Wave effect on the ocean circulations through mass transport and wave-induced pumping

The wave Coriolis-Stokes-Force-modified ocean momentum equations are reviewed in this paper and the wave Stokes transport is pointed out to be part of the ocean circulations. Using the European Centre for Medium-Range Weather Forecasts 40-year reanalysis data (ERA-40 data) and the Simple Ocean Data Assimilation (SODA) version 2.2.4 data, the magnitude of this transport is compared with that of wind-driven Sverdrup transport and a 5-to-10-precent contribution by the wave Stokes transport is found. Both transports are stronger in boreal winter than in summers. The wave effect can be either contribution or cancellation in different seasons. Examination with Kuroshio transport verifies similar seasonal variations. The clarification of the efficient wave boundary condition helps to understand the role of waves in mass transport. It acts as surface wind stress and can be functional down to the bottom of the ageostrophic layer. The pumping velocities resulting from wave-induced stress are zonally distributed and are significant in relatively high latitudes. Further work will focus on the model performance of the wave-stress-changed-boundary and the role of swells in the eastern part of the oceans.     

Beach Morphology and Coastline Evolution in the Southern Bohai Strait

The beach studied in this paper spans a length of 51 km and is one of several long sandy beaches in the southern Bohai Strait. Due to the obstruction of islands in the northeast and the influence of the underwater topography, the wave environment in the offshore area is complex; beach types and sediment transport characteristics vary along different coasts. The coastlines extracted from six aerial photographs in different years were compared to demonstrate the evolving features. Seven typical beach profiles were selected to study the lateral beach variation characteristics. Continuous wind and wave observation data from Beihuangcheng ocean station during 2009 were employed for the hindcast of the local wave environment using a regional spectral wave model. Then the results of the wave hindcast were incorporated into the LITDRIFT model to compute the sediment transport rates and directions along the coasts and analyze the longshore sand movement. The results show that the coastline evolution of sand beaches in the southern Bohai Strait has spatial and temporal variations and the coast can be divided into four typical regions. Region(I), the north coast of Qimudao, is a slightly eroded and dissipative beach with a large sediment transport rate; Region(II), the southwest coast of Gangluan Port, is a slightly deposited and dissipative beach with moderate sediment transport rate; Region(III), in the central area, is a beach that is gradually transformed from a slightly eroded dissipative beach to a moderately or slightly strong eroded bar-trough beach from west to east with a relatively moderate sediment transport rate. Region(IV), on the east coast, is a strongly eroded and reflective beach with a weak sediment transport rate. The wave conditions exhibit an increasing trend from west to east in the offshore area. The distribution of the wave-induced current inside the wave breaking region and the littoral sediment transport in the nearshore region exhibit a gradual weakening tendency from west to east, which is opposite to the trend of the wave conditions outside the breaking region. The presence of submerged shoal(Dengzhou Shoal), deep trough(Dengzhou Channel), islands and irregular topography influnces the wave climate, beach types, wave-induced current features, littoral sediment transport trends and coastline evolution patterns in the southern Bohai Strait. Human activities, such as the sand exploitation of Dengzhou Shoal and other coastal engineering projects, also influence the beach morphology and coastline evolution.     

Morphology,sedimentary bedforms and sand transport across a ridge- and- runnel beach under the action of summer waves

As part of a collaborative study between the 3rd Institute of Oceanography, Xiamen, and the U. K. Universities of East Anglia and St. Andrews, a 4-day experiment was conducted on a ridge- and- runnel beach of north Norfolk on the North Sea coast. Detailed surveys were made of every low water of an area 10m by 30m and electromagnetic current meters were used to measure wave-induced currents over the ridge and in the runnel. The locations of bedform fields were noted, fluorescent sand was used to follow the sand movement and, at the end of the experiment, lacquer peels were taken of the top 0.2m of a vertical section through the ridge- and- runnel. During the 4 days 0.75m³ of sand per metre width of beach accreted in the runnel and a similar volume was eroded from the upper foreshore. The dominant shoreward transport, identified qualitatively by the movement of the fluorescent sand, suggests the ridge- and- runnel system migrated shorewards up the general beach slope of 1^o by 2–3m. The wave orbital currents were used to predict the bedforms to be expected over the tidal cycle: an upper phase plane- bed was predicted for most of the period but vortex and rolling- grain ripples were predicted and observed when the water level over the ridge was low. As the tide dropped ripples on the ridge were eliminated by swash action but the ripples in the runnel were protected by the ridge and remained on the beach after the tide dropped. The observed accretion of the beach in the runnel and on the lee slope of the ridge was used to calculate that a net average shoreward transport of 0.11g/cm·s⁻¹ occurred over the ridge crest during the period it was underwater. The current meter measurements of the wave orbital currents and the mean currents over the ridge crest were used with the wave- current interaction model of Grant and Madsen (1982), ripple dimensions defined by Nielsen (1981), and resuspension coefficient of Vincent and Green (1990), to compute bedload sand transport rates from the equations of Madsen and Grant (1976), Sleath (1978), and Vincent et al. (1981), and also the suspended sand transport rates. The results from one of these bedload equations (Madsen and Grant, 1976) compared well with the observed net transport. The calculated suspended load transport rates (due to steady currents alone) were a factor of 5 too great, and were also several orders of magnitude greater than suspended transport rates measured directly under similar or more energetic wave and current conditions.     

On the Lagrangian residual current and residual transport in a multiple time scale system of shallow seas

A multiple time scale perturbation method is used to discuss the Lagrangian residual current and residual transport on the basis of a weakly nonlinear dynamic model of shallow seas. The governing equations for the long-term variation of zero order “apparent concentration” (which is a linear combination of salinity, temperature of seawater and the concentration of any tracer which is conservative and passive) and its mean value over tidal cycles are obtained for the system with single tidal constituent, and for the one with multi-constituents, winds and thermohaline. The equations for the two cases are in the same form and show this long-term variation resulted from the cumulative effect of residual convection and turbulent diffusion. The multiple time scale variation of current is caused by tides, winds, and the thermohaline and the nonlinear effects of the system. The derived set of governing field equations of the Lagrangian current for this multiple time scale system is also in the same form as that for a single time scale system.     

A three-dimensional weakly nonlinear dynamics on tide-induced Lagrangian residual current and mass-transport

In recent years, studies of the environmental hydrodynamics in coastal seas and tidal estuaries have placed focus on the processes which determine the “fate” of longer-term transport. The lagrangian residual current has been recognized as an important factor which affects the longer term transport processes since it is more relevant to use a Lagrangian mean velocity rather than an Eulerian mean velocity to determine the origin of Water masses. In the present paper, an attempt is made to formulate a three-dimensional dynamics on the tideinduced Lagrangian residual current and mass-transport based upon a three-dimensional weakly-nonlinear model of tides. The Lagrangian residual velocity is shown to be the sum of the mass-transport velocity, which is the sum of the Eulerian residual velocity and the Stokes’ drift velocity, and the Lagrangian residual drift velocity which is dependent on the tidal current phase. This reveals that it is the mass-transport velocity which is the tidal cycle Eulerian mean of the Lagrangian residual velocity and that the mass-transport velocity is correct to the second order of approximation rather than to the first order. And then, a new longer-term transport equation which correctly describes the Lagrangian nature of transport processes without introducing the Fickian hypothesis for tidal dispersion is derived. In fact, the convection can be correctly represented by the Eulerian mean of the Lagrangian residual velocity, as the convective velocity in the longer-term transport equation is nothing but the mass-transport velocity. Submitted for IAMAP/IAPSO Joint Assembly, August 5–16, 1985, Honolulu, Hawaii U.S.A.     

Effect of wave-induced Stokes drift on the dynamics of ocean mixed layer

The wave-forcing ’Coriolis-Stokes forcing’ and ’Stokes-vortex force’ induced by Stokes drift affect the upper ocean jointly.To study the effect of the wave-induced Stokes drift on the dynamics of the ocean mixed layer,a new three-dimensional(3D) numerical model is derived using the primitive basic equations and Eulerian wave averaging.The Princeton Ocean Model(POM),a 3D primitive equation ocean model is used with the upper wave-averaged basic equations.The global ocean circulation is simulated using the POM model,and the Stokes drift is evaluated based on the wave data generated by WAVEWATCH III.We compared simulations with and without the Stokes drift.The results show that the magnitude of the Stokes drift is comparable with the Eulerian mean current.Including the Stokes drift in the ocean model affects both the Eulerian current and the Lagranian drift and causes the vertical mixing coefficients to increase.     

The suspended sediment concentration distribution in the Bohai Sea, Yellow Sea and East China Sea

The distribution of the suspended sediment concentration (SSC) in the Bohai Sea, Yellow Sea and East China Sea (BYECS) is studied based on the observed turbidity data and model simulation results. The observed turbidity results show that (i) the highest SSC is found in the coastal areas while in the outer shelf sea areas turbid water is much more difficult to observe, (ii) the surface layer SSC is much lower than the bottom layer SSC and (iii) the winter SSC is higher than the summer SSC. The Regional Ocean Modeling System (ROMS) is used to simulate the SSC distribution in the BYECS. A comparison between the modeled SSC and the observed SSC in the BYECS shows that the modeled SSC can reproduce the principal features of the SSC distribution in the BYECS. The dynamic mechanisms of the sediment erosion and transport processes are studied based on the modeled results. The horizontal distribution of the SSC in the BYECS is mainly determined by the current-wave induced bottom stress and the fine-grain sediment distribution. The current-induced bottom stress is much higher than the wave-induced bottom stress, which means the tidal currents play a more significant role in the sediment resuspension than the wind waves. The vertical mixing strength is studied based on the mixed layer depth and the turbulent kinetic energy distribution in the BYECS. The strong winter time vertical mixing, which is mainly caused by the strong wind stress and surface cooling, leads to high surface layer SSC in winter. High surface layer SSC in summer is restricted in the coastal areas.     

Improved Numerical Computing Method for the 3D Tidally Induced Lagrangian Residual Current and Its Application in a Model Bay with a Longitudinal Topography

An improved method for computing the three-dimensional(3 D) first-order Lagrangian residual velocity(uL) is estab-lished. The method computes tidal body force using the harmonic constants of the zeroth-order tidal current. Compared with using the tidal-averaging method to compute the tidal body force, the proposed method filters out the clutter other than the single-frequency tidal input from the open boundary and obtains uL that is more consistent with the analytic solution. Based on the new method, uL is calculated for a wide bay with a longitudinal topography. The strength and pattern of uL are mostly determined by the parts of the tidal body force related to the vertical mixing of the Stokes' drift and the Coriolis effect, with a minor contribution from the advection effect. The geometrical shape of the bay can influence uL through the topographic gradient. The magnitude of uL increases with the increases in tidal energy input and vertical eddy viscosity and decreases in terms of the bottom friction coefficient.     

The baroclinic residual circulation in shallow seas

There are two different modeling approaches which have been proposed and utilized to derive residual currents: the first approach is equivalent to deducing residual currents from current-meter records using filtering techniques or time averages of time-series records to remove tidal variations; in the second approach, filters or time averages over several tidal cycles are applied to the hydrodynamic equations to generate the governing equations for residual circulation. Based on the latter, both the baroclinic dynamic models of residual circulation are proposed, of which one is a two-dimensional transport model and the other is a three-dimensional model with variable eddy viscosity. The two-dimensional transport model is a direct generalization from the barotropic model of residual circulation presented by Nihoul and Randy (1975) and Heaps (1978) to the baroclinic model. In the three-dimensional model with variable eddy viscosity, using a Sturm-Liouville system adopted in the reference [5], the nondimensional problem for residual circulation reduces to the nondimensional problem of the elevation and the expression of residual currents. It should be pointed out that both the baroclinic models developed in the present paper are confined to describe the Eulerian residual circulation only.     

COMPARISON OF THE EULERIAN AND LAGRANGIAN TIDAL RESIDUALS IN THE BOHAI SEA

Tidal residual is very important to the transport of water particles, nutrients, plank-ton, etc. in the coastal sea. Eulerian scheme and Lagrangian scheme are two different ways to get the time averaged residual. Solution of the Bohai Sea‘s hydrodynamic system using a semi-implicit layer aver-aged numerical model yielded different direction Eulerian and Lagrangian tidal residuals. The latter were stronger than the former in most sea areas. Their different directions produced different ciretdation pattern in some areas. Compared with the Eulerian residual, the Lagranglan residual seemed to be more in accord with the observation.     

Preliminary results of assessing the mixing of wave transport flux residualin the upper ocean with ROMS

The effects of the mixing of wave transport flux residual(Bvl) on the upper ocean is studied through carrying out the control run(CR) and a series of sensitive runs(SR) with ROMS model.In this study,the important role of Bvl is revealed by comparing the ocean temperature,statistical analysis of errors and evaluating the mixed layer depth.It is shown that the overestimated SST is improved effectively when the wave-induced mixing is incorporated to the vertical mixing scheme.As can be seen from the vertical structure of temperature 28℃ isotherm changes from 20 min CR to 35 m in SR3,which is more close to the observation.Statistic analysis shows that the root-mean-square errors of the temperature in 10 m are reduced and the correlation between model results and observation data are increased after considering the effect of Bvl.The numerical results of the ocean temperature show improvement in summer and in tropical zones in winter,especially in the strong current regions in summer.In August the mixed layer depth(MLD) which is defined as the depth that the temperature has changed 0.5℃ from the reference depth of 10 m is further analyzed.The simulation results have a close relationship with undetermined coefficient of Bvl,sensitivity studies show that a coefficient about 0.1 is reasonable value in the model.     

Rotary spectrum analysis of tidal current in the southern Yellow Sea

A complete set of one-month Acoustic Doppler Profiler (ADP) current data at a station in the southern Yellow Sea (SYS) is analyzed using the rotary spectrum method. The results revealed different rotary properties between barotropic and baroclinic tidal currents. The barotropic and baroclinic tidal currents rotate elliptically counter-clockwise and clockwise, respectively. Meanwhile, baroclinic bottom tidal currents are almost along-isobath. The baroclinic cross-isobath velocities attenuate quickly at the bottom, implying important effects of bottom topography on the cross-isobath motions.     

Geostrophic meridional transport in tropical Northwest Pacific based on Argo profiles

Absolute geostrophic currents in the North Pacific Ocean were calculated using P-vector method from newly gridded Argo profiling float data collected during 2004–2009. The meridional volume transport of geostrophic currents differed significantly from the classical Sverdrup balance, with differences of 10×10⁶–20×10⁶m³/s in the interior tropical Northwest Pacific Ocean. Analyses showed that errors of wind stress estimation could not explain all of the differences. The largest differences were found in the areas immediately north and south of the bifurcation latitude of the North Equatorial Current west of the dateline, and in the recirculation area of the Kuroshio and its extension, where nonlinear eddy activities were robust. Comparison of the geostrophic meridional transport and the wind-driven Sverdrup meridional transport in a high-resolution OFES simulation showed that nonlinear effects of the ocean circulation were the most likely reason for the differences. It is therefore suggested that the linear, steady wind-driven dynamics of the Sverdrup theory cannot completely explain the meridional transport of the interior circulation of the tropical Northwest Pacific Ocean.     

Sedimentary Changes of a Sand Layer in Liquefied Silts

A flume experiment was conducted to investigate the restratification of liquefied sediment strata under a wave load with the focus on the interbedded strata of coarse and fine sediments formed in estuarine and coastal areas. The aim of this research was to study the characteristics and processes of liquefied sediment strata in terms of wave-induced liquefaction. In the experiment, the bottom bed liquefied under the wave action and the liquefied soil moved in the same period with the overlying waves, and the track of the soil particles in the liquefied soil was an ellipse. The sand layer consisting of coarse particles in the upper part, settled into the lower silt layer. The sinking of coarse particles and upward migration of the fine particles of the lower layer induced by liquefied sediment fluctuations are the likely reasons for sedimentation of the sand layer in liquefied silt.     

CHARACTERISTICS OF THE OXYGEN REDUCTIONIN ATMOSPHERIC CORROSION

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Distribution of vertical turbulent mixing parameter caused by internal tidal waves and solitary waves in the South Yellow Sea

Many observations show that in the Yellow Sea internal tidal waves (ITWs) possess the remarkable characteristics of internal Kelvin wave, and in the South Yellow Sea (SYS) the nonlinear evolution of internal tidal waves is one of the mechanisms producing internal solitary waves (ISWs), which is different from the generation mechanism in the case where the semidiurnal tidal current flows over topographic drops. In this paper, the model of internal Kelvin wave with continuous stratification is given, and an elementary numerical study of nonlinear evolution of ITWs is made for the SYS, using the generalized KdV model (GKdV model for short) for a continuous stratified ocean, in which the different effects of background barotropic ebb and flood currents are considered. Moreover, the parameterization of vertical turbulent mixing caused by ITWs and ISWs in the SYS is studied, using a parameterization scheme which was applied to numerical experiments on the breaking of ISWs by Vlasenko and Hutter in 2002. It is found that the vertical turbulent mixing caused by internal waves is very strong within the upper layer with depth less than about 30m, and the vertical turbulent mixing caused by ISWs is stronger than that by ITWs.     

Bottom Currents Observed in and Around a Submarine Valley on the Continental Slope of the Northern South China Sea

Bottom currents at about 1000 m depth in and around a submarine valley on the continental slope of the northern South China Sea were studied by a 14-month long experiment from July 2013 to September 2014. The observations reveal that bottom currents are strongly influenced by the topography, being along valley axis or isobaths. Power density spectrum analysis shows that all the currents have significant peaks at diurnal and semi-diurnal frequencies. Diurnal energy is dominant at the open slope site, which is consistent with many previous studies. However, at the site inside the valley the semi-diurnal energy dominates, although the distance between the two sites of observation is quite small(11 km) compared to a typical horizontal first-mode internal tide wavelength(200 km). We found this phenomenon is caused by the focusing of internal waves of certain frequencies in the valley. The inertial peak is found only at the open slope site in the first deployment but missing at the inside valley site and the rest of the deployments. Monthly averaged residual currents reveal that the near-bottom currents on the slope flow southwestward throughout the year except in August and September, 2013, from which we speculate that this is a result of the interaction between a mesoscale eddy and the canyon/sag topography. Currents inside the valley within about 10 mab basically flow along slope and in the layers above the 10 mab the currents are northwestward, that is, from the deep ocean to the shelf. The monthly mean current vectors manifest an Ekman layer-like vertical structure at both sites, which rotate counter-clockwise looking from above.     

The effect of sloping bottom topography on the source-driven deep tropical circulation

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THE DYNAMIC EFFECTS OF A FINITE DEPTH AMBIENT FLUID ON BOTTOM EDDY

Scaling analysis shows that if o(ε~2, β_1ε, γε) ~o (δ), frontal geostrophic dynamics governs the behav-ior of an isolated bottom eddy in a finite depth ambient fluid; and that the ambient flow induced bybottom eddy migration satisfies quasi-geostrophic dynamics. This two layer model includes the impor-tant processes of advection of bottom eddy due to ambient flow, baroclinic instability, and form dragintroduced by Rossby waves. The numerical results show that the three processes enhance theinstability and alter the migration speed of the bottom eddy, and that the form drag induces asignificant meridional drift of the eddy.     

Wave-induced seepage and its possible contribution to the formation of pockmarks in the Huanghe (Yellow) River delta

Wave-induced seepage and its possible contribution to the formation of pockmarks in the Huanghe (Yellow) River delta were investigated experimentally and numerically. Laboratory experiments were carried out to explore the response of a layered silty seabed with various saturation conditions under cyclic wave loads, in which the pore pressure and seepage-related phenomena were particularly monitored. Numerical models to simulate wave-induced seepage in the seabed were presented and evaluated, then applied to the Huanghe River delta. The experimental results show that the excess pore pressure decreases more rapidly at the surface layer, while the seepage-related phenomena are more pronounced when large cyclic loads are applied and the underlying layer is less saturated. The proposed numerical models were verified by comparing with the experiments. The calculated seepage depth agreed well with the depth of the pockmarks in the Huanghe River delta. The experimental and numerical results and the existing insitu investigations indicate that the wave-induced seepage may be a direct cause of the pockmarks in the Huanghe River delta. Extreme storm waves and the dual-layered structure of hard surface layer and weak underlying layer are essential external and internal factors, respectively. Wave- or current-induced scour and transport are possible contributors to the reformation of pockmarks at a later stage.