存在流体介质夹层时瑞利波频散曲线的完整求解

应用介质分界面上位移应力连续性的变化关系,采用δ矩阵法和固体层状介质中的瑞利波频散方程,推导了含流体介质夹层情况下瑞利波的频散方程。利用推导的频散方程对理论模型进行模拟计算,并与以往文献计算方法进行比较,模拟结果吻合较好,验证了公式的正确性;同时,模拟计算结果也说明了本文公式的普遍适用性和计算结果的完整性。根据文中对4个理论模型的模拟结果来看,与固体层状介质的情况相比,当存在流体夹层时,瑞利波频散曲线模式中多出了一个文中定义的0阶模式,在今后的多道瞬态瑞利波法应用中,应该可以将其看成是流体介质夹层存在的标志性曲线。     

Kongeåens udløb i Vadehavet

Jacobsen, N. Kingo, 1975: Kongeåens udløb i Vadehavet. Geografisk Tidsskrift 74: 55–67. København, juni 1, 1975.

The problem of drainage at the outlet of streams in the Danish Wadden Sea. Outside the sluice of Kongeåen a canal was established ig63 to guarantee drainage, i.e. a low water-table at the sluice at low-tide. Bors at the outlet of the canal cause difficulties. The topography of the tidal flat, the ebb- and flood currents, the volume of water-masses etc. are investigated, and another technical arrangement proposed.     

均匀流场中并列圆柱涡激振动的现状与预测

并列圆柱体在均匀流场中的涡激振动十分复杂，但又广泛存在于实际工程之中。当两柱在流体激励作用下产生振动时，由于同时存在着流固耦合作用和柱间干扰作用，而使周围流场变得更加复杂。本文对并列刚性和弹性圆柱的流场分类，Ｓｔｒｏｕｈａｌ数及流体载荷等问题进行了综述，在此基础上提出了进一步研究的建议。     

Condensed hyperelements method of non-vertical consistent boundaries for wave propagation analysis in irregular media

The study of wave propagation in finite/infinite media has many applications in geotechnical and structural earthquake engineering and has been a focus of research for the past few decades. This paper presents an analysis of 2D anti- plane problems （Love waves） and 2D in-plane problems （Rayleigh waves） in the frequency domain in media consisting of a near-field irregular and a far-field regular part. The near field part may contain structures and its boundaries with the far-field can be of any shape. In this study, the irregular boundaries of the near-field are treated as consistent boundaries, extending the concept of Lysmer＇s vertical consistent boundaries. The presented technique is called the Condensed Hyperelements Method （CHM）. In this method, the irregular boundary is limited to a vertical boundary at each end that is a consistent boundary at the far-field side. Between the two ends, the medium is discretized with hyperelements. Using static condensation, the stiffness matrix of the far-field is derived for the nodes on the irregular boundary. Examples of the application of the CHM illustrate its excellent accuracy and efficiency.     

On the impossibility of mean-field dynamos with some spherical symmetry of the motions

Abstract

A spherical mean-field dynamo model is considered in which both the mean motion and the mean electro-motive force due to fluctuating motions show some spherical symmetry. It is shown that under some reasonable assumptions the magnetic field is bound to decay to zero.     

The influence of a coastal headland on oceanic boundary currents

Abstract

The steady state circulation of a constant barotropic current around a coastal headland, bay, or combination of the two, located on a flat bottom, mid-latitude β-plane is considered. The maximum displacement of the coastal features from the mean straight coastline is assumed to be small compared to the longshore variation of the coastline. Under this slowly varying coastline approximation, a linearised vorticity equation is derived for the perturbation stream function. An analytical solution for the perturbation stream function is obtained using a Green's function technique. For a specified coastline the effects of coastal orientation, linear friction and the strength of the mean flow are investigated. The model predicts that the flow field will adopt the pattern of the coastline. The question of whether a coastal feature is likely to induce linear flow dynamics within the coastal boundary layer is also addressed. In the case when a single Gaussian headland or bay violates the slowly varying longshore condition the model predicts that flow stagnation will not occur. However for multiple headlands and bays, flow stagnation is possible when the slowly varying longshore condition is sufficiently violated.

Cape Mendocino and Point Conception along the California coast can be modelled using either a single Gaussian headland coastline or a multiple headland and bay coastline. In either case the model coastline does not vary slowly alongshore and nonlinear flow in the coastal region is likely. A permanent eddy to the south of Point Conception is likely to testify to the non-linear flow regime induced by the headland.     

Residual vorticity induced by the action of tidal currents in combination with bottom topography in the Southern Bight of the North Sea

Abstract

Results are presented of calculations on the generation of residual vorticity by tidal currents over the bottom topography of the Southern Bight of the North Sea. A typical order of magnitude is 10^?6 to 10^?7 s ^?1. This is compared with current measurements on calm days, when similar magnitudes are found. At windspeeds less than about 5 m/s tidal generation of residual vorticity is important; at higher windspeeds wind effects begin to dominate. Our results are relevant in understanding the spatial variability of residual currents, because a non-zero vorticity implies the existence of horizontal gradients in the residual current field.     

Macrodynamics of α2 dynamos

Abstract

Two distributions of the α-effect in a sphere are considered. The inviscid limit is approached both by direct numerical solution and by solution of a simpler nonlinear eigenvalue problem deriving from asymptotic boundary layer analysis for the case of stress-free boundaries. The inviscid limit in both cases is dominated by the need to satisfy the Taylor constraint which states that the integral of the Lorentz force over cylindrical (geostrophic) contours in a homogeneous fluid must tend to zero. For a small supercritical range in α, this condition can only be met by magnetic fields which vanish as the viscosity goes to zero. In this range, the agreement of the two approaches is excellent. In a portion of this range, the method of finite amplitude perturbation expansion is useful, and serves as a guide for understanding the numerical results. For larger α, evidence from the nonlinear eigenvalue problem suggests both that the Taylor state exists, and that the transition from small to large amplitude can require a finite amplitude (oscillatory) instability in accord with the findings of Soward and Jones (1983). However, solutions of the full equations have not been found which are independent of viscosity at larger values of α.     

Dielectrophoretic,thermal instability in a spherical shell of fluid

Abstract

This paper is concerned with the dielectrophoretic instability of a spherical shell of fluid. A dielectric fluid, contained in a spherical shell, with rigid boundaries is subjected to a simultaneous radial temperature gradient and radial a.c. electric field. Through the dependence of the dielectric constant on temperature, the fluid experiences a body force somewhat analogous to that of gravity acting on a fluid with density variations. Linear perturbation theory and the assumption of exchange of stabilities lead to an eighth order differential equation in radial dependence of the perturbation temperature. The solution to this equation, satisfying appropriate boundary conditions, yields a critical value of the electrical Rayleigh number and corresponding critical wave number at which convective motion begins. The dependence of each critical number is presented as a function of the gap size and temperature gradient. In the limit of zero shell thickness both the critical Rayleigh number and critical wave number agree with results for the case in the infinite plane problem.     

Paramater regimes for studying isolated eddies

Abstract

The parameter ranges relevant to propagating oceanic eddies are explored with a view to simplifying the equation sets previously used to simulate such eddies. The reduced gravity shallow-water model is used as a starting point. We consider eddies whose width is of the same order as, or somewhat larger than, the Rossby deformation radius. Two model equations emerge from these scalings, both permitting modon solutions and easy numerical integration. Both, too, give fair simulations of the shallow-water model, but disagree in details.

Using another approach, an ad hoc vortex model is used to predict the path of an eddy. This also gives a fair but not perfect simulation of the one-layer results. It appears that the only ideal way to reproduce primitive equation results accurately is to use the primitive equations themselves.