Effect of ice cover on oscillations of fluid in a closed basin

Within the framework of the linear theory of long waves, the problem of the effect of ice cover on seiche oscillations of fluid in a two-dimensional constant-depth basin is solved. The eigenfrequencies and eigenfunctions of seiche oscillations are obtained for different boundary conditions at ice edges: rigid coupling and free edges. The forced oscillations of fluid and ice under the action of a moving disturbance of atmospheric pressure are investigated. The change in the stress of ice bending is considered and it is shown that the coast ice can be broken.     

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.     

Nonlinear effects in the process of propagation of internal waves with regard for the turbulent viscosity and diffusion

By the method of asymptotic multiscale expansions in the Boussinesq approximation, we study nonlinear effects observed in the process of propagation of internal waves with regard for the turbulent viscosity and diffusion. We determine the decrement of attenuation of waves and the boundary-layer solutions at the bottom and on the free surface. The wave-induced mean current is found in the second order of smallness in the wave steepness. The coefficients of the nonlinear Schr?dinger equation are obtained for the envelope of the wave packet. It is shown that a weakly nonlinear plane wave is stable under longitudinal modulation in the long-wave limit. If the wavelength is smaller than a certain critical value, then the wave is unstable under modulation.     

Thermohydrodynamics of the ocean decay of nonlinear oscillations in a bounded basin of variable depth

We study the time decay of surges of a liquid in a round shallow-water basin of variable depth. The dependence of the logarithmic decrement of oscillations on the bottom topography and wind velocity is analyzed. The role of convective acceleration and bottom friction in the formation of both the level of vertical displacement of the surface of the basin and the velocity field of horizontal wave currents is estimated. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 2, pp. 3–11, March–April, 2006.     

Nonlinear inertial oscillations of a multilayer eddy: An analytical solution

Nonlinear axisymmetric oscillations of a warm baroclinic eddy are considered within the framework of an reduced-gravity model of the dynamics of a multilayer ocean. A class of exact analytical solutions describing pure inertial oscillations of an eddy formation is found. The thicknesses of layers in the eddy vary according to a quadratic law, and the horizontal projections of the velocity in the layers depend linearly on the radial coordinate. Owing to a complicated structure of the eddy, weak limitations on the vertical distribution of density, and an explicit form of the solution, the latter can be treated as a generalization of the exact analytical solutions of this form that were previously obtained for homogeneous and baroclinic eddies in the ocean.     

Transient fluid motion due to the forced horizontal oscillations of a vertical cylinder

The problem of the forced horizontal oscillations of a vertical cylinder extending throughout the fluid depth is considered on the basis of the linearised theory of water waves. A new integral form is given for the frequency-domain solution and the procedure is then used to obtain an explicit time-domain solution.     

Nonlinear adjustment of a heavy rotating fluid to equilibrium

We consider the problem of geostrophic adjustment of nonlinear axially symmetric formations in a two-layer fluid with infinitely deep lower layer and demonstrate the existence of a new integral of motion, which enables us to determine the final equilibrium state of perturbations without analyzing the transient (wave) stage of the process. It is shown that the final motions caused by initial perturbations of the opposite signs are not equivalent. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

On the influence of salinity exchange on the circulation of a fluid in an enclosed basin

The mechanism responsible for fluid circulation in an internal basin of the Black Sea type is studied using a two-dimensional model for convective currents generated by the inhomogeneous horizontal gradient of salinity exchange. Analytical investigations and calculations have shown that the generation of cyclonic motions occurs due to an imbalance of salt fluxes at the fluid lateral boundaries of the basin. Under the influence of salt fluxes from the straits and the fresh water from rivers, the circulation tends to become streamlike. At the site of reduced salinity, the stream narrows and becomes more intensive. Translated by V. Puchkin.     

The influence of the gulf’s geometry on seiche oscillations in an enclosed basin

The finite-elements technique is applied to study the effect of a basin’s geometry (bays, harbours) and location of the characteristics of seiche oscillations in the basin and in the gulf proper. An increase of the length of the bay is shown to contribute to the periods of natural oscillations and to cause their restructuring. Translated by Vladimir A. Puchkin.     

Nonlinear dynamics of a fluid-conveying pipe under the combined action of cross-flow and top-end excitations

We report a theoretical investigation of an elastic and slender fluid-conveying pipe with a top-end excitation subjected to uniform cross flows. Considering the mean drag force and the time varying vortex-induced lift force which is modeled using a nonlinear van der Pol oscillator, the nonlinear partial differential equations of the motion of coupled fluid-structure system are constructed and simplified to a reduced-order model through the Galerkin-type discretization. By virtue of quasi-static displacement conditions, the characteristics of vortex-induced vibration of the pipe are evaluated for the first two lock-in modes. The results show that the top-end excitation can increase the vibration amplitude of the pipe when the cross-flow speed is out of the lock-in regions. When the cross-flow speed is within the lock-in region, however, the top-end oscillation causes a transition between quasi-periodic and periodic in the responses of the pipe, significantly reducing or increasing the vibration amplitudes depending on the excitation acceleration and frequency. This finding has an important guidance in suppressing vortex-induced vibrations by balancing the internal fluid velocity and the top-end excitation.     

Verification of a parabolic equation for propagation of weakly-nonlinear waves

Verification tests of linear wave propagation models for cases of waves propagating through a refractive focus typically overpredict peak amplitudes in the vicinity of the focus. Using a parabolic equation model for the combined refraction-diffraction of weakly-nonlinear waves [valid for Ursell number U_r < O(1)], we show that, in a particular experiment, much of the discrepancy between laboratory measurements and linear wave model predictions can be accounted for by including the effect of nonlinearity, which is important in the region of the focus.     

Nonstationary dynamics of turbulent axisymmetric jets in a stratified fluid: Part 2. Mechanism of excitation of axisymmetric oscillations in a submerged jet

It was shown based on laboratory experiments in a Large Thermally Stratified Tank (LTST) at the Institute of Applied Physics of the Russian Academy of Sciences that a turbulent axisymmetric jet in a stratified fluid with a sharp density drop (a pycnocline) intensively generates internal waves. An axisymmetric oscillation mode, for which a sufficient condition of stability in the parallel flow approximation is met, served as their source. This paper studies the stability of a nonparallel flow (with self-similar velocity profiles) that simulates a jet flow in the lower part of the pycnocline with respect to the axisymmetric mode. The estimates of the axisymmetric mode near the pycnocline are in agreement with the experimental data. The signs of the self-oscillating mode of the jet were experimentally revealed and the possibility of self-oscillations was theoretically proved: it was shown that the flow in the pycnocline vicinity is absolutely unstable.     

Scattering of surface waves in a basin with a statistically uneven bottom

The propagation of surface waves over a statistically uneven bottom is considered on the basis of equations of the linear potential theory. The expression which emphasizes the dispersion influence is obtained for the spatial decrement of the average field. The north-east Pacific is considered as an example.Translated by Mikhail M. Trufanov.     

波浪与带窄缝多箱体作用共振现象的模拟研究

针对波浪与带有窄缝多箱体结构作用产生的流体共振问题,建立了基于域内源造波技术的二维非线性时域数值波浪水槽模型,其中自由水面满足完全非线性运动学和动力学边界条件,窄缝内流体引入人工阻尼来等效由于涡旋运动和流动分离引起的黏性耗散,计算域边界采用高阶边界元进行离散。通过模拟三箱体间两窄缝内相对波高变化,并与已发表的数值与实验结果对比,验证了本模型的准确性。同时通过大量的数值计算,分析了箱体数量对窄缝内水体共振频率、共振波高以及对结构反射波高和透射波高的影响。     

Ship waves in a continuously stratified basin with ice cover

Ship waves generated in an exponentially stratified fluid when an axisymmetrical area of pressure of constant intensity moves over a floating ice cover are studied in a linear statement. The influence of ice rigidity on the distribution of amplitudes of the internal wave disturbances along the constant phase lines is analysed.Translated by Mikhail M. Trufanov.     

Rational approximations in the parabolic equation method for water waves

Approximations based on minimax principles are developed in order to allow for large-angle propagation in the parabolic equation method. Numerical studies show that the minimax approximations do not cause any significant degradation of accuracy at small angles of incidence when compared with an existing model based on a (1,1) Padé approximant, and that they allow for much more successful treatment of large angles of incidence than is possible using the previously available methods.     

一类受持续扰动的非线性时滞系统的扰动抑制

研究一类受已知动态特性的外部扰动作用的非线性时滞系统的扰动抑制问题。基于内模原理构造能够抵消扰动影响的伺服补偿器,然后利用极大值原理及灵敏度法设计带有补偿器的最优控制律,使得系统在无扰动作用时以1种最优方式运行,而有扰动作用时,控制律能够消除扰动引起的稳态误差,实现无静差扰动抑制。最后,通过仿真算例验证提出算法的有效性。     

带乘性噪声的一类非线性系统的滤波算法

针对带乘性噪声的一类非线性系统,给出了1种带单重渐消因子的强跟踪状态滤波算法。该算法将非线性系统线性化后,采用了线性最小方差估计方法来进行状态估计,通过运用正交原理和引入渐消因子,使得滤波效果具有强跟踪的优良性能。该算法扩展了卡尔曼滤波在带乘性噪声非线性系统状态估计中的应用范围。仿真结果表明了该算法的有效性。     

Numerical experiment aimed at modeling the hydrophysical fields in the sea of Marmara with regard for Bosporus and Dardanelles

We performed a long-term prognostic experiment aimed at the investigation of the process of formation of the hydrodynamic structure of the Sea-of-Marmara waters with regard for the influence of Bosporus and Dardanelles. It is shown that the mutual adaptation of hydrophysical fields and their adjustment to the physical and geographical conditions of the sea proceed as a result of the action of rapid (tens of days) and slow (several tens of years) mechanisms of adaptation. An S-like jet current directed from Bosporus to Dardanelles was formed. Two stable anticyclonic formations are well visible in the central part of the sea. In deeper layer, an abyssal jet current was formed as a result of penetration of heavy Mediterranean waters. The established specific features of the circulation of waters in the Sea of Marmara are confirmed by the data of observations. We conclude that the principal features of the dynamics of waters in the Sea of Marmara are formed under the influence of two straits. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 3, pp. 28–41, May–June, 2007.