Evaluation of Nonbreaking Wave-Induced Mixing Parameterization Schemes Based on a One-Dimensional Ocean Model

Surface waves have a considerable effect on vertical mixing in the upper ocean.In the past two decades,the vertical mixing induced through nonbreaking surface waves has been used in ocean and climate models to improve the simulation of the upper ocean.Thus far,several nonbreaking wave-induced mixing parameterization schemes have been proposed;however,no quantitative comparison has been performed among them.In this paper,a one-dimensional ocean model was used to compare the performances of five schemes,including those of Qiao et al.(Q),Hu and Wang(HW),Huang and Qiao(HQ),Pleskachevsky et al.(P),and Ghantous and Babanin(GB).Similar to previous studies,all of these schemes can decrease the simulated sea surface temperature(SST),increase the subsurface temperature,and deepen the mixed layer,thereby alleviating the common thermal deviation problem of the ocean model for upper ocean simulation.Among these schemes,the HQ scheme exhibited the weakest wave-induced mixing effect,and the HW scheme exhibited the strongest effect;the other three schemes exhibited roughly the same effect.In particular,the Q and P schemes exhibited nearly the same effect.In the simulation based on observations from the Ocean Weather Station Papa,the HQ scheme exhibited the best performance,followed by the Q scheme.In the experiment with the HQ scheme,the root-mean-square deviation of the simulated SST from the observations was 0.43℃,and the mixed layer depth(MLD)was 2.0 m.As a contrast,the deviations of the SST and MLD reached 1.25℃ and 8.4 m,respectively,in the experiment without wave-induced mixing.

A Method for Reducing Ocean Wave-Induced Magnetic Noises in Shallow-Water MT Data Using a Complex Adaptive Filter

In shallow-water areas,the marine magnetotelluric(MT)method faces a challenge in the investigation of seabed conductivity structures due to electrical and magnetic noises induced by ocean waves,which seriously contaminate MT data.Ocean waves can affect electric and magnetic fields to different extents.In general,their influence on magnetic fields is considerably greater than that on electric fields.In this paper,a complex adaptive filter is adopted to reduce wave-induced magnetic noises in the frequency domain.The processing results of synthetic and measured MT data indicate that the proposed method can effectively reduce wave-induced magnetic noises and provide reliable apparent resistivity and phase data.

Numerical Simulation of Spatial Lag Between Wave Breaking Point and Location of Maximum Wave-Induced Current

A quasi three-dimensional numerical model of wave-driven coastal currents with the effects of surface rollers is developed for the study of the spatial lag between the location of the maximum wave-induced current and the wave breaking point. The governing equations are derived from Navier-Stokes equations and solved by the hybrid method combining the fractional step finite different method in the horizontal plane with a Galerkin finite element method in the vertical direc- tion. The surface rollers effects are considered through incorporating the creation and evolution of the roller area into the free surface shear stress. An energy equation facilitates the computation process which transfers the wave breaking energy dissipation to the surface roller energy. The wave driver model is a phase-averaged wave model based on the wave action balance equation. Two sets of laboratory experiments producing breaking waves that generated longshore currents on a planar beach am used to evaluate the model＇s performance. The present wave-driven coastal current model with the roller effect in the surface shear stress term can produce satisfactory results by increasing the wave-induced nearshore current velocity inside the surf zone and shifting the location of the maximum longshore current velocity landward.

Experimental and Numerical Study of Wave-Induced Long-Shore Currents on A Mild Slope Beach

The long-shore current distribution on a mild slope beach is studied by combining the numerical model and the physical experiment. The experiments of long-shore currents under the action of regular and irregular waves are conducted on mild beaches with different slopes in a wave basin. A numerical model is established, which includes a wave propagation model, a wave breaking model and a long-shore current model. The validity of the numerical model is proved by the comparison of its results with the results of the experimental model. It is concluded that the wave-ioduced long-shore current is influenced significantly by the incident wave height, the wave angle and the beach slope. Its application to the Bohai Bay indicates that the wave-induced currents have the same order of magnitude as the tide currents in the near-shore zone of mill slope beach. In the design of wastewater ouffall locations on a mild-slope beach with shallow water of the Bohai Bay, the position of the outfall should be 10 km away from the shoreline, which is outside of the surf-zone.

Wave-induced pore water pressure in marine cohesive soils

Cyclic triaxial tests and numerical analyses were undertaken, in order to evaluate the wave-induced pore water pressure in seabed sediments in the Hangzhou Bay. The cyclic triaxial tests indicate that the rate of pore water pressure generation in cohesive soils decreases with time, and the development of the pore water pressure can be represented by a hyperbolic curve. Numerical analyses, taking into account the generation and dissipation of pore water pressure simultaneously, suggest that the pore water pressure buildup in cohesive soils may increase with time continuously until the pore water pressure ratio approaches to 1, or it may decrease after a certain time, which is controlled by drain conditions. These phenomena are different from those in sands. For waves with a retum period of 100 a in the Hangzhou Bay, if the wave duration is more than 60 h, then the pore water pressure ratio will be close to 1 and soil fabric failure will take place.

Wave-Induced Loads on Very Large FPSOs at Restricted Water Depth

The effects of water depth on the wave-induced vertical bending moment and shearing force on a very large FPSO are studied by experiments and computations for regular and irregular waves. The restricted water depth composite Green function is employed to develop a program for the computation of the hydrodynamic coefficients of the very large FPSO at shallow water. A three-segment model with 1∶100 scale is tested in the State Key Laboratory of Ocean Engineering at Shanghai Jiao Tong University for the verification of the numerical method. The experimental and computational results show that the water depth has a substantial effect on wave-induced loads. The wave-induced vertical loads increase with the decrease of water depth for shallow water. Especially, for ultra-shallow water these loads increase very evidently with the decrease of water depth. The long-term prediction values of wave-induced vertical loads increase with the decrease of the ratio of water depth to draught. The long-term prediction values of wave-induced vertical loads are about 8% larger than those for deep water when the ratio of water depth to draught is 3.0. However, water depth hardly affects the long-term prediction values of wave-induced loads when the ratio of water depth to draught is larger than 5.0.

Wave-induced mixing in the Yellow Sea

Vertical wave-induced mixing parameter Bv expressed in wave number spectrum was estimated in the Yellow Sea. The spatial distributions of Bv averaged over upper 20 m in 4 seasons were analyzed. It is the strongest in winter because of winter monsoon, and the weakest in spring. Since in summer it plays an important role for circulation of upper layers, its vertical structure was also discussed. Two simulations with and without wave-induced mixing in this season were performed to evaluate its effect on temperature distribution. Numerical results indicate that wave-induced mixing could increase the mixed layer thickness greatly.

Parameterization of ocean wave-induced mixing processes for finite water depth

Three dimensional wave-induced mixing plays an important role in shallow water area. A quite direct approach through the Reynolds average upon characteristic length scale is proposed to parameterize the horizontal and vertical shallow water mixing. Comparison of finite depth case with infinite depth results indicates that the difference of the wave-induced mixing strength is evident. In the shallow water condition, the infinite water depth approximation overestimates the mixing strength in the lower layers. The nonzero horizontal wave-induced mixing presents anisotropic property near the shore. The Prandtl＇s mixing length theory underestimated the wave-induced mixing in the previous studies.

Modeling of suspended sediment transport with wave-induced longshore current in Huanghe (Yellow) River Delta

A three-dimensional suspended sediment model （SED） developed by the present authors is coupled with the combinatorial model of COHERENS （Luyten et al., 1999） （the three-dimensional coupled hydrodynamical-ecological model for Regional and Shelf Seas） and SWAN （Holthuijsen et al., 2004） （the third generation wave model）. SWAN is regarded as a subroutine of COHERENS and gets time- and space-varying current velocity and surface elevation from COHERENS. COHERENS gets time- and space- varying wave relevant parameters provided by SWAN. Effects of wave on current are applied in bottom shear stress, wave-induced depth-dependent radiation stress and surface drag coefficient calculation. At the same time, the damping function of suspended sediment on turbulence is introduced into COHERENS. So the sediment model SED has feedback on circulation model COHERENS. The SED obtains current associated parameters from COHERENS. Then a coupled hydrodynamic-sediment model COHERENS-SED being able to account for interaction between wave and current is obtained. COHERENS-SED is adopted to simulate three-dimensional suspended sediment transport in the Huanghe River delta. In terms of simulation results, there is obvious difference between top and bottom layer of wave-induced longshore current. The values of time series of sediment concentration gotten by COHERENS-SED have, generally, an accepted agreement extent with measurement. Significant wave heights and wave periods obtained by COHERENS-SED show that wave simulation case with currentts effect can give better agreement extent with measurement than case without current＇s effect. In the meantime, suspended sediment concentration distributing rule obtained by COHERENS-SED is similar to former researches and measurement.

The improvement of the one-dimensional Mellor-Yamada and K-profile parameterization turbulence schemes with the non-breaking surface wave-induced vertical mixing

Both the level 2.5 Mellor-Yamada turbulence closure scheme （MY） and K-profile parameterization （KPP） are popularly used by the ocean modeling community. The MY and the KPP are improved through including the non-breaking surface wave-induced vertical mixing （Bv）, and the improved schemes were tested by using continuous data at the Papa ocean weather station （OWS） during 1961-1965. The numerical results showed that the Bv can make the temperature simulations fit much better with the continuous data from Papa Sta- tion. The two improved schemes overcame the shortcomings of predicting too shallow upper mixed layer depth and consequently overheated sea surface temperature during summertime, which are in fact com- mon problems for all turbulence closure models. Statistical analysis showed that the Bv effectively reduced the mean absolute error and root mean square error of the upper layer temperature and increased the corre- lation coefficient between simulation and the observation. Furthermore, the performance of vertical mixing induced by shear instability and the Bv is also compared. Both the temperature structure and its seasonal cycle significantly improved by including the Bv, regardless of whether shear instability was included or not, especially for the KPP mixing scheme, which suggested that Bv played a dominant role in the upper ocean where the mean current was relatively weak, such as at Papa Station. These results may provide a clue to improve ocean circulation models.

Effects of bottom shear stresses on the wave-induced dynamic response in a porous seabed:PORO-WSSI (shear) model

When ocean waves propagate over the sea floor,dynamic wave pressures and bottom shear stresses exert on the surface of seabed.The bottom shear stresses provide a horizontal loading in the wave-seabed interaction system,while dynamic wave pressures provide a vertical loading in the system.However,the bottom shear stresses have been ignored in most previous studies in the past.In this study,the effects of the bottom shear stresses on the dynamic response in a seabed of finite thickness under wave loading will be examined,based on Biot＇s dynamic poro-elastic theory.In the model,an ＂u-p＂ approximation will be adopted instead of quasi-static model that have been used in most previous studies.Numerical results indicate that the bottom shear stresses has certain influences on the wave-induced seabed dynamic response.Furthermore,wave and soil characteristics have considerable influences on the relative difference of seabed response between the previous model（without shear stresses） and the present model（with shear stresses）.As shown in the parametric study,the relative differences between two models could up to 10% of p0,depending on the amplitude of bottom shear stresses.

Numerical Simulation of Wave-Induced Currents Combined with Parabolic Mild-Slope Equation in Curvilinear Coordinates

Researches on breaking-induced currents by waves are summarized firstly in this paper. Then, a combined numerical model in orthogonal curvilinear coordinates is presented to simulate wave-induced current in areas with curved boundary or irregular coastline. The proposed wave-induced current model includes a nearshore current module established through orthogonal curvilinear transformation form of shallow water equations and a wave module based on the curvilinear parabolic approximation wave equation. The wave module actually serves as the driving force to provide the current module with required radiation stresses. The Crank-Nicolson finite difference scheme and the alternating directions implicit method are used to solve the wave and current module, respectively. The established surf zone currents model is validated by two numerical experiments about longshore currents and rip currents in basins with rip channel and breakwater. The numerical results are compared with the measured data and published numerical results.

Vertical variations of wave-induced radiation stress tensor

The distributions of the wave-induced radiation stress tensor over depth are studied by us- ing the linear wave theory, which are divided into three regions, i. e., above the mean water level, be- low the wave trough level, and between these two levels. The computational expressions of the wave-in- duced radiation stress tensor at the arbitrary wave angle are established by means of the Eulerian coordi- nate transformation, and the asymptotic forms for deep and shallow water are also presented. The verti- cal variations of a 30°incident wave-induced radiation stress tensor in deep water, intermediate water and shallow water are calculated respectively. The following conclusions are obtained from computations. The wave-induced radiation stress tensor below the wave trough level is induced by the water wave parti- cle velocities only, whereas both the water wave particle velocities and the wave pressure contribute to the tensor above the wave trough level. The vertical variations of the wave-induced radiation stress ten- sor are influenced substantially by the velocity component in the direction of wave propagation. The dis- tributions of the wave-induced radiation stress tensor over depth are nonuiniform and the proportion of the tensor below the wave trough level becomes considerable in the shallow water. From the water surface to the seabed, the reversed variations occur for the predominant tensor components.

Numerical simulation of sediment transport in coastal waves and wave-induced currents

Prediction of coastal sediment transport is of particularly importance for analyzing coast erosion accurately and solving the corresponding coast protection engineering problems.The present study provided a numerical scheme for sediment transport in coastal waves and wave-induced currents.In the scheme,the sand transport model was implemented with wave refraction-diffraction model and near-shore current model.Coastal water wave was simulated by using the parabolic mild-slope equation in which wave refraction,diffraction and breaking effects are considered.Wave-induced current was simulated by using the nonlinear shallow water equations in which wave provides radiation stresses for driving current.Then,sediment transport in waves and wave-induced currents was simulated by using the two-dimensional suspended sediment transport equations for suspended sediment and the bed-load transport equation for bed load.The numerical scheme was validated by experiment results from the Large-scale Sediment Transport Facility at the US Army Corps of Engineer Research and Development Center in Vicksburg.The numerical results showed that the present scheme is an effective tool for modeling coastal sediment transport in waves and near-shore currents.

Effects of the surface wave-induced mixing on circulation in an isopycnal-coordinate oceanic circulation model

The influence of the nonbreaking surface wave-induced mixing under the mixed layer on the oceanic cir- culation was investigated using an isopycnal-coordinate oceanic circulation model. The effect of the wave- induced mixing within the mixed layer was eliminated via a bulk mixed layer model. The results show that the wave-induced mixing can penetrate through the mixed layer and into the oceanic interior. The wave- induced mixing under the mixed layer has an important effect on the distribution of temperature of the upper ocean at middle and high latitudes in summer, especially the structure of the seasonal thermocline. Moreover, the wave-induced mixing can affect the oceanic circulation, such as western boundary currents and the North Equatorial Currents through changes of sea surface height associated with the variation of the thermal structure of the upper ocean.

Experimental and Numerical Studies of the Wave-Induced Responses of a River-to-Sea Ship

The ship motions and wave-induced loads of a new type of river-to-sea ship are investigated experimentally and numerically. A river-to-sea ship is an unconventional type of container ship characterized by high breadth to draft ratio and low length to breadth ratio, which makes it more prone to hydroelasticity than conventional ships of the same size. A segmented model was tested under two loading conditions, namely, ballast and loaded conditions, to determine the vertical motions and wave-induced loads under each condition. Results are compared with numerical simulations in the frequency domain. The wave-induced responses are calculated by a nonlinear time domain code at each time step. The response amplitude operators of vertical ship responses in regular waves are analyzed, and the wave-induced responses are consistent with the experimental results.

Numerical study on water waves and wave-induced longshore currents in Obaky coastal water

In this paper, the water waves and wave-induced longshore currents in Obak6y coastal water which is located at the Mediterranean coast of Turkey were numerically studied. The numerical model is based on the parabolic mild-slope equation for coastal water waves and the nonlinear shallow water equation for the wave-induced currents. The wave transformation under the effects of shoaling, refraction, diffraction and breaking is considered, and the wave provides radiation stresses for driving currents in the model. The numerical results for the water wave-induced longshore currents were validated by the measured data to demonstrate the efficiency of the numerical model. Then the water waves and longshore currents induced by the waves from main directions were numerically simulated and analyzed based on the numerical results. The numerical results show that the movement of the longshore currents was different while the wave proDaRated to a coastal zone from different directions.

Influence of the earth rotation on the interfacial wave solutions and wave-induced tangential stress in a two-layer fluid system

Interfacial waves and wave-induced tangential stress are studied for geostrophic small amplitude waves of two-layer fluid with a top free surface and a fiat bottom. The solutions were deduced from the general form of linear fluid dynamic equations of two-layer fluid under the f-plane approximation, and wave-induced tangential stress were estimated based on the solutions obtained. As expected, the solutions derived from the present work include as special cases those obtained by Sun et al. （2004. Science in China, Ser. D, 47（12）： 1147-1154） for geostrophic small amplitude surface wave solutions and wave-induced tangential stress if the density of the upper layer is much smaller than that of the lower layer. The results show that the interface and the surface will oscillate synchronously, and the influence of the earth＇s rotation both on the surface wave solutions and the interfacial wave solutions should be considered.

Contribution of surface wave-induced vertical mixing to heat content in global upper ocean

Compared with observations,the simulated upper ocean heat content(OHC)determined from climate models shows an underestimation bias.The simulation bias of the average annual water temperature in the upper 300 m is 0.2℃lower than the observational results.The results from our two numerical experiments,using a CMIP5 model,show that the non-breaking surface wave-induced vertical mixing can reduce this bias.The enhanced vertical mixing increases the OHC in the global upper ocean(65°S–65°N).Using non-breaking surface wave-induced vertical mixing reduced the disparity by 30%to 0.14℃.The heat content increase is not directly induced by air-sea heat fluxes during the simulation period,but is the legacy of temperature increases in the first 150 years.During this period,additional vertical mixing was initially included in the climate model.The non-breaking surface wave-induced vertical mixing improves the OHC by increasing the air-sea heat fluxes in the first 150 years.This increase in air-sea heat fluxes warms the upper ocean by 0.05–0.06℃.The results show that the incorporation of vertical mixing induced by nonbreaking surface waves in our experiments can improve the simulation of OHC in the global upper ocean.

Influence of stress wave-induced disturbance on ultra-low friction in broken blocks

Deep rock mass tends to be broken into blocks when mining for materials deep below the surface.The rock layer of the roof of the mine can be regarded as a system of blocks of fractured rock mass.When subjected to high ground stress and mining-induced disturbance,the efect of the ultra-low friction of the block system easily becomes apparent,and can induce rock burst and other accidents.By taking the block of rock mass as research object,this study developed a test system for ultra-low friction to experimentally examine its efects on the broken blocks under stress wave-induced disturbance.We used the horizontal displacement of the working block as the characteristic parameter refecting the efect of ultra-low friction,and examine its characteristic laws of horizontal displacement,acceleration,and energy when subjected to the efects of ultra-low friction by changing the frequency and amplitude of the stress wave-induced disturbance.The results show that the frequency of stress wave-induced disturbance is related to the generation of ultra-low friction in the broken block.The frequency of disturbance of the stress wave is within 1–3 Hz,and signifcantly increases the maximum acceleration and horizontal displacement of the broken blocks.The greater the intensity of the stress wave-induced disturbance is,the higher is the degree of block fragmentation,and the more likely are efects of ultra-low friction to occur between the blocks.The greater the intensity of the horizontal impact load is,the higher is the degree of fragmentation of the rock mass,and the easier it is for the efects of ultra-low friction to occur.Stress wave-induced disturbance and horizontal impact are the main causes of sliding instability of the broken blocks.When the dominant frequency of the kinetic energy of the broken block is within 20 Hz,the efects of ultra-low friction are more likely.