Combined Wave-current Flow Research Articles

Effects of submergence ratio on flow around a circular pier in combined wave–current flows using particle image velocimetry

The present study illustrates an experimental investigation of flow hydrodynamics in the vicinity of a submerged circular pier across various submergence levels under only current and wave–current combined flow conditions. The instantaneous velocity data are collected using particle image velocimetry for three distinct frequencies of waves to determine the influence of wave superimposition on the current-induced turbulence parameters. The distribution of phase averaged turbulence quantities, such as mean velocities, Reynolds shear stress, turbulent kinetic energy, flow patterns, and vorticity analysis by Q-criterion, are presented. The results provide insight into the impacts of wave frequency and submergence ratio on the formation of horseshoe vortices, trailing vortex, and reverse flow zones. From the results it is observed that a decrease in the submergence level of the structure causes the formation of strong horseshoe vortices and reverse flow zones in the absence of waves. Also, an increase in wave frequency intensifies the turbulence kinetic energy at the upstream of the pier and eddy generation behind the pier. The present findings highlight the effects of pier submergence and wave characteristics, such as frequency, wave height, and wave period, on flow patterns and turbulent flow characteristics and aid in the design of marine structures. Furthermore, experimental data serve as a valuable resource for validating theoretical or mathematical models related to combined wave–current environments.

Investigation on the turbulent structures in combined wave-current boundary layers

The problem of turbulent vortices and vortex dynamics under the influence of ocean waves is a subject of continuing research in the field of wave-current interaction. Thus, this study investigates the evolution of turbulence structures and vortex interactions in combined wave-current boundary layers, where water waves propagate with currents. Experiments were performed in two glass-walled laboratory channels with water depths of 160 and 400 mm. A two-dimensional two-component (2D2C) Particle Image Velocimetry (PIV) system was used to measure the velocities. Periodic variations in turbulence are observed for combined wave-current flows. Pairs of counter-rotating vortices are identified in the outer region when the combined flow is reversed, leading to destructive vortex interactions. This process leads to a reduction in the turbulent kinetic energy (TKE) and TKE production and dissipation during the passage of the wave trough. A conceptual model of hairpin vortices in combined wave-current flows is proposed in this study. The results of this study provide novel insights into the hydrodynamics of combined wave-current flows.

How Artificial Salt Marsh Vegetation Reduces The Threshold For Sediment Resuspension In Wave-Current Flows

Suspended sediment transport and retention within salt marshes is a key factor in their resilience against erosion associated with threats such as sea level rise and coastal squeeze. Salt marshes are vegetated intertidal wetlands found in temperate climate zones. Their presence contributes to flood protection, coastal flora and fauna, and carbon sequestration (Temmerman et al., 2013). Vegetation-induced resuspension of fine sediment helps to transport fine particles deeper into salt marshes. The interaction between waves, currents, and vegetation may resuspend sediment sooner than it would without vegetation. It has been shown in conditions with only currents (Liu et al., 2021; Tinoco & Coco, 2014) or only waves (Tinoco & Coco, 2018) that the threshold for resuspension is lower within vegetated meadows than without vegetation. However, the threshold has not yet been studied for combined wave-current conditions, which often exist in the marsh environment. Identifying this threshold will enable us to predict when in a tidal cycle sediment resuspension occurs and can be used to improve sediment transport model. We use flume experiments to methodically identify the threshold of sediment resuspension in artificial salt marsh meadows of three different area densities under combined wave-current flows.

Time development of live-bed scour around an offshore-wind monopile under large current–wave ratio

Scour around a circular monopile in coastal regions has been investigated extensively over the past decades, but the time development of scour depth around an offshore-wind monopile under large current–wave ratio still lacks a predictive model. By considering the conservation of sand volume and adopting the conventional exponential law for temporal variation, a semi-empirical model, which has three parameters, i.e., an equilibrium scour depth, a shape coefficient and a scour characteristic time scale, is developed for predicting the time development of scour depth around a monopile under live-bed conditions of combined wave–current flows. A series of laboratory experiments was conducted in current-only and wave–current flows to obtain data for model calibration and validation. Experimental results indicate that adding weak waves on current accelerates scour development, which is successfully captured by the proposed model through using the far-field bottom shear stress as a key model input. The overall model inaccuracy is within 25%, and the model’s applicability is further confirmed by field measurements from an offshore wind farm in east China. This model can help to determine the timing of installing scour protection around offshore monopiles, especially for the circumstances with very strong local sediment transport (live-bed).

Scour around twin-piles under combined wave–current flows

The paper presents three dimensional simulations of scour around a pair of piles arranged side-by-side configurations under combined wave–current flow conditions using a computational fluid dynamics model. The Reynolds-averaged Navier–Stokes (RANS) equation is solved using the k-ω turbulence model in the present work. The Exner equation is used to measure the variations in bed elevation. The level-Set approach is used to capture the free surface realistically. The numerical model couples the hydrodynamic module with the morphological module to simulate the scour process. For accurate erosion and deposition calculations in the sediment bed, the morphological model employs a modified bed shear stress formula on a sloping bed in combination with a sand slide algorithm. In the present study, the simulations have been done in a truncated numerical wave tank with the Dirichlet boundary condition and active wave absorption method. The numerical model is validated with the experimental results of combined wave–current hydrodynamics and scour around a pair of piles. The validated numerical model is utilized to study the effect of the gap ratio and the effect of KC number in the various combined wave–current environment. In low KC conditions, normalized scour depth increments owing to waves alone, weak currents, and moderate currents are less, whereas the scour depth increases dramatically for waves with high currents. It is also found that the gap flow between the piles increases the depth of scour in a significant manner. For a given pile gap ratio, the scour depth is dependent on the KC number, which implies the larger the KC number, the larger scour depth. For a given KC number, the scour hole stretch in the flow direction reduces as the gap ratio increases, whereas the perpendicular stretch increases. It is also observed that the normalized scour depth decreases as the gap ratio increases for a fixed KC number and fixed Ucw. It is evident from the present research that the normalized scour depth increases with increase in KC number for a fixed wave–current parameter (Ucw).

Double-averaged turbulence statistics of wave current flow over rough bed with staggered arrangement of hemispherical blocks

Double-average turbulence characteristics of combined wave-current flow are studied over a rough bed comprising hemispheres arranged in a staggered pattern with different spacing (p/r = 4, 6, and 8; p = pitch length, r = height). The instantaneous velocity data was collected by Acoustic Doppler Velocimetry for the evaluation of double-average (DA) velocity, turbulence intensity, form-induced intensity, Reynolds stress, and form-induced stresses. The smallest DA velocity was obtained for p/r = 4 at the bottom region, signifying that p/r = 4 offered the maximum resistance to the flow among the tested cases. DA Reynolds stress is decreased for the entire flow depth due to superimposed waves. The advection of momentum-flux of normal stress in stream-wise and bottom-normal directions is increased at the outer layer and decreased at the near-bed region after wave-imposition. Maximum TKE production and diffusion are obtained just above the interfacial sub-layer and the middle of the form-induced sub-layer respectively. The turbulence structure is strongly anisotropic at the bottom region for p/r = 4 and near the outer layer, the tendency towards the return to isotropic state is dominant while with the increase in roughness spacing, a decrease in anisotropy is observed. Furthermore, an increase in wave-frequency decreased the tendency for the return to isotropy at the free surface.

A new model for quantifying wave damping by vegetation in combined wave–current flow

The propagation of waves in nearshore areas is often accompanied by the presence of tidal currents, which have an impact on the dissipation of wave energy in coastal vegetation regions. However, the existing models generally do not consider the in-canopy velocity, resulting incomplete energy dissipation terms and thus inaccurate estimation of drag coefficients. In this study, we developed a new analytical model to incorporate vertical velocity distribution and full energy dissipation terms in energy flux balance equation. This model is applied to interpret the data from a new flume experiment of vegetation in combined wave-current flows. New CD-Re relationships were derived by applying the new model. Additionally, we extracted the wave energy passage time and decay rate from both the experimental data and the model results, which shows that the wave energy passage time of opposing currents is up to 75% longer than that of following currents. This disparity in passage time is the primary factor contributing to the greater wave dissipation observed in the cases of opposing currents. This study offers novel insights into the process of wave dissipation, and can potentially improve our capability in predicting wave dissipation.

Experimental and numerical modelling of scour at vertical wall abutment under combined wave-current flow in low KC regime

The present study investigates the scour at vertical-wall abutments under a strong current-dominated combined wave-current and current-only environment using experiments and computational fluid dynamics (CFD) modeling. The CFD modelling is performed using an open-source three-phase numerical model (REEF3D), which solves Reynolds-Averaged Navier Stokes (RANS) equations with k-ω turbulence closure. The CFD model is first validated using the experiments and then used for further investigation. The Exner equation was used to compute alterations in bed elevation, while the Level-Set method recorded the free surface and bed topography in a realistic manner. The experimental findings demonstrate that the initial phase of scour development is more rapid under combined wave-current flow, but the equilibrium scour depth is higher in current-only conditions. The increase in Keulegan Carpenter (KC) number increases the scour depth at vertical-wall abutments for a specific relative flow velocity (Ucw). In contrast, a mild increase in vertical-wall abutment scour depth is observed with an increase in Ucw. To the best of the authors’ knowledge, the present work is the first of a kind of experimental and three-dimensional CFD study that estimates abutment scour under strong current-dominated combined wave-current flow.

Experimental study of Stokes drift in combined wave-current flows using Particle Image Velocimetry

In the present study, Eulerian velocities were obtained using the PIV system to investigate the problem of Stokes drift in combined wave-current flows. Time-averaged mean Eulerian velocity profiles were presented after the flow has achieved its equilibrium status. Waves with various wave periods and amplitudes were generated and propagated with the turbulent current possessing a Reynolds number of 32000. Results of the time-averaged mean velocity profiles suggest the absence of a return flow in an open flume. The discrepancies of the depth-averaged mean velocity with and without waves superimposed were found to be in good agreements with the return flow speeds as predicted by Kim (1984). This further confirmed the applicability of their solution for calculating the return flow under the condition of waves propagating with currents.

3D CFD Study of Scour in Combined Wave–Current Flows around Rectangular Piles with Varying Aspect Ratios

This study utilizes three-dimensional simulations to investigate scour in combined wave–current flows around rectangular piles with various aspect ratios. The simulation model solves the Reynolds-averaged Navier–Stokes (RANS) equations using the k–ω turbulence model, and couples the Exner equation to compute bed elevation changes. The model also employs the level-set approach to realistically capture the free surface, and couples a hydrodynamic module with a morphological module to simulate the scour process. The morphological module employs a modified critical bed shear stress formula on a sloping bed and a sand-slide algorithm for erosion and deposition calculations in the sediment bed. To validate the numerical model, simulations are conducted in a truncated numerical wave tank with the Dirichlet boundary condition and active wave absorption method. After validation, the numerical model is used to investigate the effect of aspect ratio and the Keulegan–Carpenter (KC) number on scour depth in a combined wave–current environment. The study finds that the normalized scour depth is highest for a rectangular pile with an aspect ratio of 2:1 and lowest for an aspect ratio of 1:2. The maximum normalized scour depth (S/D) for aspect ratios of 2:1 are 0.151, 0.218, and 0.323 for KC numbers 3.9, 5.75, and 10, respectively, whereas the minimum normalized scour depth (S/D) for aspect ratios of 1:2 are 0.132, 0.172, and 0.279. Additionally, the research demonstrates that the normalized scour depth increases with an increase in the KC number for a fixed wave–current parameter (Ucw).

On the hydrodynamic response and slamming impact of a cylindrical FPSO in combined wave-current flows

Owing to the lower construction and transportation costs, cylindrical floating production storage offloading (CFPSO) has received extensive attention in the industry. Currently, attention has primarily been focused on the damping performance of heave plate while few studies have touched upon hydrodynamic characteristics under complex combined wave-current condition. In this paper, we numerically investigate the hydrodynamic response and slamming impact of a CFPSO under combined wave-current flows. The active wave generating-absorbing boundary condition (GABC) along with the buoyancy-modified k-omega SST turbulence model are utilized to generate high-precision waves and current based on the open source computational fluid dynamics (CFD) framework OpenFOAM. A self-developed six degree of freedom (6DOF) motion module is used for solving rigid body motion and updating mesh motion. The numerical results of motion response and impact pressure are compared with the experimental data to verify the accuracy of present simulations. The correlation between impact pressure and relative wave elevation and wave velocity is analyzed and three types of slamming events have been identified. The flow fields such as vorticity, pressure and streamlines in the vicinity of the CFPSO are also presented and discussed, which provides a reference for structural design for the CFPSO under complex sea conditions.

Numerical study of sediment suspension affected by rigid cylinders under unidirectional and combined wave–current flows

Sediment transport modeling for flows with cylinders is very challenging owing to the complicated flow–cylinder–sediment interactions, especially under the combined wave-current flows. In this paper, an improved formulation for incipient sediment suspension considering the effect of cylinder density (i.e., solid volume fraction) is employed to simulate the bottom sediment flux in the flow with cylinders. The proposed model is calibrated and validated using laboratory measurements under unidirectional and combined wave-current flows in previous studies. It is proved that the effects of cylinders on sediment suspension can be accounted for through a modified critical Shields number, and the proposed model is capable of simulating sediment suspension under both unidirectional and combined wave–current flows reasonably well with the average the coefficients of determination and model skills greater than 0.8 and 0.64.

Wave-Current Impact on Shear Stress Patterns around 3D Shallow Bedforms

Observations from wave basin experiments and wave-resolving numerical simulations demonstrate the effect of wave-current interaction on shear stress around a sandy mound. Observations from the wave basin show that the mound deformation rate and morphological patterns depend on the mixture of waves and currents in the incident flow conditions. A SWASH nonhydrostatic numerical model was used to expand the parameter space of wave-current conditions observed in the flume and characterize the response of the near-bed shear stress to the mound. The model was validated with observations from wave-alone, current-alone, and wave-current flume tests and then ran for a suite of numerical flow conditions which isolate the impact of the ratio of wave-current energy on the bed shear stress. Results show how the current-to-wave ratio impacts the spatial heterogeneity of shear stress across the mound, with the region of shear stress intensification around the mound and the location of the peak shear stress becoming asymmetric with more mixed wave-current flows. These results show the nonlinear response of shear stress patterns to combined wave-current flows and how these patterns may impact eventual sediment transport and mound evolution.

Experimental investigation of time-invariant eddy viscosity in wave-current interaction

An experimental study of the turbulent boundary layer, where waves propagate with a current, is presented in this paper. A wide range of test conditions have been covered, namely, flows over a rough bed and a smooth bed, combined flows in a large-scale oscillatory water tunnel and combined waves and currents in two flumes with different scales. Particle Image Velocimetry and Laser Doppler Velocimetry were employed to obtain the velocity field. Detailed analysis of eddy viscosity profiles calculated from the experiments leads to the conclusion that previous assumed profiles do not always accurately describe eddy viscosity distributions in a combined wave-current flow. The distributions of eddy viscosity are categorised into two types (two-layer or three-layer), based on the influence of wave motions superimposed. For those cases in the current-dominated regime, eddy viscosity profiles are similar to unidirectional turbulent currents. When combined flows are in the wave-dominated regime, three-layer eddy viscosity distributions are observed. For both types, a linear eddy viscosity profile is found to be present in the bottom 10 per cent of the turbulent boundary layer. Above this, the classic parabolic profile is observed, over the whole turbulent boundary layer for the first type and over 40 per cent of the turbulent boundary layer thickness for the second type. An empirical eddy viscosity distribution in the outer region is proposed for the second type. This newly developed eddy viscosity distribution provides guidance for numerical modellers in the field of wave-current interaction and for coastal engineers wishing to predict sediment transport.

Sediment suspension affected by submerged rigid vegetation under waves, currents and combined wave–current flows

Laboratory experiments and mathematical analyses were carried out to investigate and quantify the impacts of submerged rigid vegetation on sediment suspension under waves, currents and combined wave–current flows. Mimic canopies constructed from wooden cylinders were used in the experiments with three configurations (sparse, dense and vertically varying density). It was found that more sediment was suspended within the vegetation canopies, where smaller velocities and higher turbulence were observed, indicating that vegetation-induced turbulence rather than mean flow was the main driver of sediment suspension over vegetated beds. Meanwhile, higher sediment concentration near the bed was observed within a denser canopy, especially in the case of vertically varying vegetation density. The near-bed suspended sediment concentration could be described by an exponential formulation using an effective bed shear velocity considering different turbulence components (i.e. vegetation wake turbulence, bed shear turbulence and near-bed coherent structures). The formula was applicable in both vegetated and bare beds with different hydrodynamic conditions. To predict the vertical distributions of sediment suspension, two theoretical models of turbulent diffusion were improved by incorporating the vertically varying turbulent intensity in the water column.

Boundary layer dynamics and bottom friction in combined wave-current flows over large roughness elements

Boundary layer dynamics and bottom friction in combined wave-current flows over large roughness elements

Boundary layer dynamics and bottom friction in combined wave–current flows over large roughness elements

In the coastal ocean, interactions of waves and currents with large roughness elements, similar in size to wave orbital excursions, generate drag and dissipate energy. These boundary layer dynamics differ significantly from well-studied small-scale roughness. To address this problem, we derived spatially and phase-averaged momentum equations for combined wave–current flows over rough bottoms, including the canopy layer containing obstacles. These equations were decomposed into steady and oscillatory parts to investigate the effects of waves on currents, and currents on waves. We applied this framework to analyse large-eddy simulations of combined oscillatory and steady flows over hemisphere arrays (diameter$D$), in which current ($U_c$), wave velocity ($U_w$) and period ($T$) were varied. In the steady momentum budget, waves increase drag on the current, and this is balanced by the total stress at the canopy top. Dispersive stresses from oscillatory flow around obstacles are increasingly important as$U_w/U_c$increases. In the oscillatory momentum budget, acceleration in the canopy is balanced by pressure gradient, added-mass and form drag forces; stress gradients are small compared to other terms. Form drag is increasingly important as the Keulegan–Carpenter number$KC=U_wT/D$and$U_c/U_w$increase. Decomposing the drag term illustrates that a quadratic relationship predicts the observed dependences of steady and oscillatory drag on$U_c/U_w$and$KC$. For large roughness elements, bottom friction is well represented by a friction factor ($f_w$) defined using combined wave and current velocities in the canopy layer, which is proportional to drag coefficient and frontal area per unit plan area, and increases with$KC$and$U_c/U_w$.

Anisotropy of Reynolds Stress Tensor in Combined Wave–Current Flow

AbstractThis study examines the turbulent stress anisotropy tensor based on the Lumley triangle technique and eigenvalues in wave–current combined flows. The invariant functions are also presented at a different vertical location from the bed to comprehend the level of anisotropy in the combined flow. The spectral variation of the ratio of momentum flux to the turbulent kinetic energy is examined and discussed in comparison to the canonical value. The combined wave–current data display spectral variation considerably smaller than the canonical value (≈ 0.3) through the spectral frequencies domain. To characterize the behaviors of eddies in the wave–current turbulent flow, the Taylor and Kolmogorov length and time scales were analyzed and discussed. Furthermore, to enumerate the degree of organization of complex eddy motions in the combined flow, the normalized Shannon entropy is also evaluated using a discrete probability distribution.

Velocity and turbulence affected by submerged rigid vegetation under waves, currents and combined wave–current flows

Vegetation can change flow structure and turbulence characteristics. However, few studies have focused on combined wave–current flows in canopy with vertically varying density. Therefore, laboratory experiments were carried out to investigate hydrodynamics affected by submerged rigid vegetation with different densities (i.e. sparse, dense and vertically varying density) under waves, currents and combined wave–current flows. In submerged canopy with vertically uniform density, large shear stress occurs around the canopy top. Thus in the vertical distributions, the greatest values of maximum wave velocity under pure waves, and the greatest values of turbulent kinetic energy (TKE) under unidirectional currents and combined wave–current flows appear around the canopy top. In canopy with vertically varying density, the shear stress at each canopy top is relatively small, resulting in the vertically smooth distributions of velocity and TKE under pure waves. While under unidirectional currents and combined wave–current flows, canopy-scale turbulence throughout the entire water column occurs owing to the influence of multiple canopy tops. An improved formula considering drag coefficient, vegetation density and diameter, was proposed to predict stem-scale turbulence using characteristic velocity. The formula is appropriate for vegetated flow in which stem-scale turbulence is dominant, and it can be further used as a simple method to assess TKE for sediment or substances transport affected by vegetation.

Explicit approximation for velocity and sediment flux above mobile sediment bed beneath current and asymmetric wave

An explicit approximation is proposed for velocity distribution and sediment flux above mobile sediment bed beneath current and asymmetric wave. The predicted velocity is decomposed into an oscillatory part and a current part such that the interaction between current and asymmetric wave can be performed directly. The oscillatory part consists of a free stream velocity and a defect function which includes phase lead, mobile sediment bed level and wave boundary layer thickness. The oscillatory part is influenced by the current due to the changes of both mobile sediment bed level and wave boundary layer thickness. The current part is influenced by a wave eddy viscosity in the wave boundary layer and by an apparent wave roughness of the combined wave-current flow outside the wave boundary layer. Eight free variables are required for the approximation, and iterative bottom shear stress and roughness height are applied for the wave boundary layer thickness and mobile sediment bed level. The mobile sediment bed level takes account of the effects of phase lag (phase shift and residual), acceleration and flow asymmetry. Therefore, the mobile bed effect, instantaneous velocity, net velocity and sediment flux in the wave boundary layer can be reasonably presented by the explicit approximation beneath current and asymmetric wave.