Model of the water exchange through the Bosphorus (a hydrodynamic estimate of blocking conditions for the Bosphorus undercurrent

A three-dimensional linear model of the stationary water circulation in the Bosphorus due to the river's outflow, density differences at the ends of the straits, and win is considered allowing for the earth's rotation and the bottom topography. The channel approximation and the method of the separation of variables are used to obtain the analytical solution of the problem. The solution obtained describes the main circulation elements which are know from observations. The influence of different parameters on the formation of vertical and horizontal structures of the velocity field is analysed.Blocking conditions for the Bosphorus undercurrent are estimated. Possible variations in the structure of flows in the straits related to the regulated outflow of the rivers of the Black Sea basin are discussed.Translated by Mikhail M. Trufanov.     

Numerical simulation of wave-induced laminar boundary layers

The three-dimensional numerical model with σ-coordinate transformation in the vertical direction is applied to the simulation of surface water waves and wave-induced laminar boundary layers. Unlike most of the previous investigations that solved the simplified one-dimensional boundary layer equation of motion and neglected the interaction between boundary layer and outside flow, the present model solves the full Navier–Stokes equations (NSE) in the entire domain from bottom to free surface. A non-uniform mesh system is used in the vertical direction to resolve the thin boundary layer. Linear wave, Stokes wave, cnoidal wave and solitary wave are considered. The numerical results are compared to analytical solutions and available experimental data. The numerical results agree favorably to all of the experimental data. It is found that the analytical solutions are accurate for both linear wave and Stokes wave but inadequate for cnoidal wave or solitary wave. The possible reason is that the existing analytical solutions for cnoidal and solitary waves adopt the first-order approximation for free stream velocity and thus overestimate the near bottom velocity. Besides velocity, the present model also provides accurate results for wave-induced bed shear stress.     

Zonally asymmetric response of the Japan Sea to synoptic pressure forcing

We investigated the sea level response of the Japan Sea to changes in atmospheric pressure using barotropic shallow water models driven by idealized synoptic pressure forcing. The regional response lags behind the synoptic pressure forcing because the adjustment is slowly established by water exchange through narrow, shallow straits. The sea level response of the realistic Japan Sea to the idealized forcing varies with geographical location and shows zonally asymmetric variations in amplitude and phase. The simulated response is in good agreement with the observed response of sea level recorded at Japanese coastal tide gauges. The results of a simple one-dimensional model indicate that the zonally asymmetric pattern, with an eastward-propagating pressure system, is essentially caused by bottom friction in shallow straits. This asymmetry arises if the typical wavelength of the synoptic pressure system is slightly larger than the spatial scale of the Japan Sea.     

修正型缓坡方程的有限元模型

与缓坡方程相比,修正型缓坡方程增加了地形曲率项和坡度平方项,从而提高了数值求解的复杂性。本文将计算域划分为内域和外域,内域为水深变化区域,使用修正型缓坡方程,其中的地形曲率项和坡度平方项可用有限单元各节点的水深信息和单元插值函数表示,外域为水深恒定区,速度势满足Helmholtz方程,通过内外域的边界匹配建立有限元方程,并用高斯消去法求解。进而分别模拟了波浪传过Homma岛和圆形浅滩的变形,其结果与相关的解析解和实验数据吻合良好,证明了本文有限元模型的正确性。同时,通过与实验数据的对比也明显看出,在地形坡度较陡的情况下,修正型缓坡方程较缓坡方程具有更高的计算精度。     

Influence of straits and bottom topography on the structure of barotropic currents in a flow-through basin

The development of currents and eddies in a basin of variable depth with two straits is studied within the framework of the nonlinear theory of long waves taking into account turbulent viscosity and the Coriolis parameter. The problem is solved numerically. We perform the comparative analysis of the results of modeling of currents in a homogeneous liquid. It is shown that these results depend on the location of the straits and bottom topography. Only jet currents are formed in basins of constant depth with symmetric straits. Eddy structures periodically appear in the presence of asymmetric straits.     

Linear wave reflection by trench with various shapes

Two types of analytical solutions for waves propagating over an asymmetric trench are derived. One is a long-wave solution and the other is a mild-slope solution, which is applicable to deeper water. The water depth inside the trench varies in proportion to a power of the distance from the center of the trench (which is the deepest water depth point and the origin of x-coordinate in this study). The mild-slope equation is transformed into a second-order ordinary differential equation with variable coefficients based on the longwave assumption [Hunt's, 1979. Direct solution of wave dispersion equation. Journal of Waterway, Port, Coast. and Ocean Engineering 105, 457–459] as approximate solution for wave dispersion. The analytical solutions are then obtained by using the power series technique. The analytical solutions are compared with the numerical solution of the hyperbolic mild-slope equations. After obtaining the analytical solutions under various conditions, the results are analyzed.     

Formation of sand banks due to tidal vortices around straits

Sand banks around straits are used as a commercial fishing ground. In order to clarify the mechanism of sand bank formation, the Lagrangian method was used to measure currents and turbidity around the banks in the Neko Seto Sea in the Seto Inland Sea of Japan. A neutrally buoyant float released in the Neko Seto Strait at the maximum tidal flow stage was engulfed in a pair of tidal vortices and moved around one of the sand banks. The vertical distribution of turbidity, which was measured by the vessel moving with the neutral float, showed an extremely high turbidity in the bottom layer of this bank area. According to the analysis of these observational data, the process of sand bank formation around straits is as follows. The tidal vortex transports water mass with suspended materials (including sand) which are whirled up at the bottom by the tidal jet. In the decaying stage of the vortex, the materials in the bottom layer are gathered in the central part of the vortex by the secondary convergent flow in the vortex. Among these materials, a large-size sand particle with a high critical erosion velocity accumulates at the bottom and forms banks. The distribution of bottom sediment and the thickness of alluvium support this result.     

Mechanism of currents through the straits of the Japan Sea: Mean state and seasonal variation

The mechanism governing the mean state and the seasonal variation of the transports through the straits of the Japan Sea is studied using a newly presented, simple analytical model and a basin scale general circulation model (GCM). The GCM reproduces the transports through the straits of the Japan Sea realistically owing to its fine horizontal resolution of about 20 km and realistic topography. A series of experiments conducted by changing surface forcing shows that the annual mean wind-driven circulation in the North Pacific Ocean is most responsible for the formation of the mean transports. It is also found that the seasonal variation of the alongshore component of monsoonal wind stress over the North Pacific basin, especially that over the Okhotsk Sea, is responsible for the seasonal variation of the transports. The simple analytical model can explain these simulated features very well. The physical concept of this model is based on the formation of the around-island circulation through the adjustment of coastally trapped waves and Rossby waves and geostrophic control at the narrow straits. It solves the sea surface heights (SSHs) at the edge of each strait and the transport through it. The value of the line integral of the SSH along the island is determined by the baroclinic Rossby waves approaching the island from the east and the alongshore wind stress around the island. The basin scale seasonal variation of SSH along the coast induced by the variation of the alongshore monsoonal wind stress can also be incorporated into this model by giving the SSH anomaly at the northeastern point of the Soya Strait. Thus, it is suggested that both the mean state and the seasonal variation are caused mainly by wind stress forcing. Minor modification by the seasonal heat flux forcing brings the amplitude and the phase of the seasonal variation closer to the observed values.     

A time‐split, forward‐backward numerical model for solving a nonhydrostatic and compressible system of equations

In this paper, we present a numerical procedure for solving a 2‐dimensional, compressible, and nonhydrostatic system of equations. A forward‐backward integration scheme is applied to treat high‐frequency and internal gravity waves explicitly. The numerical procedure is shown to be neutral in time as long as a Courant–Friedrichs–Lewy criterion is met. Compared to the leap‐frog‐scheme most models use, this method involves only two time steps, which requires less memory and is also free from unstable computational modes. Hence, a time‐filter is not needed. Advection and diffusion terms are calculated with a time step longer than sound‐wave related terms, so that extensive computer time can be saved. In addition, a new numerical procedure for the free‐slip bottom boundary condition is developed to avoid using inaccurate one‐sided finite difference of pressure in the surface horizontal momentum equation when the terrain effect is considered. We have demonstrated the accuracy and stability of this new model in both linear and nonlinear situations. In linear mountain wave simulations, the model results match the corresponding analytical solution very closely for all three cases presented in this paper. The analytical streamlines for uniform flow over a narrow mountain range were obtained through numerical integration of Queney's mathematical solution. It was found Queney's original diagram is not very accurate. The diagram had to be redrawn before it was used to verify our model results. For nonlinear tests, we simulated the famous 1972 Boulder windstorm and a bubble convection in an isentropic enviroment. Although there are no analytical solutions for the two nonlinear tests, the model results are shown to be very robust in terms of spatial resolution, lateral boundary conditions, and the use of the time-split scheme.     

台湾海峡台风暴潮非线性数值计算

台湾海峡平均水深不大于50米,台风侵袭频繁.由于台湾岛的“墙壁效应”和台湾海峡的“狭管效应”的影响,台湾海峡的台风暴潮显得较为独特.以前,我们及其他兄弟单位对福建沿海台风暴潮的研究,大多数仅局限于单站的气-水动力相互作用的研究,很少涉及整个海峡.虽说我们也曾作过福建沿岸台风暴潮现场调查,但进行次数有限,了解的也仅是海峡西岸局部地区的情况,它仅能反映台湾海峡台风暴潮的一个侧面,而无法了解整个海峡地区的风暴潮全貌.     

A note on the accuracy of the mild-slope equation

The mild-slope equation is a vertically integrated refraction-diffraction equation, used to predict wave propagation in a region with uneven bottom. As its name indicates, it is based on the assumption of a mild bottom slope. The purpose of this paper is to examine the accuracy of this equation as a function of the bottom slope. To this end a number of numerical experiments is carried out comparing solutions of the three-dimensional wave equation with solutions of the mild-slope equation.For waves propagating parallel to the depth contours it turns out that the mild-slope equation produces accurate results even if the bottom slope is of order 1. For waves propagating normal to the depth contours the mild-slope equation is less accurate. The equation can be used for a bottom inclination up to 1:3.     

Flow resistance in the Great Belt,the biggest strait between the North Sea and the Baltic Sea

The Danish Straits are part of the transition area between the North Sea and the central Baltic Sea. More precisely, the Danish Straits connect Kattegat to the Arkona Basin and includes the relatively narrow and shallow sub-areas: Great Belt, Little Belt, Fehmarn Belt and Sound. The flow resistances in the straits are hydraulically determined by among other factors, the contractions, sills and stratification found in the straits. Close to the entrance to the Arkona Basin the Darss and Drogden Sills are located that trap inflowing dense water partially before it enters the central Baltic Sea. Hence, the resistances in the Danish Straits are of crucial importance for the stratification and ecosystems in the central Baltic Sea. The present work comprises calculations of flow resistance in the Great Belt based on measurements collected as part of the Great Belt Fixed Link investigations. The specific resistance in the Great Belt is determined to be an average of 41.2 × 10⁻¹² s² m⁻⁵, but it depends heavily on the interface position. When calculating long-term discharge time-series on the basis of the momentum equation it is advised to apply a seasonal varying resistance.     

带有侧摩擦和底摩擦的绕岛理论

绕岛理论来自于Sverdrup理论,被广泛用于估计和分析通过岛屿之间海峡的输运情况。以往的研究得到了带有侧摩擦或底摩擦的单岛理论或多岛理论。本文在线性情况下考虑了风驱动环流下的解析模型。在同时考虑侧摩擦和底摩擦的情况下,推导出了岛屿周围输运流函数的解析解,并给出了通过岛屿之间通道的流量输运。其结果与Wajsowicz相似,但摩擦常数表示不同的值。从解析解上看,摩擦常数与侧摩擦和底摩擦之间的关系比较复杂,为了推导出它们之间的相互作用原理,本文在正压β平面上随机选取了一些侧摩擦和底摩擦的值。结果表明,在构成摩擦常数方面,侧摩擦和底摩擦近似呈线性关系。我们研究了宽度对通道输运值的影响,结果表明摩擦在一定宽度内提高了流量,这种现象和只考虑侧摩擦时比较相似。本文也比较了在不同深度下的流量,发现当水平涡粘性系数和底部拖曳系数固定时,水深越大,输运减少率越小。为了进一步揭示侧摩擦和底摩擦耗散的联合作用,在两个岛屿的情况下,本文在不同宽度的通道中与Wajsowicz的只考虑底摩擦或侧摩擦的模型进行了比较。结果表明,当通道比较窄,尤其是在小于Munk边界层厚度时,侧摩擦的作用大于底摩擦。当通道宽度远大于Munk边界层厚度时,底摩擦的作用大于侧摩擦。将模型应用到印尼贯穿流,得到大约20%的输运减少量。     

Transport properties of entrained topographic waves during their interaction with turbulence

In the Boussinesq approximation, topographic waves entrained by a sloping bottom are considered with allowance for turbulent viscosity and diffusion. The mean flows induced by a wave through nonlinearity are determined. The turbulent exchange coefficients are expressed in terms of the density of turbulent energy by using the relations of the semiempirical theory of turbulence. The equation for boundary-layer wave solutions and the equation of turbulent energy balance are solved jointly, which makes it possible to determine the vertical distribution of the density of turbulent energy in the area of the given wave. In the diffusion approximation, the vertical distribution of the concentration of wave-suspended sediments is obtained for the case when the tangential bottom stress exceeds the critical values corresponding to the start of sediment motion.     

The effect of cyclone-anticyclone asymmetry at small Rossby numbers

Cyclone-anticyclone asymmetry in a rotating fluid results in vortices with cyclonic rotation being attenuated more rapidly than vortices with anticyclonic rotation due to the Ekman bottom friction. To explain this effect, some authors invoked rather complex integral (averaged along the vertical) models with the parametrization of nonlinear friction. A simple analytical model, free of the procedure of formal averaging and based on a separate consideration of the equations for external flow in the nonviscous region and internal flow in the boundary layer, is investigated in this work. The corresponding equations are written in the so-called geostrophic momentum approximation, which makes it possible to take into account the nonlinear advective mass transport in the boundary layer at small Rossby numbers. The nonlinear equation of the hyperbolic type for the tangential velocity, which describes the process of attenuation of an axisymmetric vortex, is obtained from the condition of total mass conservation. Based on the solutions to this equation, it was shown that distinctions in the character of vortex attenuation are caused by deviations from the geostrophic regime in the nonviscous region. It was established that the concentration (compression) of anticyclonic vortices and the extension of cyclonic ones take place in the process of attenuation.     

On nonlinear planetary waves: A class of solutions missed by the traditional quasi-geostrophic approximation

Weakly nonlinear quasi-geostrophic planetary waves on a beta-plane and topographic waves over a linearly inclined bottom are examined by use of shallow water equations for a small beta parameter. Long solitary wave solutions missed by the use of the traditional quasi-geostrophic approximation are found in a channel ocean with neither a sheared current nor a curved (non-linearly inclined) bottom topography. The solutions are missed in the traditional approach because the irrotational motion associated with the geostrophic divergence is neglected by the quasi-geostrophic approximation. Another example which calls attention to the limitation of the traditional quasi-geostrophic approximation is the nonlinear evolution of divergent planetary eddies whose scale is much larger than the Rossby's radius of deformation. Some aspects of a new evolution equation are briefly discussed.     

舟山群岛峡道底部高程及其冲刷对浙闽沿海泥沙供给的影响

根据舟山群岛峡道地区的钻孔资料，在有孔虫、花粉和沉积特性分析结果的基础上，分析了晚更新世海面变化，探讨了晚更新世末期峡道内的地面高程，进而根据海图量算结果，讨论了舟山群岛峡道底部的泥沙冲淤及其对浙闽沿海泥沙供给的影响。本文认为，晚更新世以来舟山群岛地区发生了三次海进海退，其中晚更新世末期低海面时，舟山群岛峡道高程约位于吴淞基面以下３８ｍ左右，全新世海侵以来，受峡道水动力的作用，除部分峡道内海湾发生淤积外，舟山群岛峡道底部发生了明显的冲刷，其最大冲刷厚度可达８０ｍ左右，为杭州湾乃至整个浙闽沿海提供了大量的泥沙     

Suspended-sediment concentration and mineralogy in the central and western Mediterranean and mineralogic comparison with bottom sediment

Concentrations and mineralogy of suspensates in the central and western Mediterranean are vertically and laterally variable. This variability is related to input by resuspension of bottom sediments and from local terrigenous sources. Bottom currents flowing through constrictions at the straits of Sicily and Gibraltar and the eastern entrance of the Alboran Sea resuspend bottom sediments, giving rise to increased concentrations of suspensates in near-bottom waters and limited inputs to higher levels. There is no evidence of a suspensate-rich bottom water in the Balearic Sea.Terrigenous sources are believed to be the cause of increasing relative amounts of montmorillonite in surface waters as they flow eastward within the Mediterranean. Montmorillomite is relatively more important in suspended sediments than in bottom sediments where kaolinite—chlorite is dominant.     

Scenarios of tsunami amplitudes in the north eastern coast of Sea of Marmara generated by submarine mass failure

In this paper the tsunamis resulting from a submarine mass failure such as slides and slumps triggered by earthquakes or other environmental effects, which is settled at the bottom of the north eastern Sea of Marmara are examined in one sample region. As the solution method, one hybrid method is developed. The main objective of this method is to combine an analytical solution presenting near-field tsunami amplitudes above the submarine mass failure with a numerical solution indicating the tsunami amplitudes in the coastal regions. For this purpose, one common linear boundary between analytical and numerical solution domains is defined. Movements of Submarine Mass Failures (SMF) are modeled using one simple kinematics source model and the amplitudes of the tsunamis at the region that are closer to the landslide are computed by using the analytical method. SMF is modeled approximately from the bottom geometry, and an average depth is used. Scenarios of SMF are established depending on the velocities and thicknesses of the failure, and near-field tsunami amplitudes are obtained in the open sea during the source time. After the source times, the solutions are found in the numerical region using TELEMAC-2D software system with the mentioned boundary above. In this boundary, the output of the analytical solutions is taken as the boundary conditions or the disturbances for the numerical method. With these disturbances, the numerical method is performed and the amplitudes are calculated in the coastal area. The generation, propagation and coastal amplifications of the tsunamis are illustrated at some certain points and regions both in the open sea and near the coast line. The results have been visualized and discussed.     

The role of tidal vortices in material transport around straits

The strong tidal current (tidal jet) in straits generates tidal vortices with a scale of several kilometers. The role of the vortices in material transport was investigated in the Neko Seto Sea, located in the western part of the Seto Inland Sea of Japan. A clockwise vortex with a diameter of about 0.8 km was observed in Nigata Bay (lying between two straits, the Neko Seto Strait and the Meneko Seto Strait). It was concluded that the clockwise vortex was the tidal vortex which was generated by the tidal jet in the Meneko Seto Strait. The vortex moved into the bay with the tide, but tended to stay on the sand bank in the bay. It was confirmed by current measurement with an ADCP and turbidity measurement that the secondary convergent flow was generated in the bottom layer of the vortex. This secondary flow seemed to contribute to the formation of the sand bank. It was suggested that tidal vortices may play an important role in the sediment transport and formation of topography in and around straits.