Numerical simulation of surf–swash zone motions and turbulent flow

A two-dimensional numerical model was presented for the simulation of wave breaking, runup and turbulence in the surf and swash zones. The main components of the model are the Reynolds-Averaged Navier–Stokes equations describing the average motion of a turbulent flow, a k–ε turbulence closure model describing the transformation and dissipation processes of turbulence and a volume of fluid technique for tracking the free surface motion. Nearshore wave evolution on a sloping bed, the velocity field and other wave characteristics were investigated. First, the results of the model were compared with experimental results for different surf zone hydrodynamic conditions. Spilling and plunging breakers were simulated and the numerical model investigated for different wave parameters. The turbulence field was also considered and the spatial and time-dependent variations of turbulence parameters were discussed. In the next stage of the study, numerical results were compared with two sets of experimental data in the swash zone. Generally, there is good agreement except for turbulence predictions near the breaking point where the model does not represent well the physical processes. On the other hand, turbulence predictions were found to be excellent for the swash zone. The model provides a precise and efficient tool for the simulation of the flow field and wave transformations in the nearshore, especially in the swash zone. The numerical model can simulate the surface elevation of the vertical shoreline excursion on sloping beaches, while swash–swash interactions within the swash zone are accounted for.     

A note on Stokes production of turbulence kinetic energy in the oceanic mixed layer: observations in the Baltic Sea

Shear- and convection-driven turbulence coexists with wind-generated surface gravity waves in the upper ocean. The turbulent Reynolds stresses in the oceanic mixed layer can therefore interact with the shear of the wave-generated Stokes drift velocity to extract energy from the surface waves and inject it into turbulence, thus augmenting the mean shear-driven turbulence. Stokes production of turbulence kinetic energy (TKE) is difficult to measure in the field, since it requires simultaneous measurement of the turbulent stress and the Stokes drift profiles in the water column. However, it is readily inferred using second moment closure models of the oceanic mixed layer provided: (1) wave properties are available, along with the usual water mass properties, and radiative and air–sea fluxes needed to drive the mixed layer model and (2) the model skill can be assessed by comparing the model results against the observed dissipation rates of TKE. Comprehensive measurements made during the Reynolds 2002 campaign in the Baltic Sea have made the estimation of Stokes production possible, and in this paper, we report on the effort and the conclusions reached. Measurements of air–sea exchange parameters and water mass properties during the campaign allowed a mixed layer model to be run and the turbulent stress in the water column to be inferred. Simultaneous wave spectrum measurements enabled Stokes drift profile to be deduced and wave breaking to be included in the model run, and the Stokes production of TKE in the water column estimated. Direct measurements of the TKE dissipation rate from an upward traversing microstructure profiler were used to assure that the model could reproduce the turbulent dissipation rate in the water column. The model results indicate that the Stokes production of TKE in the mixed layer is of the same order of magnitude as the shear production and must therefore be included in mixed layer models.     

Air–water two-phase flow modeling of turbulent surf and swash zone wave motions

Wave breaking and wave runup/rundown have a major influence on nearshore hydrodynamics, morphodynamics and beach evolution. In the case of wave breaking, there is significant mixing of air and water at the wave crest, along with relatively high kinetic energy, so prediction of the free surface is complicated. Most hydrodynamic studies of surf and swash zone are derived from single-phase flow, in which the role of air is ignored. Two-phase flow modeling, consisting of both phases of water and air, may be a good alternative numerical modeling approach for simulating nearshore hydrodynamics and, consequently, sediment transport. A two-phase flow tool can compute more realistically the shape of the free surface, while the effects of air are accounted for. This paper used models based on two-dimensional, two-phase Reynolds-averaged Navier–Stokes equations, the volume-of-fluid surface capturing technique and different turbulence closure models, i.e., k–ε, k–ω and re-normalized group (RNG). Our numerical results were compared with the available experimental data. Comparison of the employed method with a model not utilizing a two-phase flow modeling demonstrates that including the air phase leads to improvement in simulation of wave characteristics, especially in the vicinity of the breaking point. The numerical results revealed that the RNG turbulence model yielded better predictions of nearshore zone hydrodynamics, although the k–ε model also gave satisfactory predictions. The model provides new insights for the wave, turbulence and means flow structure in the surf and swash zones.     

Turbulence-particle interactions under surface gravity waves

The dispersion and transport of single inertial particles through an oscillatory turbulent aquatic environment are examined numerically by a Lagrangian particle tracking model using a series of idealised test cases. The turbulent mixing is incorporated into the Lagrangian model by the means of a stochastic scheme in which the inhomogeneous turbulent quantities are governed by a one-dimensional k- ε turbulence closure scheme. This vertical mixing model is further modified to include the effects of surface gravity waves including Coriolis-Stokes forcing, wave breaking, and Langmuir circulations. To simplify the complex interactions between the deterministic and the stochastic phases of flow, we assume a time-invariant turbulent flow field and exclude the hydrodynamic biases due to the effects of ambient mean current. The numerical results show that the inertial particles acquire perturbed oscillations traced out as time-varying sinking/rising orbits in the vicinity of the sea surface under linear and cnoidal waves and acquire a non-looping single arc superimposed with the high-frequency fluctuations beneath the nonlinear solitary waves. Furthermore, we briefly summarise some recipes through the course of this paper on the implementation of the stochastic particle tracking models to realistically describe the drift and suspension of inertial particles throughout the water column.     

Summer surface layer thermal response to surface gravity waves in the Yellow Sea

The Princeton Ocean Model (POM) with generalized coordinate system (POMgcs) is used to study the summer surface-layer thermal response to surface gravity waves in the Yellow Sea (YS). The parameterization schemes of wave breaking developed by Mellor and Blumberg (J Phys Oceanogr 34:693–698, 2004) and Kantha and Clayson (Ocean Model 6:101–124, 2004), respectively, and Stokes production developed by Kantha and Clayson (Ocean Model 6:101–124, 2004) are both included in the Mellor–Yamada turbulence closure model Mellor and Yamada (Rev Geophys 20:851–875, 1982) of POMgcs. Numerical results show that surface gravity waves impact the depth of surface mixed layer of temperature in the YS in summer. The surface mixed layer in the YS cannot be reproduced well and has a visible difference from the observation if the parameterization schemes are not included. A diagnostic analysis of turbulent kinetic energy suggests that both Stokes production and wave breaking play key roles in enhancing the turbulent mixing near the sea surface in the YS. Stokes production seems to have a greater impact throughout the upper mixed layer in the YS in summer than that of wave breaking. In addition, a diagnostic analysis of the momentum balance shows that Coriolis–Stokes forcing has a significant effect on the momentum budget in the upper layer in the YS, and surface gravity waves are able to reduce the velocity of mean flow near the surface and make the mean flow near the surface more homogeneous vertically in the YS.     

Numerical modelling of wind effects on breaking waves in the surf zone

Wind effects on periodic breaking waves in the surf zone have been investigated in this study using a two-phase flow model. The model solves the Reynolds-averaged Navier–Stokes equations with the k ? ?? turbulence model simultaneously for the flows both in the air and water. Both spilling and plunging breakers over a 1:35 sloping beach have been studied under the influence of wind, with a focus during wave breaking. Detailed information of the distribution of wave amplitudes and mean water level, wave-height-to-water-depth ratio, the water surface profiles, velocity, vorticity, and turbulence fields have been presented and discussed. The inclusion of wind alters the air flow structure above water waves, increases the generation of vorticity, and affects the wave shoaling, breaking, overturning, and splash-up processes. Wind increases the water particle velocities and causes water waves to break earlier and seaward, which agrees with the previous experiment.     

Numerical simulation of two-phase flow for sediment transport in the inner-surf and swash zones

A two-dimensional two-phase flow framework for fluid–sediment flow simulation in the surf and swash zones was described. Propagation, breaking, uprush and backwash of waves on sloping beaches were studied numerically with an emphasis on fluid hydrodynamics and sediment transport characteristics. The model includes interactive fluid–solid forces and intergranular stresses in the moving sediment layer. In the Euler–Euler approach adopted, two phases were defined using the Navier–Stokes equations with interphase coupling for momentum conservation. The k–ε$k''–''\epsilon$ closure model and volume of fluid approach were used to describe the turbulence and tracking of the free surface, respectively. Numerical simulations explored incident wave conditions, specifically spilling and plunging breakers, on both dissipative and intermediate beaches. It was found that the spatial variation of sediment concentration in the swash zone is asymmetric, while the temporal behavior is characterized by maximum sediment concentrations at the start and end of the swash cycle. The numerical results also indicated that the maximum turbulent kinetic energy and sediment flux occurs near the wave-breaking point. These predictions are in general agreement with previous observations, while the model describes the fluid and sediment phase characteristics in much more detail than existing measurements. With direct quantifications of velocity, turbulent kinetic energy, sediment concentration and flux, the model provides a useful approach to improve mechanistic understanding of hydrodynamic and sediment transport in the nearshore zone.     

Spectral analysis of mean flow and turbulence forced by waves in a horizontally homogeneous zone of the Iroise sea

The 1D version of the Model for Applications at Regional Scale is used to parameterize the effects of sea surface waves in 2D in a horizontally homogeneous offshore zone of the Iroise sea. Here we present the first simulation of the Iroise sea including sea surface waves forcing, and more generally, the first study of a boundary layer including the Hasselmann force with a tidal wave. We use a single equation turbulence closure based on a non-local diagnosis for energetic and dissipation length scales. The turbulent energy flux at the surface due to whitecaps and the Hasselmann force induced by Stokes drift are assessed using the whole sea surface waves spectrum given by the Wave Watch Third generation model. The ability of the parameterization to reproduce surface currents over a period of 1 year (2007) is tested with high frequency radar using spectral and time-frequency analysis. One problem with 1D modelling, corresponding to overestimation of current oscillating at inertial frequency is illustrated by comparing 1D and 3D simulations. We found an overall improvement by including the Hasselmann force mainly within the bandwidth of less than one cycle per day to one cycle per day for surface currents. Turbulence is induced by whitecaps decaying rapidly below the ocean surface but the mixed layer below 40 m is deeper due to waves breaking on the sea surface.     

Cutting management of riparian vegetation by using hydrodynamic model simulations

This study numerically investigates effects of cutting riparian vegetation on flow characteristics by using a two-dimensional numerical model. The numerical model is based on depth-averaging the time- and volume-averaged Navier–Stokes equation with turbulent effects determined by the standard k–ε turbulence model. Drag forces exerted by the flow on vegetation are considered by adding source terms into momentum equations. In a rectangular channel and compound channel with vegetation along one side, numerical predictions show are in good agreement with those of previous studies. Five cutting scenarios, including the original, cutting along the main channel side, cutting along the bank side, alternative cutting, and reducing vegetative density, are analyzed in this study. The influences of the cutting scenarios on hydrodynamic behaviors are evaluated via numerical simulations. Simulation results suggest that cutting along the main channel side is the most effective scenario for reducing water depth and flow velocities.     

Two-phase hydrodynamic and sediment transport modeling of wave-generated sheet flow

This numerical investigation was carried out to advance mechanistic understanding of sediment transport under sheet flow conditions. An Euler–Euler coupled two-phase flow model was developed to simulate fluid–sediment oscillatory sheet flow. Since the concentration of sediment particles is high in such flows, the kinematics of the fluid and sediment phases are strongly coupled. This model includes interaction forces, intergranular stresses and turbulent stress closure. Each phase was modeled via the Reynolds-Averaged Navier–Stokes equations, with interphase momentum conservation accounting for the interaction between the phases. The generation and transformation of turbulence was modeled using the two-equation k–ε$k''–''\epsilon$ turbulence model. Concentration and sediment flux profiles were compared with experimental data for sheet flow conditions considering both symmetric and asymmetric oscillatory flows. Sediment and fluid velocity variations, concentration profiles, sediment flux and turbulence parameters of wave-generated sheet flow were studied numerically with a focus on sediment transport characteristics. In all applications, the model predictions compared well with the experimental data. Unlike previous investigations in which the flow is driven by a horizontal pressure gradient, the present model solves the Navier–Stokes equations under propagating waves. The model’s ability to predict sediment transport under oscillatory sheet flow conditions underscores its potential for understanding the evolution of beach morphology.     

Turbulence in the presence of internal waves in the bottom boundary layer of the California inner shelf

Turbulence measurements were collected in the bottom boundary layer of the California inner shelf near Point Sal, CA, for 2 months during summer 2015. The water column at Point Sal is stratified by temperature, and internal bores propagate through the region regularly. We collected velocity, temperature, and turbulence data on the inner shelf at a 30-m deep site. We estimated the turbulent shear production (P), turbulent dissipation rate (ε), and vertical diffusive transport (T), to investigate the near-bed local turbulent kinetic energy (TKE) budget. We observed that the local TKE budget showed an approximate balance (P?≈?ε) during the observational period, and that buoyancy generally did not affect the TKE balance. On a finer resolution timescale, we explored the balance between dissipation and models for production and observed that internal waves did not affect the balance in TKE at this depth.     

Simulation of airflow around rain gauges: Comparison of LES with RANS models

Wind is responsible for systematic errors that affect rain gauge measurements. The authors investigate the use of computational fluid dynamics (CFD) to calculate airflow around rain gauges by applying a high-resolution large eddy simulation (LES) model to determine the flow fields around a measuring system of two rain gauges. The simulated air flow field is characterized by the presence of massive separation which induces the formation and shedding of highly unsteady eddies in the detached shear layers and wakes. Parts of these detached structures occur over the orifice of the rain gauges and may substantially affect the dynamics of the raindrops in this critical region. Non-dissipative LES methods used with fine enough meshes can successfully predict these eddies and their associated fluctuations. The authors compare statistics from LES with steady-state Reynolds averaged Navier–Stokes (RANS) simulations using the k–ε and shear stress transport k–ω turbulence models. They find that both RANS and LES models predict similar mean velocity distributions around the rain gauges. However, they determine the distribution of the resolved turbulent kinetic energy (TKE) to be strongly dependent on the RANS model used. Neither RANS model predictions of TKE are close to those of LES. The authors conclude that the failure of RANS to predict TKE is an important limitation, as TKE is needed to scale the local velocity fluctuations in stochastic models used to calculate the motion of raindrops in the flow field.     

Wave effects in global ocean modeling: parametrizations vs. forcing from a wave model

One of the main challenges of the Copernicus Marine Service is the implementation of coupled ocean/waves systems that accurately estimate the momentum and energy fluxes provided by the atmosphere to the ocean. This study aims to investigate the impact of forcing the Nucleus for European Modelling of the Ocean (NEMO) ocean model with forecasts from the wave model of Météo-France (MFWAM) to improve classical air-sea flux parametrizations, these latter being mostly driven by the 10-m wind. Three wave-related processes, namely, wave-state-dependent stress, Stokes drift-related effects (Stokes-Coriolis force, Stokes drift advection on tracers and on mass), and wave-state-dependent surface turbulence, are examined at a global scale with a horizontal resolution of 0.25°. Three years of sensitivity simulations (2014–2016) show positive feedback on sea surface temperature (SST) and currents when the wave model is used. A significant reduction in SST bias is observed in the tropical Atlantic Ocean. This is mainly due to the more realistic momentum flux provided by the wave model. In mid-latitudes, the most interesting impact occurs during the summer stratification, when the wind is low and the wave model produces a reduction in the turbulence linked with wave breaking. Magnitudes of the large-scale currents in the equatorial region are also improved by 10% compared to observations. In general, it is shown that using the wave model reduces on average the momentum and energy fluxes to the ocean in tropical regions, but increases them in mid-latitudes. These differences are in the order of 10 to 20% compared with the classical parametrizations found in stand-alone ocean models.     

Turbulent viscosity optimized by data assimilation

As an alternative approach to classical turbulence modelling using a first or second order closure, the data assimilation method of optimal control is applied to estimate a time and space-dependent turbulent viscosity in a three-dimensional oceanic circulation model. The optimal control method, described for a 3-D primitive equation model, involves the minimization of a cost function that quantifies the discrepancies between the simulations and the observations. An iterative algorithm is obtained via the adjoint model resolution. In a first experiment, a k ± L model is used to simulate the one-dimensional development of inertial oscillations resulting from a wind stress at the sea surface and with the presence of a halocline. These results are used as synthetic observations to be assimilated. The turbulent viscosity is then recovered without the k + L closure, even with sparse and noisy observations. The problems of controllability and of the dimensions of the control are then discussed. A second experiment consists of a two-dimensional schematic simulation. A 2-D turbulent viscosity field is estimated from data on the initial and final states of a coastal upwelling event.     

Multimodal particle size distributions of fine-grained sediments: mathematical modeling and field investigation

Multimodal particle size distributions (PSDs) of fine-grained cohesive sediments are common in marine and coastal environments. The curve-fitting software in this study decomposed such multimodal PSDs into subordinate log-normal PSDs. Four modal peaks, consisting of four-level ordered structures of primary particles, flocculi, microflocs, and macroflocs, were identified and found to alternately rise and sink in a flow-varying tidal cycle due to shear-dependent flocculation. The four modal PSD could be simplified further into two discrete size groups of flocculi and flocs. This allowed the development of a two-class population balance equation (TCPBE) model with flocculi and flocs to simulate flocculation involving multimodal PSDs. The one-dimensional vertical (1-DV) TCPBE model further incorporated the Navier-Stokes equation with the k-ε turbulence closure and the sediment mass balance equations. Multimodal flocculation as well as turbulent flow and sediment transport in a flow-varying tidal cycle could be simulated well using the proposed model. The 1-DV TCPBE was concluded to be the simplest model that is capable of simulating multimodal flocculation in the turbulent flow field of marine and coastal zones.     

A case study of the evolution of a Kelvin–Helmholtz wave and turbulence in noctilucent clouds

Bright and extensive noctilucent clouds (NLC) were observed in Århus (Denmark) on 3/4 July of 2008 with an automatic digital camera taking images every minute. This event was unique in the sense that bright NLC were seen at high elevation angles (more than 30°) that allowed observing the evolution of a Kelvin–Helmholtz (KH) wave, resulted in well-developed turbulence. In particular, coherent vortex structures of a horseshoe-shaped form were observed for the first time in noctilucent clouds. The turbulent diffusion coefficient and turbulent energy dissipation rate around the mesopause are estimated in the range 162–667 m²/s and 300–1235 mW/kg, respectively, representing a case of strong neutral air turbulence in noctilucent clouds. Turbulent structures were observed to be in the vicinity of breaking small-scale gravity waves that seems to be responsible for a high level of turbulence.At the same time, it has been demonstrated that it is of importance to take into account non-turbulent process such as the gravity wave motion that is always present in NLC layers. Unless non-turbulent process is taken into account, this certainly leads to overestimating of the value of the turbulent diffusion coefficient. More accurate characteristics of turbulence in NLC can be obtained by analyzing a sequence of high-resolution images with a high frame-rate high-resolution digital camera.     

Bubble size distribution in surface wave breaking entraining process

From the similarity theorem, an expression of bubble population is derived as a function of the air en-trainment rate, the turbulent kinetic energy (TKE) spectrum density and the surface tension. The bubble size spectrum that we obtain has a dependence of a?2.5 nd on the bubble radius, in which nd is positive and dependent on the form of TKE spectrum within the viscous dissipation range. To relate the bubble population with wave parameters, an expression about the air entrainment rate is deduced by intro-ducing two statistical relations to wave breaking. The bubble population vertical distribution is also derived, based on two assumptions from two typical observation results.     

Turbulent mixing in the Northern North Sea: a numerical model study

The aim of this study is to intervalidate observations and numerical simulation results for the turbulent dissipation rate under strong wind conditions in the Northern North Sea during one week in October 1998. The observations were obtained by spatially and temporally averaging measurements of small-scale shear with a free-falling shear probe. The 1D numerical model used for this study is based on a state-of-the-art two-equation k− turbulence model with an algebraic second-moment closure scheme. It is discussed by means of annual and seasonal model simulations how the influence of heat and salt advection and internal waves can be accounted for. After these precautions, the agreement between observations and simulations of the turbulent dissipation rate are fairly good. Remaining differences cannot only be explained by problems such as undersampling and noise level, but also by idealising model assumptions.     

Effects of rainfall on oil droplet size and the dispersion of spilled oil with application to Douglas Channel,British Columbia,Canada

Raindrops falling on the sea surface produce turbulence. The present study examined the influence of rain-induced turbulence on oil droplet size and dispersion of oil spills in Douglas Channel in British Columbia, Canada using hourly atmospheric data in 2011–2013. We examined three types of oils: a light oil (Cold Lake Diluent - CLD), and two heavy oils (Cold Lake Blend - CLB and Access Western Blend - AWB). We found that the turbulent energy dissipation rate produced by rainfalls is comparable to what is produced by wind-induced wave breaking in our study area. With the use of chemical dispersants, our results indicate that a heavy rainfall (rain rate > 20 mm h^? 1) can produce the maximum droplet size of 300 μm for light oil and 1000 μm for heavy oils, and it can disperse the light oil with fraction of 22–45% and the heavy oils of 8–13%, respectively. Heavy rainfalls could be a factor for the fate of oil spills in Douglas Channel, especially for a spill of light oil and the use of chemical dispersants.