Forced Waves in a Bounded Basin with Two Pycnoclines

The behavior of waves induced in a continuously stratified fluid with two pycnoclines by periodic variations of pressure on the free surface is studied within the framework of the linear theory by taking into account the action of the Coriolis force. The fluid fills a bounded basin of constant depth. We establish the dependences of the amplitudes and velocities of waves on the period of disturbing pressure. The process of transition of generated waves from the barotropic character of propagation to baroclinic with changes in the period of disturbing pressure is studied in detail.     

Forced Waves in a Bounded Basin with One Thermocline

Within the framework of the linear theory taking into account the action of the Coriolis force, we study waves induced in a continuously stratified fluid with one thermocline by periodic variations of pressure on the free surface. The fluid fills a bounded basin of constant depth. We establish the dependences of the wave amplitudes and wave velocities on the period of disturbing pressure. The sequence of transformations of generated waves from the barotropic character of motion to baroclinic depending on changes in the period of disturbing pressure is studied in detail.     

Forced Oscillations in a Bounded Basin of Variable Depth

We study forced long-wave oscillations of a liquid in a ring-shaped basin of variable depth within the framework of the linear theory of long waves with regard for the influence of the Coriolis force. The oscillations are induced by disturbances of atmospheric pressure periodic as functions of time. The parameters of the basin (bottom topography and linear sizes) are chosen to approximate the Antarctic region located between 60 and 70°S. The wave velocities and the structure of the modes of elevations of the free surface are determined by using numerical methods. We also establish the dependences of the characteristics of the wave process on the period of surface pressure.     

Nonlinear Surface Waves in a Basin with Floating Broken Ice

The method of multiple scales is used to deduce equations for three nonlinear approximations of a wave disturbance in a basin of constant depth covered with broken ice. In deducing these equations, we take into account the space and time variability of the wave profile in the expression for the velocity potential on the basin surface. These equations are used to construct uniformly suitable asymptotic expansions up to quantities of the third order of smallness for the liquid-velocity potential and elevations of the basin surface formed by a periodic running wave of finite amplitude. We analyze the dependence of the amplitude-phase characteristics of elevations of the basin surface on the thickness of ice, nonlinearity of its vertical acceleration, and the amplitude and wavelength of the fundamental harmonic.     

Influence of Nonlinear Interaction on the Evolution of Waves in a Shallow Basin

Izvestiya, Atmospheric and Oceanic Physics - The influence of nonlinear interaction of oppositely directed nonlinear waves in a shallow basin is studied theoretically and numerically within the...     

Nonlinear Capillary-Gravity Waves Produced by a Vertically Oscillating Plate

The nonlinear capillary-gravity wave produced by a vertically oscillating plate,in which thecontact-angle model is considered,is studied by use of the Boundary Integral Equation Method(BIEM).The present numerical experiment shows that the code is robust and efficient for modeling the generationand propagation of capillary-gravity waves.It is found that the wave heights of stationary periodicnonlinear waves radiated away from the plate are dependent on the parameters involved in the contact-an-gle model.The effect of the contact-angle hysteresis and the nonlinearity of capillary-gravity waves on thewave profile is discussed in the paper.     

Interaction of Surface Waves in a Basin with Floating Broken Ice

The multiscale method is used to obtain asymptotic expansions up to the quantities of the third order for the elevations of the surface of the basin and the velocity potential of motion of liquid particles in the wave disturbances formed in the process of nonlinear interaction of periodic running waves of the first and second harmonics in a homogeneous ideal incompressible liquid of constant finite depth covered with broken ice. The dependences of the amplitude-phase structure of disturbances on the ice thickness, depth of the basin, and the parameters of interacting harmonics are investigated. We estimate the error of evaluation of the characteristics of the formed vertical displacement of the surface of the basin and nonlinear mass transfer introduced by neglecting the curvature of the wave profile in the expression for the velocity potential in deducing the kinematic and dynamic surface boundary conditions for nonlinear approximations.     

Nonlinear Gravitational Waves and Atmospheric Instability

Izvestiya, Atmospheric and Oceanic Physics - This is an outline of the main results of the study of dust devils (a type of atmospheric vortices) with a focus on the mechanism of vortex generation...     

完全非线性孤立波的稳态解

报道了应用边界积分方法模拟完全非线性孤立波的传播,给急剧记解的波形,流束和数值计算结果。结果表明,本模型对计算孤立波的传播是有铲的。当ａ／ｈ〉０．３时,自由液面上的水平流速、底部流速和垂向平均流速之间的差别是明显的。三阶Ｂｏｕｓｓｉｎｅｓｑ方程的孤立波解比低阶方程的孤立波解更接近本文完全非线性的数值解。     

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.     

Nonlinear Model of Mean Free Surface of Waves

-A nonlinear model of mean free surface of waves or wave set-up is presented.The model isbased on that of Roelvink(1993),but the numerical techniques used in the solution are based on theWeighted-Average Flux(WAF)method(Watson et al,1992),with Time-Operator-Splitting(TOS)usedfor the treatment of the source terms.This method allows a small number of computational points to beused,and is particularly efficient in modeling wave set-up.The short wave(or primary wave)energy equa-tion is solved by use of a more traditional Lax-Wendroff technique.A nonlinear wave theory(James,1974)is introduced.The model described in this paper is found to be satisfactory in most respects whencompared with the measurements conducted by Stive(1983)except in modeling the mean free surface veryclose to the mean shoreline.     

A Model for Nonlinear Irregular Waves in Coastal Area

Based on the refraction-diffraction theory of irregular waves in the waters of slowly-varying cur-rents and depths,and the generation dissipation theory of wind wave,a model for nonlinear irregular wavesin coastal area is developed.In light of the specific conditions of coastal wave character and engineering ap-plication,a practical mathematical model for the nonlinear irregular waves is presented.with directional spec-trum in coastal area.Coast effect,refraction,whitecapping.bottom friction.current,wind and nonlinearaction are considered in this model.The numerical methods and schemes for wave refraction ray,energy con-servation of propagation,energy balance of the generation and dissipation of wind waves have been studied.Finally,the model is used for the directional wave spectrum computation in the Daya Bay.Compared withthe measured data with 956 wave bouys in the Daya Bay,the model results are in good agreement with themeasured results.     

水槽中浅水非线性长波传播的 Boussinesq 数值模拟

浅水非线性长波传播变形中会产生波-波相互作用,为较好地模拟这种现象,在非交错网格下建立了近似在阶完全非线性的高阶 Boussinesq 数值模型.数值模型中采用了混合 4 阶 Adams- Bashforth -Moulton 格式和内部造波技术.数值计算了非线性长波在波浪水槽中的传播变形,计算结果与相关实验数据吻合较好,验证了该数值模型实用性.     

Nonlinear Dynamic Behaviors of A Floating Structure in Focused Waves

Floating structures are commonly seen in coastal and offshore engineering. They are often subjected to extreme waves and, therefore, their nonlinear dynamic behaviors are of great concern. In this paper, an in-house CFD code is developed to investigate the accurate prediction of nonlinear dynamic behaviors of a two-dimensional (2-D) box-shaped floating structure in focused waves. Computations are performed by an enhanced Constrained Interpolation Profile (CIP)-based Cartesian grid model, in which a more accurate VOF (Volume of Fluid) method, the THINC/SW scheme (THINC: tangent of hyperbola for interface capturing; SW: Slope Weighting), is used for interface capturing. A focusing wave theory is used for the focused wave generation. The wave component of constant steepness is chosen. Comparisons between predictions and physical measurements show good agreement including body motions and free surface profiles. Although the overall agreement is good, some discrepancies are observed for impact pressure on the superstructure due to water on deck. The effect of grid resolution on the results is checked. With a fine grid, no obvious improvement is seen in the global body motions and impact pressures due to water on deck. It is concluded that highly nonlinear phenomena, such as distorted free surface, large-amplitude body motions, and violent impact flow, have been predicted successfully.     

Experimental Study of Nonlinear Behaviors of A Free-Floating Body in Waves

Nonlinear behaviors of a free-floating body in waves were experimentally investigated in the present study. The experiments were carried out for 6 different wave heights and 6 different wave periods to cover a relatively wide range of wave nonlinearities. A charge-coupled device (CCD) camera was used to capture the real-time motion of the floating body. The measurement data show that the sway, heave and roll motions of the floating body are all harmonic oscillations while the equilibrium position of the sway motion drifts in the wave direction. The drift speed is proportional to wave steepness when the size of the floating body is comparable to the wavelength, while it is proportional to the square of wave steepness when the floating body is relatively small. In addition, the drift motion leads to a slightly longer oscillation period of the floating body than the wave period of nonlinear wave and the discrepancy increases with the increment of wave steepness.     

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.     

Numerical Study of Influence of Currents on Nonlinear Focusing Waves

In this paper,a numerical model for nonlinear wave propagation in currents is formulated by a set of enhanced fully nonlinear Boussinesq equations with ambient currents.This model is verified by comparison with the published results.Then the influence of currents on nonlinear focusing waves is studied by use of the numerical model.It is found that the effect of currents on the surface elevations at the focal location is negligible.Following currents can augment the maximum crest of focusing wave while decre...     

非线性相互作用对高频方向谱估计的影响

海浪组成波之间的三阶非线性相互作用产生的高次谐波,不仅改变了波面的外观形状,而且使得高频域不再满足通常的线性频散关系,当ｆ＞１．７ｆｐ时,频散关系应修改为ω２＝２ｇｋ。用最大似然法（ＭＬＭ）分析方向分布的结果表明：在二倍峰频附近,方向分布再次变窄,且能量在方向上的集中程度与海浪的成长状态有关,得到的高频方向分布跟Ｃａｕｄａｌ和Ｈａｕｓｅｒ（１９９６）的微波遥感结果定性一致。     

2-D Composite Model for Numerical Simulations of Nonlinear Waves

—A composite model,which is the combination of Boussinesq equations and Volume of Fluid(VOF)method,has been developed for 2-D time-domain computations of nonlinear waves in a large re-gion.The whole computational region Ω is divided into two subregions.In the near-field around a struc-ture,Ω_2,the flow is governed by 2-D Reynolds Averaged Navier-Stokes equations with a turbulenceclosure model of k-εequations and numerically solved by the improved VOF method;whereas in thesubregion Ω_1(Ω_1=Ω-Ω_2) the flow is governed by one-D Boussinesq equations and numerically solvedwith the predictor-corrector algorithm.The velocity and the wave surface elevation are matched on thecommon boundary of the two subregions.Numerical tests have been conducted for the case of wave propa-gation and interaction with a wave barrier.It is shown that the composite model can help perform efficientcomputation of nonlinear waves in a large region with the complicated flow fields near structures taken in-to account.     

Nonlinear Waves in a Rotating Ocean (The Ostrovsky Equation and Its Generalizations and Applications)

Izvestiya, Atmospheric and Oceanic Physics - This review presents theoretical, numerical, and experimental results of a study of the structure and dynamics of weakly nonlinear internal waves in a...