Investigation of Internal Waves in a Basin with Parabolic Profile of the Bottom

Within the framework of the linear theory of long waves, we study baroclinic free waves in a bounded basin of variable depth without vertical walls. We consider the case of two-layer stratification. The profile of the bottom of the basin and the form of the interface vary according to the parabolic law. Under these conditions, for the first three modes, we obtain analytic expressions for the frequencies of free oscillations, wave velocities, and the profiles of the free surface and interface. We analyze the dependences of frequencies, wave amplitudes, and wave velocities on the parameters of stratification and geometric characteristics of the basin.     

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.     

Effect of the Geometric Characteristics of a Basin on the Space Structure of Forced Oscillations

By the method of mathematical simulation, we study the effect of changes in the width and depth of a ring-shaped basin with parabolic profile of the bottom on the space structure of waves generated by variations of atmospheric pressure periodic as a function of time. Our investigation is carried out under the assumptions of the linear theory of long waves with regard for the action of the Coriolis force. The structures of the profiles of liquid surface are compared for the cases of free and forced waves. We also establish the dependences of the period of atmospheric disturbances on the geometry of the basin for which the number of nodal points of the free-surface profile in the case of forced oscillations coincides with the number of nodal points of the profile of liquid surface in the case of free oscillations.     

Generation of long barotropic waves by moving baric disturbances in a system of basins connected by a channel

We consider long barotropic waves in a system of two rectangular basins connected by a channel in the case where waves are generated by the moving region of disturbances of atmospheric pressure passing above one of the basins. By using a numerical model, we compute the characteristics of the wave process for various values of the parameters of this system. The results of numerical calculations are compared with the corresponding characteristics obtained for the case of a closed basin. We also analyze the distinctive features of long-wave processes induced in the presence of the channel. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Topographically constrained deep-water flows in the Baltic Sea

Density-driven currents have a significant impact on the deep-water characteristics of the Baltic Sea since they account for the water exchange between the deeper parts of neighbouring basins. The essential quantitative problem is to determine the flow rates in relation to a set of external parameters such as the strait topography, the stratification, and the internal circulation of the upstream basin. Using hydraulic theory it is possible to accomplish this by analysing the dynamical constraints that limit the deep-water flux between adjacent basins. On the basis of these results, the deep-water flows through the Bornholm Channel and the Irbe Strait are compared.     

Surface manifestations of internal waves investigated by a subsurface buoyant jet: Part 2. Internal wave field

In a large test reservoir with artificial temperature stratification at the Institute of Applied Physics, Russian Academy of Sciences, a major simulation of internal wave actuation by buoyant turbulent jets generated by wastewater flows from underwater collector diffusers in conditions of temperature stratification with deep and shallow thermocline has been performed. Using a modification of the particle tracing velocimetry (PTV) method in the stratification mode with shallow thermocline, the velocities of currents generated by internal waves at the surface of the water area are measured. A theoretical model is developed describing the fields of internal waves in the presence of jet stream. Dispersion relations and structures of lower (first and second) modes of internal waves in the stratified basin for different rates of liquid outflow from the collector model are obtained. The experimentally measured field of isothermal shifts with respect to the system of characteristic modes of internal waves is decomposed. A mixed regime of internal wave actuation with the simultaneous existence of the first and second modes is observed. The characteristics of perturbations in the liquid column and on its surface are compared. This analysis allows us to prove that the velocity fields on the surface are indeed surface manifestations of internal waves.     

Thermohydrodynamics of the ocean generation of seiches by moving baric fronts in bounded basins

We consider a plane problem of barotropic seiches generated by a front of atmospheric pressure moving over a bounded basin. A system of nonlinear equations of long waves is solved by the finite-difference method with regard for the bottom friction and Earth's rotation. The numerical analyses are performed for two basins with distributions of depths typical of the Black Sea. It is shown that the passage of a baric front over the basin leads to the generation of lower seiches. The oscillations of level and the corresponding currents are especially intense in the shallow-water zones of the basins. The seiches become more intense as the velocity of transfer of the atmospheric front increases and the width of the front decreases. Earth's rotation leads to the generation of longshore currents and promotes the process of weakening of residual oscillations of the fluid following the passage of the front. The influence of nonlinearity on seiches is small for the analyzed basins. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 2, pp. 3–18, March–April, 2008.     

Baroclinic seiches in rotating basins of variable depth in the case of two-layer density stratification

We solve a plane problem of linear baroclinic seiches in closed rotating basins of variable depth with two-layer density stratification. In the long-wave approximation, we get a boundary-value problem for a system of ordinary differential equations and propose a numerical procedure for finding internal seiches. The analytic solutions of the problem are obtained for a basin of constant depth. The numerical analysis of seiches is performed for the distributions of depth corresponding to the zonal and meridional sections of the Black Sea and model basins including the cases of a shelf zone and an underwater ridge. It is shown that the baroclinic seiches become more intense in shallow-water regions and that the intense longshore currents caused by Earth’s rotation are formed in the shelf zones and over the underwater ridges.     

台风移行速度与登陆角度对风暴潮的影响:一个理想模型数值实验

The effects of hurricane forward speed(V) and approach angle(θ) on storm surge are important and a systematic investigation covering possible and continuous ranges of these parameters has not been done before. Here we present such a study with a numerical experiment using the Finite Volume Community Ocean Model(FVCOM).The hurricane track is simplified as a straight line, such that V and θ fully define the motion of the hurricane. The maximum surge is contributed by both free waves and a forced storm surge wave moving with the hurricane.Among the free waves, Kelvin-type waves can only propagate in the down-coast direction. Simulations show that those waves can only have a significant positive storm surge when the hurricane velocity has a down-coast component. The optimal values of V and θ that maximize the storm surge in an idealized semi-circular ocean basin are functions of the bathymetry. For a constant bathymetry, the maximum surge occurs when the hurricane approaches the coast from the normal direction when the free wave generation is minimal; for a stepped bathymetry, the maximum surge occurs at a certain acute approach angle which maximizes the duration of persistent wind forcing; a step-like bathymetry with a sloped shelf is similar to the stepped bathymetry, with the added possibility of landfall resonance when the free and forced waves are moving at about the same velocity. For other cases, the storm surge is smaller, given other parameters(hurricane size, maximum wind speed, etc.)unchanged.     

Generation of seiches by moving baric formations

We consider a plane problem of generation of barotropic seiches in the case of motion of a region of disturbances of atmospheric pressure over a bounded basin. The nonlinear system of equations of long waves with regard for the quadratic dependence of bottom friction is solved by the finite-difference method. The calculations are carried out for three basins of variable depth corresponding to rectangular sections of the Black Sea and Sea of Azov. It is shown that the passage of the baric anomaly over the basin is accompanied by the generation of the lowest seiches. The oscillations of fluid are especially intense in the shallow-water zones of the basins. Seiches exhibit a trend to intensification as the velocity of motion of the atmospheric disturbance increases. The dependence on the width of the baric anomaly is not monotonic. In the shelf zone, the amplitude of oscillations of the level can be several times higher that the pure hydrostatic response of the sea surface. In the analyzed basins, the influence of nonlinearity on the seiches is weak. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 6, pp. 3–15, November–December, 2007.     

沉积盆地分类及相关问题探讨

沉积盆地是沉积作用的主要场所和沉积物堆积的大型空间。沉积盆地分类的基础之一是其大地构造属性。商业性油气藏均发现于沉积盆地中,不同类型的沉积盆地具有不同的含油气性。沉积盆地分析以及分类涉及地球科学诸多学科,具有很强的综合性、理论性和实践性,关系到对盆地油气资源潜力的评价,日趋受到重视。     

南海罗斯贝变形半径的地理及季节变化

根据南海 1°× 1°网格的标准层季节平均温、盐度资料 ,在未引入Boussinesq近似条件下 ,采用改进的Thompson Haskell算法求解线性化斜压海洋水平大尺度波的垂直结构方程 (重力内波方程 ) ,从而得到了南海各网格点的第一斜压重力波相速度和相应的罗斯贝变形半径 ,并探讨其地理分布和季节变化特征 ,以期有助于南海环流和中尺度涡旋以及有关海洋侧边界效应的研究。     

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.     

Weakly non-linear free oscillations in a basin of variable depth

Weakly non-linear free oscillations in a basin of variable depth filled with non-viscous fluid are investigated in terms of the long waves theory using the perturbation technique. Solutions to the initial two approximations for the horizontal velocity component and free surface departure are numerically derived. An attempt is made to determine the area of applicability of the linear theory by applying a parabolic bottom profile to the basin.Translated by V. Puchkin.     

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.     

西地中海的弧后盆地

地中海是太平洋之外弧后盆地较为发育的海区。巴利阿里海盆和第勒尼安海盆是西地中海两个位置相邻、互有成因联系的弧后盆地。海盆莫霍面埋深分别为 1 2～ 1 5km和 1 0 km,热流密度分别为 1 0 0 m W/m2和 2 0 0 m W/m2 ,发育有大洋型磁条带异常 ,大洋钻探和拖网取样均采到了拉斑玄武岩。较之巴利阿里海盆 ,第勒尼安海盆更富年青性。两弧后盆地的成生演化是与欧洲板块与非洲 -阿普利亚板块的相互作用息息相关的。中新世 ,随着非洲 -阿普利亚板块向西、西北俯冲 ,科西嘉、撒丁裂离欧洲大陆 ,巴利阿里海盆被打开 ;上新世 ,阿普利亚微板块进一步俯冲 ,导致亚平宁与科西嘉、撒丁之间的裂离 ,形成第勒尼安海盆。     

Seiches in a circular basin of variable depth

Free waves (seiches) in a circular basin of variable depth are studied numerically within the framework of the linear theory of long waves taking into account the action of the Coriolis force. We determine the frequencies of axisymmetric and circular waves, study the structure of the modes of elevation of the free surface and wave velocities, and establish the dependences of the phase velocities of circular waves on the number of mode and wavelength. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Group bounded long waves in physical models

During the last few years it has been shown that the results of model tests of harbour basins and moored ships are highly dependent on the correct reproduction of wave groups and the attached long waves. Although these bounded long waves are of second order and thus of a rather limited height, resonance and shoaling effects can increase their influence on the results of model investigations. In traditional first order wave generation, the boundary conditions at the wave board are not fulfilled for the bounded long waves, and consequently various spurious, free long waves are unintentionally produced. This paper outlines the general equations and the solution for a rotating and translating wave board. The translatory case is treated in detail, i.e. a physical interpretation of all the second order terms is given, and an approximate control signal for the suppression of spurious long waves for practical use is described. Finally, laboratory experiments successfully verify the various long wave terms and the effectiveness of the suppression terms.     

Investigation of the Energy Balance in the Water–Air Boundary Layer under the Conditions of Developing Wind Waves

We present the results of the analysis of the energy balance in a wind–water system under the conditions of developing waves. Our investigation is based on the use of the experimental data obtained in a water channel and taken from the literature. We propose an expression for the energy balance between the air flow and wavy water surface based on the data of simultaneous measurements of the vertical wind profiles and drift currents and the parameters of waves for various fetches and indifferent density stratification.     

Laboratory research on effective test area of short-crested waves generated by two-sided segmented wavemakers

The size and shape of the effective test area are crucial to consider when short-crested waves are created by segmented wavemakers. The range of the effective test area of short-crested waves simulated by two-sided segmented wavemakers is analyzed in this paper. The experimental investigation on the wave field distribution of short-crested waves generated by two-sided segmented wavemakers is conducted by using an array of wave gauges. Wave spectra and directional spreading function are analyzed and the results show that when the main direction is at a certain angle with the normal line of wave generators, the wave field of 3D short-crested waves generated by two-sided segmented wavemakers has good spatial uniformity within the model test area. The effective test area can provide good wave environments for seakeeping model tests of various ocean engineering structures in the deep ocean engineering basin.