Weakly non-linear waves forced by atmospheric disturbances in a confined basin of variable depth

Forced weakly non-linear oscillations of a homogeneous non-viscous fluid in a confined basin of variable depth are considered in a long-wave approximation. Fluid oscillations are caused by time-periodic fluctuations of the atmospheric pressure, whose spatial distribution corresponds to the first mode of free linear waves.Translated by V. Puchkin.     

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.     

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     

Tidal oscillation of water in a rotating rectangular basin of variable depth

The free oscillation of water in a rotating rectangular basin of variable depth is discussed. The depth is assumed to decrease from the center to the edges according to a paraboloidal law. The solution is obtained in terms of double series of zonal harmonics. Numerical solutions were worked out. Complete sets of modes will be evaluated by an electronic computer.     

Numerical simulation of currents in a basin of variable depth with two straits

Within the framework of the linear theory of long waves, with regard for the turbulent viscosity, we study the development of tidal currents in a basin of variable depth with two straits. The problem is solved numerically. The velocity field on the strait-basin boundary is regarded as known. The numerical analysis is performed for different depths of the straits. We study the influence of the geometric characteristics of the basin on the amplitudes of the profile of free surface and wave velocity and establish the dependences of the wave characteristics on the period of current velocities in the strait and the parameters of the basin. In particular, it is shown that the increase in the period of current velocities in the strait leads to significant changes in the level and structure of currents. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 4, pp. 3–12, July–August, 2007.     

Polynomial approximations of Berkhoff's model for waves in a basin of variable depth

On the basis of the polynomial approximation of the dispersion relation for gravity waves, a generalized version of Berkhoff's model for a non-stationary case has been obtained. The standard problem of the transition of a wave from deep water into shallow water in a basin with a slowly varying topography is applied to study analytically Berkhoff's model polynomial approximations. It has been demonstrated that all qualitative characteristics of wave transformation can be described in the framework of this model.Translated by V. Puchkin.     

Evolution of waves induced by periodic variations of pressure in a bounded basin of variable depth

Within the framework of the linear theory of long waves, we study the evolution of a wave process caused by the action of surface pressure periodically varying in time in a bounded basin of variable depth without vertical walls. We assume that the basin is filled with a homogeneous liquid nonperturbed at the initial time and take into account the action of dissipative forces. We obtain the analytic solution of the posed problem. It is used to perform the detailed analysis of the influence of the dissipative forces and the frequency of perturbing pressure on the characteristics of the process of evolution of waves. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

The generation of waves in a two-dimensional basin of variable depth by periodic atmospheric pressure disturbances

An analytical solution to the problem of the generation of long waves by periodic surface pressures in a confined basin has been derived in the framework of linear theory. If the change in the basin depth follows a paraboloidal law, being reduced to zero at the borders, the surface pressure amplitude is a power function of the space coordinate; dissipation and the Coriolis force are considered. Resonance frequencies have been determined, and the effect of forces upon the wave amplitude in the resonance domain has been investigated. Translated by Vladimir A. Puchkin.     

波浪在浅水传播中的弱非线性效应

在波浪从深水向浅水传播过程中,考虑弱非线性效应具有重要的实用价值,因此得到广泛的讨论和研究。本文根据文献「６」导出的考虑能耗的定常缓坡方程,结合文献「５」给出的显式非线弥散关系,得出了含弱非线性效应的缓坡方程,用该方程对浅水中波浪的传播 计算,将计算结果和试验数据进行了比较,结果表明,含弱非线性效应的缓坡方程可以用于讨论浅水中波浪传播的弱非线性效应,所得计算计算结果与试验结果更为吻合。     

Investigation of the space structure of the free-surface profile of forced circular waves in a bounded basin of variable depth

We perform the numerical analysis of the influence of variations of the geometric characteristics of an annular basin of variable depth on the space structure of wave motions generated by the oscillations of atmospheric pressure periodic as functions of time. Within the framework of the linear theory of long waves, we determine (with regard for the action of the Coriolis force) the ranges of periods inside which the free surface of liquid has a fixed number of nodes. The dependence of these ranges on the parameters of the basin is established and the shapes of the free-surface profiles are compared for circular and axisymmetric waves.Translated from Morskoi Gidrofizicheskii Zhurnal, No. 5, pp. 14–23, September–October, 2004.This revised version was published online in May 2005 with corrections to cover date.     

Generation of long waves in a basin of variable depth in the process of formation of a region of perturbations of atmospheric pressure

We perform the numerical analysis of the long-wave response of the free surface of a fluid in a basin of variable depth to the formation of an anomaly of the baric field for a finite period of time. In numerical experiments, we use the distribution of depths typical of the south coast of the Crimea. We also study the dependence of the dynamics of the sea level in the zone of the baric anomaly and in the shelf zone on the space and time scales of local changes in the field of atmospheric pressure in the open part of the basin. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Effects of depth discontinuity on harbor oscillations

The effects of water depth discontinuity near the harbor mouth on harbor oscillations are examined. Linear long-wave equations are used as the basis of the present study. For simplicity, only the normal incident waves are considered. Assuming that the harbor mouth is small in comparison with wavelength, the method of matched asymptotic expansion is employed to obtain the ocean impedance and the harbor responses. It is found that the incident waves can be trapped over the depth discontinuity which causes large oscillations near the harbor mouth. The radiation damping also decreases because of the appearance of the depth discontinuity, which leads to large amplifications at the lowest mode.     

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.     

Long non-linear waves in a confined basin, induced by transient atmospheric disturbances

In the non-linear statement, the paper studies long waves induced in a confined basin of variable depth by a low atmospheric pressure area, translating at constant speed over the basin. The study is conducted in terms of a non-stationary finite-difference model. Emphasis is made on the behaviour of the wave process after the departure of the disturbance. The dependence of the modal composition of fluid oscillations on the basin parameters and baric disturbances is determined. Translated by Vladimir A. Puchkin.     

Note on the propagation of a shallow water wave in water of variable depth

In this technical note, the phenomena of non-linear water-wave propagation above a seabed with variable depth is re-examined. The conventional Korteweg-de Vries (KdV) equation is re-derived for the general case of variable water depth. In the new form of KdV equation, the seabed bottom function is included. Two different bottom profiles are considered in this study; case 1: $b^{\prime }\left(x^{\prime }\right)=c\epsilon \sin \lambda x^{\prime }$ and case 2: $b^{\prime }\left(x^{\prime }\right)=c\epsilon {\mathrm{e}}^{-\lambda {\left(x^{\prime }-x_0^{\prime }\right)}^2}$. The effects of three bottom profile parameters, c, λ and ε on the wave profile are examined. Numerical results indicate that both ε and λ affect the wave profile significantly in case 1, while ε significantly affects the wave profile in case 2.     

A new approximation for ocean waves propagating over a beach with variable depth

In this paper, the phenomenon of ocean waves propagating over a beach with variable water depth is re-examined. Based on the assumption of shallow water, a linearised shallow water equation is solved with an arbitrary beach profile. These irregular beach profiles form a set of partial differential equation with variable coefficient as the governing equation, which is the main obstacle in obtaining analytical solutions. In this paper, two families of beach profile are used as examples. A parametric study is conducted to investigate the influence of the beach profiles on the water surface elevation (η) and velocities (u).     

Adaptive depth controller design for a submerged body moving near free surface

A submerged body that moves near a free surface needs to keep its attitude and position to accomplish its missions, which are required to validate the performance of a designed controller before sea trial. Hydrodynamic maneuvering coefficients are generally obtained by experiments or computational fluid dynamics, but these coefficients suffer from uncertainty. Environmental loads such as wave excitation, current, and suction forces act on the submerged body when it moves near the free surface. Therefore, a controller for the submerged body should be robust to parameter uncertainty and environmental loads. In this paper, six-degree-of-freedom equations of motion for the submerged body are constructed. An adaptive control method based on the neural network and proportional–integral–derivative controller is used for the depth controller. Simulations are performed under various depth and environmental conditions, and the results show the effectiveness of the designed controller.