water. The three-dimensional velocity field reveals quasi-organized structures consisting of pairs of surface-intensified counter-rotating vortices, aligned approximately downwind. Maximum downward velocities are stronger than upward velocities, and the downwelling region of each cell, defined as a pair of vortices, is narrower than the upwelling region. Maximum downward vertical velocity occurs at or above mid-depth, and scales approximately with wind speed. The estimated crosswind scale of cells is roughly 3–6 times their vertical scale, set under these conditions by water depth. The long axis of the cells appears to lie at an angle ∼10°–20° to the right of the wind. A major difference from deep-water observations is strong near-bottom intensification of the downwind ‘jets’ found typically centred over downwelling regions. Accessible observational features such as cell morphology and profiles of mean velocities, turbulent velocity variances, and shear stress components are compared with the results of associated large-eddy simulations (reported in Part 2) of shallow water flows driven by surface stress and the Craik–Leibovich vortex forcing generally used to represent generation of Langmuir cells. A particularly sensitive diagnostic for identification of Langmuir circulations as the energy-containing eddies of the turbulent flow is the depth trajectory of invariants of the turbulent stress tensor, plotted in the Lumley ‘triangle’ corresponding to realizable turbulent flows. When Langmuir structures are present in the observations, the Lumley map is distinctly different from that of surface-stress-driven Couette flow, again in agreement with the large-eddy simulations (LES). Unlike the LES, observed velocity fields contain two distinct and significant scales of variability, documented by wavelet analysis of observational records of vertical velocity. Variability with periods of many minutes is that expected from Langmuir cells drifting past the instrument at the slowly time-varying crosswind velocity. Shorter period variability, of the order of 1–2 min, has roughly the observed periodicity of surface wave groups, suggesting a connection with the wave groups themselves and/or the wave breaking associated with them in high wind conditions.

Suspended sand transport in surf zones

Three tests were conducted in a wave flume to investigate time‐averaged suspended sediment transport processes under irregular breaking waves on equilibrium beaches consisting of fine sand. Free surface elevations were measured at ten locations for each test. Velocities and concentrations were measured in the vicinity of the bottom at 94 elevations along 17 vertical lines. The relations among the three turbulent velocity variances are found to be similar to those for the boundary layer flow. The vertical variation of the mean velocity, which causes offshore transport, is fitted by a parabolic profile fairly well. The vertical variation of the mean concentration is fitted by the exponential and power‐form distributions equally well. The ratio between the concentration standard deviation σC and the mean varies little vertically. The correlation coefficient γUC between the horizontal velocity and concentration, which results in onshore transport, is of the order of 0.1 and decreases upward linearly. The offshore and onshore transport rates of suspended sediment are estimated and expressed in terms of the suspended sediment volume per unit area. A time‐averaged numerical model is developed to predict as well as the mean and standard deviation of the free surface elevation and horizontal velocity. The bottom slope effect on the wave energy dissipation rate DB due to wave breaking is included in the model. The computation can be made well above the still water shoreline with no numerical difficulty. Reflected waves from the shoreline are estimated from the wave energy flux remaining at the shoreline. The numerical model is in agreement with the statistical data except that the undertow current is difficult to predict accurately. The measured turbulent velocities are found to be more related to the turbulent velocity estimated from the energy dissipation rate Df due to bottom friction. The suspended sediment volume expressed in terms of DB and Df can be predicted only within a factor of about 2. The roller effect represented by the roller volume flux does not necessarily improve the agreement for the three tests.