Quasi- determinism of sea wave groups

Summary Provided we know that at a point x ₀,y ₀ within an irregular gravity wave field, like those generated by wind on sea, at a time instant t ₀ there is a wave with a height H great with respect to the mean, we can predict that that wave, with high probability, has been formed because of the transit of a well defined (deterministic) group, like that in Fig. 1. In mathematical terms: if the ratio between the known wave height H and the mean wave height tends to infinity, the probability that the true wave group is equal to the deterministic wave group plus a lower order random noise approaches 1 [1]. The effect of the random noise is the object of this paper. In particular, the effect on the mean heights and periods of the waves forming the group is estimated within errors of an order smaller than (H/ m ₀)^–1 (m ₀ being the variance of the free surface elevation of the irregular wave field), The knowledge of the infinitesimal differences between the true wave group and the deterministic wave group, for H/ m ₀,proves to be useful for assessing the differences in the case that H is realistically great for a sea state. To that end data from numerical simulations of irregular gravity wave fields are used too. The conclusion is that, for a realistically great H, the deterministic wave group closely reflects the essential features of the true wave group.

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Sommario Ammesso di sapere che in un punto x ₀,y ₀ di un campo di onde irregolari di gravità, come quelle generate dal vento sul mare, ad un certo istante t ₀ c' è un'onda con un'altezza H grande rispetto alla media, si può prevedere che, con grande probabilità, tale onda si sia formata per il passaggio di un ben definito (deterministico) gruppo come quello di Fig. 1. In forma matematica: se il rapporto tra l'altezza H nota e l'altezza media tende ad infinito, la probabilità tende ad 1 che il gruppo di onde vero sia uguale al gruppo deterministico più un disturbo aleatorio di ordine inferiore [1].L'effetto del disturbo aleatorio è l'oggetto di questa memoria. In particolare l'effetto sull'altezza e sul periodo medio delle onde nel gruppo viene stimato a meno di errori di ordine inferiore a (H/ m ₀)^–1 (m ₀ essendo la varianza della quota del pelo libero del campo di onde irregolari). La conoscenza delle differenze inflnitesime tra il gruppo di onde vero e il gruppo di onde deterministico, per H/ m ₀,si dimostra utile per prevedere quali possano essere le differenze nel caso che H sia realisticamente grande per uno stato di mare. Allo scopo si utilizzano anche i dati di simulazioni numeriche dei campi di onde di gravita irregolari. La conclusione è che, per H realisticamente grande, il gruppo di onde deterministico rispecchia da vicino i caratteri essenziali del gruppo di onde vero.

     

Equations of hydrodynamics for wind wave circulation on a shelf

In order to predict the propagation of an impurity and water quality on a shelf it is necessary to know the water mass dynamics and the water exchange. However, the hydrodyamics of the shelf zone differ considerably from those of the open expanses of seas and lakes owing to the steepness of the bottom, the complex structure of the shoreline, the major role of wind waves, and their breaking [1]. In [2, 3] the importance of surface waves and their breaking for inshore flows was demonstrated and the equations of hydrodynamics, averaged over the depth, were derived. For regions of the shelf remote from the shoreline it is also necessary to take into account the interaction of waves with the bottom and with essentially three-dimensional flows. In this note the equations of hydrodynamics are derived for wind wave flows averaged over the wave period in the threedimensional formulation.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1-, pp. 174–176, January–February, 1987.     

Calculation of wind currents in the edge zone of a sea ice sheet

The steady wind currents in the ocean near the edge of an ice sheet simulated by a rigid cover are studied. The characteristic horizontal scales of the problem correspond to several tens of kilometers. In this case, depending on the depth and viscosity of the fluid, the effect of the Coriolis force on its motion may be comparable with the effect of the wind shear stresses applied to the ice-free surface. Taking the Coriolis force into account leads to the formation of a spiral flow structure in the vertical direction.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 132–141, November–December, 1992.     

Internal fractures in spheres due to stress wave focusing

The locations and times of occurrence of internal fractures in Perspex spheres subjected to localized explosive loading are investigated. An analysis of stress wave reflection from free boundaries based on the method of geometrical acoustics is found to give predictions which are in good agreement with results obtained from high speed photographs.     

Modeling ocean wave propagation under sea ice covers

Operational ocean wave models need to work globally, yet current ocean wave models can only treat ice covered regions crudely. The purpose of this paper is to provide a brief overview of ice effects on wave propagation and different research methodology used in studying these effects. Based on its proximity to land or sea, sea ice can be classified as: landfast ice zone, shear zone, and the marginal ice zone. All ice covers attenuate wave energy. Only long swells can penetrate deep into an ice cover. Being closest to open water, wave propagation in the marginal ice zone is the most complex to model. The physical appearance of sea ice in the marginal ice zone varies. Grease ice, pancake ice,brash ice, floe aggregates, and continuous ice sheet may be found in this zone at different times and locations. These types of ice are formed under different thermal-mechanical forcing. There are three classic models that describe wave propagation through an idealized ice cover: mass loading,thin elastic plate, and viscous layer models. From physical arguments we may conjecture that mass loading model is suitable for disjoint aggregates of ice floes much smaller than the wavelength, thin elastic plate model is suitable for a continuous ice sheet, and the viscous layer model is suitable for grease ice. For different sea ice types we may need different wave ice interaction models. A recently proposed viscoelastic model is able to synthesize all three classic models into one. Under suitable limiting conditions it converges to the three previous models. The complete theoretical framework for evaluating wave propagation through various ice covers need to be implemented in the operational ocean wave models. In this review, we introduce the sea ice types, previous wave ice interaction models, wave attenuation mechanisms,the methods to calculate wave reflection and transmission between different ice covers, and the effect of ice floe breaking on shaping the sea ice morphology. Laboratory experiments,field measurements and numerical simulations supporting the fundamental research in wave-ice interaction models are discussed. We conclude with some outlook of future research needs in this field.     

Intensification of a detonation wave in the zone of secondary reactions in a two-phase medium

A method is proposed for the numerical calculation of one-dimensional nonsteady-state flows of a mixture of a gas with particles, based on the separation of a system of differential equations for a two-phase medium into two subsystems. The problem is solved concerning the propagation of a plane detonation wave in a mixture of a detonating gas with particles, behind the front of which secondary chemical reactions are taking place between the vapors of the particle material and the detonation products. The velocity profiles of the gas and of the thermodynamic functions behind the detonation wave front are determined, and also the dependence of the detonation velocity on the distance to the point of initiation. The conditions for intensification of the detonation wave are obtained in the zone of secondary reactions.Leningrad. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 92–96, September–October, 1972.     

Internal wave generation by a fountain in a stratified fluid

The purpose of the study is the direct numerical and theoretical modeling of fountain dynamics in a fluid with density stratification in the form of a pycnocline. The fountain is formed as a vertical jet penetrates through the pycnocline. In numerical simulation the jet flow is initiated by means of preassigning a boundary condition in the form of an upward-directed laminar flow of a neutral-buoyancy fluid with an axisymmetric Gaussian velocity profile. The calculations show that at a Froude number Fr greater than a certain critical value the flow becomes unstable and the fountain executes self-oscillations accompanied by internal wave generation in the pycnocline. Depending on Fr, two self-oscillation modes can be distinguished. At fairly low Fr the fountain executes circular motion in the horizontal plane, in the vicinity of the center of jet, its shape remaining almost invariant. In this case, internal waves in the form of unwinding spirals are radiated. At fairly high Fr another mode predominates, when the fountain top chaotically “strays” in the vicinity of the center of the jet and, periodically breaking down, generates wave packets propagating toward the periphery of the computation domain. In both cases, the main peak in the frequency spectrum of the internal waves coincides with the fountain top oscillation frequency which monotonically decreases with increase in Fr. In numerical simulation the Fr-dependence of the fountain top oscillation amplitude is in good agreement with that predicted by the theoretical model of the concurrence of the interacting modes in the soft self-excitation regime.     

Evolution of slowly modulated wave train on porous sea bed

In this paper, the problem of evolution of slowly modulated wave train on porous sea bed is investigated with the method of multiple scales. For the sea water in the upper region, the classical potential theory is used while the fluid motion in the porous sea bed is described by Darcy’s law. The equations of the first and second order modulations of wave amplitude are derived by using matching conditions on the sea bed. The corresponding solutions are found and seepage pressures are also given at the same time.     

Internal wave computations using the ghost fluid method on unstructured grids

Two‐layer incompressible flows are analysed using the ghost fluid method on unstructured grids. Discontinuities in dynamic pressure along interfaces are captured in one cell without oscillations. Because of data reconstructions based on gradients, the ghost fluid method can be adopted without additional storages for the ghost nodes at the expense of modification in gradient calculations due to the discontinuity. The code is validated through comparisons with experimental and other numerical results. Good agreements are achieved for internal waves generated by a body moving at transcritical speeds including a case where upstream solitary internal waves propagate. The developed code is applied to analyse internal waves generated by a NACA0012 section moving near interfaces. Variations of the lift acting on the body and configurations of the interfaces are compared for various distances between the wing and the interface. The effects of the interface are compared with the effects of a solid wall. Copyright © 2004 John Wiley & Sons, Ltd.     

Formation of a shock wave at the boundary of a local supersonic zone

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No.1, pp. 24–32, January–February, 1993.     

Internal wave radiation by a turbulent fountain in a stratified fluid

Large eddy simulation is applied to model a fountain in a density-stratified fluid. The fountain is formed, as a vertical turbulent jet penetrates through a pycnocline. The jet flow is initiated by the formulation of a boundary condition in the form of an upward neutral-buoyancy fluid flow with the Gaussian axisymmetric mean-velocity profile and a given fluctuation level. It is shown that at a Froude number Fr higher than a certain critical value the fountain executes self-oscillations accompanied by internal wave generation within the pycnocline. The predominant self-oscillation mode is axisymmetric, when the fountain top periodically breaks down generating internal wave packets traveling toward the periphery of the computation domain. The characteristic frequency of the internal waves coincides with that of the fountain top oscillations and monotonically decreases with increase in Fr. The Fr-dependence of the fountain top oscillation amplitude obtained in the numerical solution is in good agreement with the predictions of the theoretical Landau model for the instability mode in the soft self-excitation regime.     

黄茅海波-流共同作用下的三维悬沙数值模拟

针对黄茅海河口区波流相互作用显著、三维空间结构明显及泥沙运动复杂等特点,联合第3代海浪模式SWAN,建立了波流共同作用下的三维悬沙数学模型.在水流计算中,考虑了波浪产生的辐射应力影响,波浪依赖的表面风应力影响及波浪影响下的底部剪切应力,并采用k-kl紊流闭合模型提供垂向涡粘系数和垂向扩散系数.悬沙扩散方程中的源函数利用切应力法确定,泥沙沉降速度考虑絮凝作用,从而提高黄茅海悬沙场数值模拟精度.通过含沙量实测资料验证,模拟值与实测值符合较好.在模型验证的基础上,讨论了不考虑波浪与考虑波浪两种情况下黄茅海的悬沙分布特征,为工程实际研究提供了依据.     

Model of an undular bore

In the shallow-water approximation, nonlinear long waves are considered with account for small-scale waves on the free surface. The undular-bore structure, which within the framework of this model is represented as a discontinuous solution with a relaxation zone adjacent to the discontinuity, is investigated. The wave-packet damping rate is found. The solution obtained is compared with the structure of the undular bore determined by the nonlinear dispersion equations of second-approximation shallow-water theory.     

Internal wave structure in a three-layer fluid with a stratified middle layer

The behavior of internal waves in a vertically bounded channel differs considerably from the wave motion in an infinite stratified fluid. In [1] the phase structure of the internal waves in an exponentially stratified layer of fluid between rigid horizontal planes was experimentally and theoretically investigated. A characteristic feature of such a channel is the boundedness of the phase and group velocities of each mode. Below, the case of an exponentially stratified channel between layers of homogeneous unbounded fluid is considered.In conclusion, the authors wish to thank A. T. Onufriev for his interest in their work.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 128–132, May–June, 1987.     

饱和水泥试样被爆炸激波损伤破碎的尺度研究

利用水中爆炸冲击波使水泥试样损伤破坏,模拟爆炸采油时激波使岩石损伤开裂的现象。实验获得了适合本实验条件的激波峰压衰减规律pm8.2(W1/3/R)1.46,得知压碎区尺度为集中装药特征尺度的2～5倍、拉伸损伤区尺度为集中装药特征尺度的20～30倍,激波使水泥试样破碎、拉裂的能量占总能量的2%～7%。     

Reducing mixing at the outlet bore of a cylinder

Summary In some technical applications mixing caused by contraction of cross section is to be avoided. An example is the outlet of a chromatographic column in preparative liquid chromatography (HPLC). First of all, it is desirable to reduce the volume of the cylinder within which the mixing occurs. This is done by placing a porous disk upstream of the contraction. Mixing within the contraction (or funnel) is avoided if a constant axial velocity component over every cross-section is achieved. Two such velocity fields have been found analytically. The funnel shapes have been taken to be the stream tubes of these fields. The mixing within these funnels, and indeed in other common funnels, is described by the breakthrough curves or residence-time distributions, which are numerically determined. An experiment has been set up to measure the breakthrough curves for different funnels. Received 6 September 1997; accepted for publication 26 January 1998