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1.
内波是海洋中普遍存在的波动形式。内孤立波是典型的非线性内波,多发于陆架边缘海,如南海等海域,对陆架海域有重要影响。本文针对内孤立波在陆架地形上的传播问题,先基于弱非线性与全非线性数值模型,模拟了不同振幅、地形高度条件下内孤立波的演化的过程,探讨了动力系数对内孤立波演化过程的影响,对比了两模型的模拟结果在内孤立波演化过程、能量分配以及能量耗散的差异,后分析了南海的动力系数分布特征。结果表明,在内孤立波不发生破碎的情况下,弱非线性模型与全非线性模拟结果相近。当发生破碎过程时,弱非线性模型可准确模拟头波,但无法通过强非线性的破碎过程耗散能量,只能以裂变的方式辐射能量。在弱非线性模型中,随地形高度增加,频散系数减小到零,平方非线性系数由负转正,立方非线性系数绝对值增大一个量级,并主导陆架地形上内孤立波的演化过程。通过对比南海夏季与冬季非线性内波动力系数空间分布,发现内孤立波在传播过程由于夏季平方非线性效应、立方非线性效应与频散效应较强的影响,其在夏季更易发生陡化与裂变,波列发生频率高。 相似文献
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旋转流体中的非线性惯性波 总被引：1，自引：1，他引：1
本文从旋转流体中非线性惯性波的基本方程出发,通过微分几何理论论证了非线性惯性波在传播方向上的周期性及不存在孤波解。采用Hamilton函数及其作用──角度变量给出非线性惯性波的解析解。并以简洁形式提出了一种有限振幅的非线性惯性波和用罗斯贝数作为控制参量的非线性频散关系和波速公式。 相似文献
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为了研究独立高斯型波群在中等水深条件下的非线性演化情况,进行了多种波况的物理试验,重点分析了波浪各要素对波群非线性演化的影响。试验结果表明,波陡在波群演化中占主导作用,其次是波群的谱宽,前者引起的非线性主要体现在高阶谐波的能量变化而后者引起的非线性主要体现在自由波能量的变化。频带下移现象只在大波陡情况下才会发生,随着波陡的增加,频带下移发生的相对更早,随着波群的谱变窄,频带下移相对越明显。波陡的增加会使得波群更早的开始分裂。大波陡的波群在演化中会发生破碎,破碎的类型以崩破为主,并且崩破是间歇发生的,连续崩破发生的距离约为1.0～1.5倍波长。此外,破碎引起的能量损耗主要来源于主频和高频成分波,耗散率约10%～18%,平均每个崩破能耗约为初始能量的2%。 相似文献
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基于二阶斯托克斯波理论推导了辐射应力的垂向分布表达式,通过算例讨论了辐射应力在深水和有限水深条件下的垂向分布规律,并与基于微幅波理论的辐射应力进行了比较.结果表明,在波浪非线性不强时,基于二阶斯托克斯波理论的辐射应力与基于微幅波理论的辐射应力表达式计算结果接近;而当水深较浅波浪非线性较强时,基于二阶斯托克斯波理论的辐射应力在近表面处明显大于基于微幅波理论的辐射应力.采用二阶斯托克斯波理论推导的波浪辐射应力更为合理地反映了波浪非线性效应. 相似文献
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非线性随机波的数值模拟 总被引：1，自引：1，他引：1
本文根据作者提出的非线性不规则波四阶近似理论解,首先导出二阶非线性谱和线性谱的关系式,并应用非线性有约束最优化方法建立了从靶谱分解线性谱和二阶非线性谱的数学模式,进而建立非线性随机波数值模拟的数学模型及其快速傅里叶交换算式,从而大大地缩短计算机时。由于采用从靶谱分解出的线性谱,模拟的非线性随机波现实谱和靶谱符合一致。最后通过算例,对模拟的非线性及线性随机波的谱估计及波面统计特性进行初步分析,本方法为浅水不规则波与水流及建筑物相互作用的研究提供随机模拟基础。 相似文献
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非线性波的计算及其应用 总被引：1，自引：0，他引：1
本文在L.W.Schwartz的关于定常二维非线性波算法基础上,提供了适用于有限水深的五阶非线性波的简化算法。该算法可以方便地用于海洋结构物波浪载荷的计算,具有工程上可以接受的精度。当前,海洋结构物波浪载荷的计算,仅限于线性波理论,有时是不能满足工程需要的。许多非线性波的算法占用计算机内存大,耗费机时多,作为海洋结构物波浪载荷计算的子程序,应用上不方便。本文的研究工作旨在简化非线性波的计算,尽可能的压缩关于波动海面下流场计算的计算机子程序的规模。 相似文献
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依据深海表面波的非线性薛定谔方程,推导深海表面波的增益谱,研究在调制不稳定条件下的非线性薛定谔方程的一阶解与增益之间的关系,又结合呼吸孤子产生畸形波的现象,得到畸形波的最大振幅为初始波振幅与增益最大值的叠加。这个结果对研究畸形波的产生具有一定的参考价值。 相似文献
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迄今为止,天文潮波和气象潮相互作用的理论研究均局限于自由波的非线性效应。 本文试图对自由潮波和受迫气象潮波的相互作用作一探讨。作者求出的非线性精确解用于给出自由天文潮波与受迫气象潮波的零级解析解。 结果表明强迫波中心处非线性效应最大。强迫波中心遇到高潮时其增水小于强迫波中心遇到低潮时的增水,并且前者增水曲线更为平缓。因此,当强迫波中心与高潮相遇时,增水的时间往往持续得更长一些。 相似文献
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从描述f平面上的正压地形拦截波的非线性动力方程出发,利用常微分方程定性理论研究了海底地形坡度和海底摩擦对线性和非线性地形拦截波的动力不稳定性的影响,分析了不稳定的性质,找出了不稳定的判据。还在特定的海底地形坡度和海底摩擦条件下,建立了线性和非线性波的频散关系,并比较了两者的差别。 相似文献
10.
水槽中浅水非线性长波传播的 Boussinesq 数值模拟 总被引：1，自引：0，他引：1
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. 相似文献
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The equations of dynamics of eddy—wave disturbances of two-dimensional stratified flows in an ideal incompressible fluid that are written in a Hamiltonian form are used to study the resonant interaction of waves of discrete and continuous spectra. A gravity—shear wave generated at a jump of the density and vorticity of the undisturbed flow and a wave generated at a weak vorticity jump, which is similar to a wave of a continuous spectrum, participate in the interaction. The equations are written in terms of normal variables to obtain the system of evolution equations for the amplitudes of the interacting waves. The stability condition for eddy—wave disturbances is derived within the framework of the linear theory. It is shown that a cubic nonlinearity may lead to the stabilization of unstable disturbances if the coefficient of the nonlinear term is positive. 相似文献
13.
For the simulation of the nonlinear wave propagation in coastal areas with complex boundaries,a numerical model is developed in curvilinear coordinates. In the model,the Boussinesq-type equations including the dissipation terms are employed as the governing equations. In the present model,the dependent variables of the transformed equations are the free surface elevation and the utility velocity variables,instead of the usual primitive velocity variables. The introduction of utility velocity variables which... 相似文献
14.
综合考虑多种变形因素的近岸规则波传播数学模型Ⅰ. 基本方程的导出 总被引：1，自引：0，他引：1
推广了Kirby的有环境水流影响的缓坡方程,得到了综合考虑环境水流(水流因子)、非线性弥散影响(非线性因子)、底摩擦波能损失(底摩擦因子)、非缓坡地形影响(地形因子)、折射、绕射、波浪破碎多种变形因素的波浪传播控制方程,并给出了非线性因子、地形因子、底摩擦因子、水流因子的确定方法。基于导出的方程做进一步推导,得到了波高和波向为变量的综合考虑多种变形因素的波浪传播基本方程,该方程有许多优点:1)其绕开了求解波势函数的困难,将椭圆型方程的边值问题化为初值问题;2)直接求解波高和波向;3)可采用有限差分法离散求解,对空间步长没有限制,适合大面积海区波场计算;4)综合考虑了多种波浪变形因素,方程更为合理,5)容易处理波浪破碎问题。 相似文献
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Methods of studying the dynamics of wave disturbances in st;ratified shear flows of an ideal incompressible fluid are considered. The equations governing the motions of interest represent Hamilton equations and are derived by writing the velocity field in terms of Clebsch potentials. Equations written in terms of semi-Lagrangian variables are integrodifferential equations, which make it possible to consider both continuous and discontinuous solutions, as well as the cases where the parameters of the undisturbed medium are step functions. Two dynamic systems are presented. The first, canonical system of equations is most suitable for describing gravity waves in a shear flow in the case where the undisturbed medium is characterized by sharp gradients of density and flow velocity. The simplest model in which disturbances obey this system of equations is the well-known Kelvin-Helmholtz model. The second dynamic system describes, in particular, gravity-shear waves and, in the case of a homogeneous medium, shear waves in a two-dimensional flow. This system is most suitable for studying the dynamics of disturbances in models with sharp gradients of vorticity. On the basis of the approach developed in this study, the problem of the dynamics of disturbances in a flow with a continuous distribution of vorticity in a finite-thickness layer is solved. If the thickness of this layer is small compared to the characteristic wavelength and the gradient of the undisturbed vorticity in this layer is large, the solution has the form of a mode whose frequency is close to the frequency of the shear wave on a vorticity jump that would be obtained by letting the layer’s thickness approach zero. The results obtained allow, in particular, the estimation of the range of validity of finite-layer approximations for models with smooth profiles of flow and density. In addition, these results can be interpreted as the basis for the development of nonlinear aspects of the theory of hydrodynamic stability. 相似文献
17.
《Ocean Engineering》1999,26(4):287-323
A set of Boussinesq-type equations with improved linear frequency dispersion in deeper water is solved numerically using a fourth order accurate predictor-corrector method. The model can be used to simulate the evolution of relatively long, weakly nonlinear waves in water of constant or variable depth provided the bed slope is of the same order of magnitude as the frequency dispersion parameter. By performing a linearized stability analysis, the phase and amplitude portraits of the numerical schemes are quantified, providing important information on practical grid resolutions in time and space. In contrast to previous models of the same kind, the incident wave field is generated inside the fluid domain by considering the scattered wave field in one part of the fluid domain and the total wave field in the other. Consequently, waves leaving the fluid domain are absorbed almost perfectly in the boundary regions by employment of damping terms in the mass and momentum equations. Additionally, the form of the incident regular wave field is computed by a Fourier approximation method which satisfies the governing equations accurately in water of constant depth. Since the Fourier approximation method requires an Eulerian mean current below wave trough level or a net mass transport velocity to be specified, the method can be used to study the interaction of waves and currents in closed as well as open basins. Several computational examples are given. These illustrate the potential of the wave generation method and the capability of the developed model. 相似文献
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A set of Boussinesq-type equations with improved linear frequency dispersion in deeper water is solved numerically using a fourth order accurate predictor-corrector method. The model can be used to simulate the evolution of relatively long, weakly nonlinear waves in water of constant or variable depth provided the bed slope is of the same order of magnitude as the frequency dispersion parameter. By performing a linearized stability analysis, the phase and amplitude portraits of the numerical schemes are quantified, providing important information on practical grid resolutions in time and space. In contrast to previous models of the same kind, the incident wave field is generated inside the fluid domain by considering the scattered wave field in one part of the fluid domain and the total wave field in the other. Consequently, waves leaving the fluid domain are absorbed almost perfectly in the boundary regions by employment of damping terms in the mass and momentum equations. Additionally, the form of the incident regular wave field is computed by a Fourier approximation method which satisfies the governing equations accurately in water of constant depth. Since the Fourier approximation method requires an Eulerian mean current below wave trough level or a net mass transport velocity to be specified, the method can be used to study the interaction of waves and currents in closed as well as open basins. Several computational examples are given. These illustrate the potential of the wave generation method and the capability of the developed model. 相似文献
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Based on a set of Boussinesq-type equations with improved linear frequency dispersion characteristics in deeper water, the present paper incorporates the simplified effect of spilling wave breaking into the equations. The analysis is restricted to a single horizontal dimension but the method can be extended to include the second horizontal dimension. Inside the surf zone the vertical variation of the horizontal velocity profile is assumed to be composed of an (initially unknown) organised velocity component below the roller and a surface roller travelling with the wave celerity. This leads to a new set of equations which is capable of simulating the transformation of waves before, during and after wave breaking. The model is calibrated and verified by comparison with several wave flume measurements. The results show that the model produces sound physical results. 相似文献
20.
Hyperbolic Mild Slope Equations with Inclusion of Amplitude Dispersion Effect： Regular Waves 总被引：4，自引：2，他引：2
A new form of hyperbolic mild slope equations is derived with the inclusion of the amphtude dispersion of nonlinear waves. The effects of including the amplitude dispersion effect on the wave propagation are discussed. Wave breaking mechanism is incorporated into the present model to apply the new equations to surf zone. The equations are solved nu- merically for regular wave propagation over a shoal and in surf zone, and a comparison is made against measurements. It is found that the inclusion of the amplitude dispersion can also improve model＇ s performance on prediction of wave heights around breaking point for the wave motions in surf zone. 相似文献