Three-dimensional numerical experiments on tidal exchange through a narrow strait in a homogeneous and a stratified sea

We have investigated the three-dimensional Lagrangian motion of water particles related with tidal exchange between two basins with a constant depth connected through a narrow strait and the effects of density stratification on the exchange processes by tracking a number of the labeled particles. Tide-induced transient eddies (TITEs), which are similar to those in two-dimensional basin, are generated behind the headlands. Upwelling appears around the center of the eddy and sinking around the boundary. When the basins are filled with homogeneous water, a pair of vortices are produced in the vertical cross section of the strait due to bottom stress, with upwellings along the side walls of the strait and sinking in the center of the strait. These circulations form the horizontally convergent field in the cross-strait direction in the upper layers while the horizontal divergence takes place in the bottom layer. These vertical water-motions produce the three-dimensional distribution of velocity shear and phase lag of the tidal current around the strait, and the Lagrangian drifts of water particles become large. As a result, water exchange through the strait is greatly enhanced: The water exchange rate reaches 94.1% which is much larger than that obtained in the vertically integrated two-dimensional model. When the basins are stratified, the stable stratification suppresses the vertical motion so that a pair of vertical vortices are confined in the lower layers. This leads to a decrease in the exchange rate, down to 88.6%. Our numerical results show that the three-dimensional structure of tidal currents should be taken into account in tidal exchange through a narrow strait.     

Lateral forces on ships in steady motion parallel to banks or beaches

A mathematical formulation for the motion of a slender ship in shallow water parallel to straight bottom contours is described. From this, a singular integral equation which determines the vorticity on the ship is derived, together with a numerical procedure for solving this integral equation. Particular attention is paid to the trailing edge of the ship, so that the correct solution of the integral equation is found. Numerical results for the cases of a bank or a uniformly sloping beach are provided. The effect of changing the water plane shape of ships is investigated, as well as the effects of changing the local water depth, distance to beach or bank, beach angle and yaw. General conclusions are drawn where possible and illustrate the properties of the bottom geometry.     

Wave-Current Propagation over a Frictional Topography

—In this paper the parabolic approximation model based on mild-slope equation is used tostudy wave propagation over a slowly varying and frictional topography under wave-current interaction.A governing equation considering the friction effects is derived by the authors for the first time.A simpli-fied form for the rate of wave energy dissipation is presented on the basis of the wave-current action conser-vation equation and the bottom friction model given by Yoo and O＇connor(1987).Examples reveal thatthe present computational method can be used for the calculation of wave elements for actual engineeringprojects with large water areas.     

An empirical time-depth model for calculating water depth,northwest Gulf of Mexico

The velocity of sound in water varies nonlinearly with depth in temperate and tropical ocean basins, limiting the accuracy of representing water velocity with a single average value. A seventh-order polynomial provides an empirical model for converting seismic travel time to water depth in the northwest Gulf of Mexico. This method works best for the continental slope where relief can vary markedly over salt structures, whereas application on the shelf is limited by local and seasonal variations in water velocity. Calculated depths may differ from those of other techniques because of difficulties interpreting competent water bottom.     

Rip current spacing

Mass, momentum and energy conservation laws, including the radiation stress, are used to derive an equation of the eigenvalues of rip current spacing.A coastal region with linear bottom slope is divided into two parts: Offshore region and surfzone separated by the breaker line. Wave set-up, wave energy and mean current are assumed to be composed of basic state, which is a function of the distance from the coast to offshore only, and of superposed two-dimensional perturbations.In the case of normal incidence of waves, basic steady current system vanishes and perturbations are found to be of cellular shape. According to the boundary conditions at the coast, stream function of perturbed motion in the surfzone can be represented by the confluent hypergeometric function, while in the offshore zone it is approximated by the modified Bessel function.Interpolation of the stream functions in the surf and offshore regions enables us to obtain a characteristic relation which gives the eigenvalues of nondimensional alongshore spacing of rip current system as a function of a parameter determined by the bottom friction coefficient, width of the surfzone and breaker height.     

Surface gravity wave interaction with elastic bottom

In the present paper, a hydroelastic model is developed to deal with surface gravity wave interaction with an elastic bed based on the small amplitude water wave theory and plate deflection in finite water depth. The elastic bottom bed is modelled as a thin elastic plate and is based on the Euler-Bernoulli beam equation. The wave characteristics in the presence of the elastic bed is analyzed in both the cases of deep and shallow water waves. Further, the linearized long wave equation is generalized to include bottom flexibility. A generalized expansion formula for the velocity potential is derived to deal with the boundary value problems associated with surface gravity waves having an elastic bed. The utility of the expansion formula is illustrated by demonstrating specific physical problems which will play significant role in the analysis of wave structure interaction problems. Behavior of the wave spectra are discussed in the case of closed basin having a free surface and an elastic bottom topography.     

The impact of salt water inflows on the distribution of polycyclic aromatic hydrocarbons in the deep water of the Baltic Sea

Salt-water inflows into the Baltic Sea are important events for renewing the deep and bottom waters of the deep basins of the Baltic Sea. These events occur only at irregular intervals. The last strong event was in January 1993 followed by minor inflows in winter 1993/1994. As a result of these inflows, the deep water of the central Baltic basins was completely renewed.Based on extensive observations of polycyclic aromatic hydrocarbons (PAHs) in water, fluffy layer material and surface sediments between 1992 and 1998, the transformation of PAHs and the modification of their distribution in the Baltic deep water is discussed in connection with the spreading of the inflowing highly saline and oxygen-rich water along its pathway from the sills into the central basins. In the course of the inflows in 1993/1994, the PAH concentration in the deep water of the different basins increased significantly. The concentrations were elevated, at least by a factor of 2 and as much as seven to eight times (for the four-ring PAHs) compared to the previous and the following years. Two hypotheses for the causes were discussed: the inflowing salt water may have entrained more highly polluted surface water in the western Baltic Sea, or it may have entrained contaminated fluffy layer material or sediment particles along the route of transport.     

Anoxic basins of the eastern Mediterranean: geological framework

A brief review of the geological knowledge on the anoxic basins of the eastern Mediterranean is presented. Anoxic basins have been discovered in two different geological settings in the eastern Mediterranean. Bannock Basin belongs to the compressional style of the Mediterranean Ridge, and Tyro and Poseidon Basins belong to the transcurrent tectonic style of the Strabo Trench. The origin of the basins is subsurface salt dissolution triggered by tectonic deformation of the sediments on the Mediterranean Ridge, and tectonic subsidence (pull-apart mechanism) in the Strabo Trench. The onset of a deep-sea brine lake is always related to the outcrop of Messinian salts on the side-walls of the basin. The rate of basin subsidence controls the evolution of the brine lakes, which can also be completely diluted by bottom water circulation.     

A short cut numerical method for determination of periods of free oscillations for basins with irregular geometry and bathymetry

A short cut numerical method for evaluation of the modes of free oscillations of the basins which have irregular geometry and bathymetry is presented in this paper. In the method, a single wave is inputted to the basin as an initial impulse. The respective agitation in the basin is computed by using the numerical method solving the nonlinear form of long wave equations. The time histories of water surface fluctuations at different locations due to propagation of the waves in relation to the initial impulse are stored and analyzed by the fast Fourier transform technique (FFT) and energy spectrum curves for each location are obtained. The frequencies of each mode of free oscillations are determined from the peaks of the spectrum curves. The method is tested by using regular shaped flat bottom basins with different depths. The computed periods of free oscillations are compared with the theoretical values. The accuracy and performance of the method are discussed. As a case study for the application to the basins of irregular shape and bathymetry, the periods of free oscillations of the sea of Marmara is determined and discussed.     

Predicting oxygen in small estuaries of the Baltic Sea: a comparative approach

Coastal eutrophication, manifested as hypoxia and anoxia, is a global problem. Only a few empirical models, however, exist to predict bottom oxygen concentration and percentage saturation from nutrient load or morphometry in coastal waters, which are successfully used to predict phytoplankton biomass both in lakes and in estuaries. Furthermore, hardly any empirical models exist to predict bottom oxygen from land-use. A data set was compiled for 19 estuaries in the northern Baltic Sea, which included oxygen concentration and percentage saturation, water chemistry, estuary morphometry, and land-use characteristics. In regression analyses, bottom oxygen was predicted both as a function of the percentage of watershed under agriculture and of mean depth. These models accounted for ca. 55% of the variation in oxygen. Additionally, oxygen was linked to fetch (diameter of the area in the direction of the prevailing wind), which accounted for 30% of the variation in oxygen. This suggests that shallow Finnish estuaries are wind-sensitive. In ‘pits’ (sub-thermocline waters of deep basins), near-bottom total nitrogen strongly correlated with oxygen percentage saturation (R²=0.81). Neither chlorophyll a, total phosphorus nor nutrient loading explained oxygen variation in entire estuaries or in ‘pits’, probably mainly due to annual sedimentation/sediment–water flux dynamics. On the basis of the results of cross-validation, the models have general applicability among Finnish estuaries.     

Yangtze Brackish water plume—circulation and diffusion

A system of 3-D linearized momentum equations, the continuity equation and a simplified equation of state for sea water are analytically solved. The solution comprises three parts. The first part is a wind-driven current, the second a jet-like current caused by Yangtze River outflow and the last a density flow. The computed current velocity is obtained by solving an advection-diffusion equation of salinity by a finite-difference method. The results show that the Yangtze brackish water plume spreads as a large low salinity tongue. At the surface, the turning of the tongue axis is mainly controlled by wind stress, Yangtze run-off and bottom topography. Near the bottom, the axis changes little all the year around. At about 10–15 m depth, there is a sharp halocline in summer, but at deeper layers the vertical distribution is almost always uniform. The computed salinity distribution agrees fairly well with the observed one.     

Analysis of some key parametrizations in a beach profile morphodynamical model

A numerical process-based model to forecast beach profile morphodynamics has been developed. In the present paper, an analysis of various modelling approaches and key parametrizations involved in the estimation of the wave-driven current and the suspended sediment concentration is carried out.Several resolution techniques for the 1DV horizontal (i.e., in the x-direction perpendicular to coastline) momentum equation governing the Mean Horizontal Velocity (MHV) are analysed. In the first kind of techniques, the mean horizontal velocity is computed from the momentum equation, whereas the Mean Water Level (MWL) is computed using a parametrization of the depth-averaged momentum equation. Two boundary or integral conditions are thus needed. In the second kind, both mean horizontal velocity and mean water level gradient in the x-direction are the unknowns of the momentum equation, thus, three boundary or integral conditions are needed. Various additional conditions are discussed. We show that using a technique of the first kind is equivalent to imposing the difference between the surface and the bottom shear stresses in the 1D vertical equation. Both techniques lead to results that are in good agreement with the Delta Flume experimental data, provided the Stokes drift flow discharge is imposed as an additional condition. The influence of the breaking roller model and of the turbulent viscosity parametrization are also analysed.Suspended sediment transport by the mean current and wave-induced bedload transport are taken into account in the sediment flux. Three turbulent diffusivity parametrizations are compared for suspended sediment concentration estimations. A linear profile for the turbulent diffusivity taking into account the wave bottom shear stress and the surface wave breaking turbulence production is shown to give the best results. Using experimental data, we put forward the poor estimation of the bottom sediment concentration given by the three implemented parametrizations. We thus propose a new parametrization relying on a Shields parameter based on the breaking roller induced surface shear stress. Using this new parametrization, the bottom profile used in the tests keeps its two bars which disappear otherwise. However, the morphodynamical model still overestimates the bars offshore motion, a bias already observed in other models.     

Observation of the bottom boundary layer off the Soya Warm Current

A mooring observation of current velocity, temperature and bottom pressure was carried out approximately 30 km off the coast of Monbetsu, between August 7 and September 2, 2005, to investigate the characteristics of bottom boundary layer (BBL) off the Soya Warm Current (SWC). We succeeded in measuring the Ekman veering and bottom Ekman transport in the BBL. On comparing the observed current velocity with that represented by the classical theoretical equation, the observed alongshore current velocity in BBL disagreed with that represented by the classical theoretical equation, but the cross-shore one agreed well. However after applying a linear extrapolation for the alongshore current velocity to estimate the alongshore geostrophic current velocity above the bottom, we could explain the alongshore current velocity by that represented in the classical theoretical equation. Consequently, our observations strongly support one of the proposed formation mechanisms of the cold-water belt observed off the SWC, that is, the convergence of bottom Ekman transport. The volume transport of vertical pumping velocity was estimated to be (0.12–0.25) Sv. In addition, the vertical profile of average temperature in all observation periods shows that slightly warmer water lies beneath the homogenous temperature layer, in the BBL. The result is considered to imply that the down-slope advection due to bottom Ekman transport supplies the SWC water in BBL and the eddy diffusivity of order of 10⁻³ m²s⁻¹ maintains the oceanic structure in the bottom mixed layer.     

Instability of Two Interacting Quasi-Monochromatic Waves in Shallow Water

The nonlinear interactions of waves with a double-peaked power spectrum have been studied in shallow water.The starting point is the prototypical equation for nonlinear unidirectional waves in shallow water,i.e.the Korteweg de Vries equation.By means of a multiple-scale technique two defocusing coupled Nonlinear Schrdinger equations are derived.It is found analytically that plane wave solutions of such a system are unstable for small perturbations,showing that the existence of a new energy exchange mechanism which can influence the behavior of ocean waves in shallow water.     

An analytical solution for the local suspended sediment concentration profile in tidal sea region

The time-averaged and oscillatory solutions of the one-dimensional vertical (1DV) advection–diffusion equation for the suspended sediment have been derived analytically in a tidal sea region of finite water depth. The basic equation assumes constant eddy diffusivity and settling velocity. No net flux condition is set at the sea surface, while a boundary condition with the erosion rate and depositional velocity is prescribed at the sea bottom. The time-averaged solution has been derived in a straightforward manner, while the advection–diffusion equation governing the oscillatory concentration has been first transformed to a simple diffusion equation and then solved using the Galerkin-eigenfunction method. The former is given in a closed form, while the latter is presented in a series solution.A set of calculations has been performed to examine the change in the vertical structure as well as magnitude of the concentration response function. A possible use of the solution to make an estimate of the erosion rate at the sea bottom based on the concentration information at the sea surface is discussed.     

Indication of bottom transport in shallow marine regions based on the data of satellite ocean color scanners

By example of a testing area in the northern Caspian Sea, a case study has been conducted to examine the feasibility of indication of near-bottom water transport from the data of ocean color scanners (OCS) for the basins whose bottom is shallower than the lower limit of the water-leaving radiance origination layer. The testing area has provided the desirable diversity of radiance origination conditions owing to an isolated underwater ridge. Based on the archived materials of the OCS SeaWiFS for 2000–2004, statistics of spectral normalized water-leaving radiances of the testing area have been computed. Hypothetically, the displacements of a radiance maximum in reference to the ridge were due to different mechanisms of interaction of water motions with bottom relief and bottom sediments. The correspondence between the patterns of radiance maximum displacements and the current notions of general water transport in the vicinity of the testing area has been established. Hopefully, the archived data of OCSs can be useful for revealing the patterns of seasonal and interannual variability of the near-bottom water transport at shallows with favorable bottom properties.     

Glacial morphology and post-glacial contourites in northern Prince Gustav Channel (NW Weddell Sea,Antarctica)

We present the results of a marine geophysical investigation of the northern Prince Gustav Channel. By comparative analysis of multibeam bathymetric data, single channel seismic reflection profiles, underway chirp sonar data, ADCP current data and sediment coring, we define the main morphological elements of the area. In particular we define the glacial morphogenesis in relation to the excavation of inner shelf basins and troughs along structural discontinuities and lithologic boundaries. We identify streamlined surfaces that testify to the grounding of ice and past ice flow directions. These glacial forms are found only on glacial tills preserved in the deepest part of the basins, while net erosion to bedrock has occurred elsewhere. Since the Last Glacial Maximum (LGM), the relict glacial morphology has been draped by hemipelagic and diatomaceous mud, and bottom currents have played a major role in focusing sedimentation within small depocentres, that we define as contouritic drifts. Based on shallow sediment architecture and supported by direct measurements, we propose that the direction of bottom water flow is from the outer shelf into the Prince Gustav channel as a result of a combination of tidal currents and ice shelf-related thermohaline circulation.     

Estimation of methane fluxes from bottom sediments of Lake Baikal

Methane bubble fluxes in gas flares from bottom sediments in Lake Baikal were estimated for the first time using hydroacoustic methods. Earlier work has demonstrated the occurrence of gas seeps both inside and outside of areas where bottom simulating reflectors were identified in seismic profiles. Fluxes ranged from 14 to 216 tons per year, with the flux for the entire area of the central and southern basins ranging from 1,400 to 2,800 tons per year. Comparison with other water bodies showed that fluxes from the most intensive Baikal flares were similar to those in the Norwegian and Okhotsk seas. Gas hydrates decompose at the lower boundary of the gas hydrate stability zone due to sedimentation. Calculation of the amount of methane produced due to sedimentation gave a total of between 2,600 and 14,000 tons per year for the central and southern basins of the lake. Based on rough estimation, the total flux from shallow- and deep-water gas seeps is similar to the amount of methane produced due to sedimentation. This suggests that gas hydrates possibly occupy much more than 10?% of the pore volume near the base of the gas hydrate stability zone, or that there are other reasons for gas hydrate dissociation and bubble flux from these bottom sediments.     

Surface perturbations generated by a stratified flow of finite depth over obstacles

We studied the structure of the surface perturbations generated by a stratified flow of an ideal fluid of finite depth around underwater obstacles. We consider a cylinder modeled by a point dipole localized near the density interface both above and below the interface. It is shown that density jumps characteristic of the marine medium significantly influence the formation and variability of the structure of the surface perturbations generated during a fluid??s flowing around an underwater obstacle. The results are compared with the data of the previous model calculations made by the authors for an infinite flow around an obstacle [4]. Significant differences between them are revealed, which should be taken into account in the solution of practical problems, for example, monitoring of coastal marine basins.