Dynamics of the internal gravity waves in the heterogeneous and nonstationary stratified me
微重力英语
微重力英语In the realm of space exploration, the term "microgravity" is a fundamental concept that describes the condition where objects appear to be weightless. This phenomenon occurs when a body is far enough from a gravitational field's source, such as Earth, to experience only minimal gravitational forces. Here's a deep dive into the nuances of microgravity and its implications for both scientific research and human spaceflight.Understanding MicrogravityMicrogravity is not the absence of gravity but rather a state where gravity's effects are so weak that they can be negligible. It's often misunderstood as zero gravity, but in reality, gravity is still present—it's just that the gravitational force is so small that it doesn't significantly affect the motion of objects within the microgravity environment.Applications in ResearchThe microgravity environment is a unique laboratory for scientific research. It allows scientists to perform experiments that are difficult or impossible on Earth due to the confounding effects of gravity. For instance, microgravity enables the study of fluid dynamics without the influence of convection currents, leading to a betterunderstanding of how fluids behave under different conditions.Impact on Human PhysiologyProlonged exposure to microgravity has significanteffects on the human body. Astronauts can experience muscle atrophy and bone density loss due to the lack of the gravitational pull that normally stimulates muscle and bone growth. To counteract these effects, astronauts on the International Space Station (ISS) engage in regular exercise and follow a strict diet to maintain their health.Technological InnovationsMicrogravity also presents opportunities fortechnological advancements. For example, the absence of convection currents allows for the precise control of crystal growth, which is crucial in the development of certain pharmaceuticals and semiconductors. Additionally, the microgravity environment is used to test new technologiesthat could be used in future space missions, such as advanced robotics and satellite deployment systems.Challenges of Living in MicrogravityDespite the benefits, living and working in microgravity poses several challenges. Everyday tasks that are simple on Earth become complex in space. Simple things like eating, sleeping, and hygiene require special adaptations. For example, food must be specially prepared to prevent crumbsfrom floating around the cabin, and sleeping bags aretethered to walls to prevent astronauts from floating uncontrollably.Future ProspectsAs space agencies and private companies continue to explore the cosmos, microgravity will remain a critical area of study. The knowledge gained from understanding and adapting to microgravity will not only aid in the development of space travel but also provide insights that can benefit life on Earth, from improving medical treatments to advancing our understanding of fundamental physics.In conclusion, microgravity is a fascinating state of being that offers a wealth of opportunities for scientific discovery and technological innovation. As we continue to venture further into space, the lessons learned from microgravity will undoubtedly play a pivotal role in shaping the future of space exploration and our understanding of the universe.。
造船的目的不是停在港湾,而是冲击风浪作文
造船的目的不是停在港湾,而是冲击风浪作文In the vast expanse of the sea, ships are no longer mere vessels. They become symbols of man's courage, tenacity,and desire to conquer the unknown. The purpose of shipbuilding goes beyond merely stopping at port; its true goal is to withstand the powerful forces of wind and waves.在广袤无边的海洋中，船只已不再仅仅是运输工具。
它们成为人类勇气、坚韧和征服未知渴望的象征。
造船的目的不仅仅是停靠港湾，而是要能够经受住强大的风浪力量。
When a ship sails into open waters, it must face nature's wrath head-on. Waves crash against its hull, attempting to toss it aside like a mere toy. Winds howl and push against its sails, striving to send it off course. In these moments, it becomes clear that a well-built ship is not only about size or materials but rather about engineering prowess and calculated designs.当一艘船驶入开阔的水域时，它必须直面自然暴怒。
波浪冲击船体，试图将其像玩具一样抛到一边。
狂风呼啸着顶着帆，努力使其偏离航线。
Einsteinsscientificachievement,爱因斯坦的科学成就
Einsteinsscientificachievement,爱因斯坦的科学成就All his life Albert Einstein was interested in trying to understand the laws of the Universe. He was atheoretical physicist, asking probing questions and carrying out experiments in his mind.In his Special Theory of Relativity, Einstein revolutionised the thinking about space and time. This theory provided the basis for the development of the famous equation E = mc2 which illustrates that matter and energy are interchangeable, and that a small amount of mass is made up of a large amount of energy.The year 1905 is sometimes called Einstein's annus mirabilis (miracle year). In that year he published four outstanding scientific papers:An explanation of the photoelectric effect indicating that light energy came in chunks or quanta.This changed thinking on the nature of light.A discussion of Brownian motion demonstrating the existence of molecules.The nature of space and time.The dynamics of individual moving bodies.These last two formed the basis of Einstein's Special Theory of Relativity and led to that famous equation,E = mc2.In 1921, Einstein was awarded the Nobel Prize for Physics 'for his services to theoretical physics and in particular for his discovery of the law of the 'photoelectric effect'. When he made his delayed acceptance speech in 1923, he ignored the citation and spoke on his theory of relativity.Einstein was a great intellect. He came up with explanationswhich at the time could not be verifiedexperimentally and many of his theories took a long time to be accepted even within the scientific world.Greater credence was attached to his theories as science and technology advanced sufficiently to allow experimentation involving high speed travel and nuclear reactions.It is still difficult for many people to accept or understand his theories since they require thinking beyond normal experiences.Following is an outline of the principles that Einstein developed in a number of scientific fields.Special Theory of RelativityRelativity explains the way an object appears to be relative to an observer. You can understand this if you consider yourself in a car, observing other cars. Imagine you are observing a car travelling at 20 km/h. If your car is stationary, then the other car's speed relative to you is 20 km/h. However if you are travelling alongside the car also doing 20 km/h, then the other car seems to be stationary compared to you. Its speed relative to you is zero! (Ever been at the traffic lights when another car has moved away and you thought you were rolling backwards?)Einstein developed the special theory of relativity by thinking about travelling alongside a light beam at the same speed as the light. He determined that the speed of light is constant, no matter what you are doing or how fast you are travelling, light always travels through empty space at 'the speed of light'. This means that time and length are not absolute, but depend on the relative motion of the object and the observer. If you are stationary, an object that is moving seems to get shorter and heavier, and time slows down for the object. In everyday situations, the slight changes are immeasurable, but they becomeobvious as the speed increases towards the speed of light. As the object travels closer to the speed of light, the length of the object appears closer to zero. Its height stays the same unless it moves up or down —the contraction only happens in the direction of movement. However if you are travelling at the same speed as the object, then everything looks normal! The 'contraction' of moving objects is the contraction of space itself not the object within space.In moving through space, time changes. Space and time are two parts of one whole called spacetime. If you stand still, you are only moving through time. If you move at the speed of light, you move throughspace only and not through time —time stands still. In between, you move partly through one and partly through the other!So the famous twin trip example: Twin A travels round the world at fast pace in a space ship while the twin B stands still. When twin A returns, (s)he will be younger than twin B. Twin B has moved only through time, twin A has moved partly through space and only partly through time —less time than the twin who stayed still.The Special theory of relativity also led to the most famous equation which first appeared in an article by Einstein in 1907. There is a fundamental relationship between rest energy and mass according to the equation E = mc2 where E is the rest energy of an object, m is the mass of the object and c is the velocity of light. The mass of something is a measure of the energy within it; matter and energy are interchangeable, and a small amount of mass is made up of a large amount of energy.In the 1930s nuclear fission was discovered. This gave a wayto release the energy stored in the nuclei of atoms, and the possibility of nuclear weapons was realised.The General Theory of RelativityThe Special Theory applies to objects moving in straight lines at constant speeds. Shortly after its publication, Einstein started work on generalising the theory to include curved paths and accelerating objects, considering the motion that makes planets move in orbit, and the fall of objects to the earth. This led to the equivalence principle which states that in free fall the acceleration and the force due to gravity are equivalent, and the force due to gravity is neutralised, ie in freefall you are weightless.In 1907 Einstein developed the ideas that space and time are not constant, but they change, and that gravity was a property of spacetime rather than being an external force. As he put it: "Matter tells space how to bend and space tells matter how to move." A glimpse into the workings of Einstein's four dimensional spacetime can be gained by imagining the spacetime as a rubber sheet. Stars and planets have mass and cause the sheet close to them to change shape and curve around them. Another massive object coming close will have its motion affected by this deformation of spacetime.The general theory predicted that a light beam passing near a massive object would actually be bent, and by how much. This prediction was supported during a total eclipse of the Sun in May 1919, and again by observations of a total eclipse in Australia in 1922.One of the predictions of the general theory is that the Universe is expanding, giving a basis for the 'big bang' theory of the origins of the Universe. It has also been used to explain black holes and quasars. Quantum TheoryThe nature of light had been debated for many years. Was it made up of particles or waves? Isaac Newton believed light to be made up of particles, Christiaan Huygens stated it was a wave phenomenon, and this was reinforced when Thomas Young demonstrated interference. Later Maxwell suggested and Hertz proved that light was part of the electromagnetic spectrum.In 1905 Einstein reintroduced the particle theory of light. A few years earlier, Max Planck had proposed that energy in an atom occurs in little chunks called quanta. Einstein suggested that light also existed in chunks or quanta. These quanta are now called photons. He concluded this by examining the photoelectric effect – the release of electrons from metals when light shines on them. To make this happen, the light needed to be high frequency (ultraviolet). Low frequency light (red) would not make it happen, no matter how bright the light was. Einstein explained this by thinking of light in terms of photons. Each electron is pushed out from the metal by one photon — as long as that photon has enough energy. Only high frequency light has photons with enough energy. Low frequency light has low energy photons, and no matter how many there are, none of them has enough energy to dislodge an electron.Between 1916 and 1925, Einstein made other contributions to the study of light, including the idea of stimulated emission of radiation – a concept which led to the development of the laser.Unified Field TheoryThe quest to explain gravity and electromagnetism together as aspects of a common phenomenon occupied Einstein's scientific thoughts for much of the last thirty years of his life until he died in 1955. He wanted to provide a basis to explain the Universe in a way other than quantum mechanics whichdescribed activities in terms of probabilities. He did not succeed. Since then the weak and strong nuclear forces have been discovered.Electromagnetism and the nuclear forces can be explained using quantum mechanics, and the search continues for a theory to explain everything!。
黑洞介绍英语作文带翻译
黑洞介绍英语作文带翻译Title: Exploring the Enigma of Black Holes。
Black holes are among the most intriguing and enigmatic phenomena in the universe. Formed from the collapse of massive stars, these cosmic entities possess gravitational forces so strong that even light cannot escape their grasp. In this essay, we delve into the mysteries of black holes, exploring their formation, properties, and the profound impact they have on our understanding of the universe.黑洞是宇宙中最引人入胜和神秘的现象之一。
这些天体是由大质量恒星的坍缩形成的，它们具有如此强大的引力，以至于连光都无法逃脱它们的吸引。
在本文中，我们深入探讨黑洞的形成、特性以及它们对我们对宇宙的理解产生的深远影响。
Formation of Black Holes。
Black holes originate from the remnants of massive stars that have exhausted their nuclear fuel and undergogravitational collapse. When a massive star reaches the end of its life cycle, it can no longer sustain nuclear fusion reactions to counteract the inward pull of gravity. Consequently, the star's core collapses under its own weight, leading to the formation of a black hole.黑洞起源于已经耗尽核燃料并且发生引力坍缩的大质量恒星的残骸。
星体之间的重力势能
星体之间的重力势能The gravitational potential energy between celestial bodies is a fundamental concept in physics that plays a crucial role in understanding the dynamics of the universe. This potential energy arises due to the attractive force of gravity between two or more objects, such as stars, planets, or moons. In this discussion, we will explore the conceptof gravitational potential energy from various perspectives, including its definition, formula, and its significance in astrophysics and cosmology.Gravitational potential energy can be defined as the energy possessed by an object or a system of objects due to their positions in a gravitational field. It is directly related to the mass of the objects and the distance between them. The greater the mass of the objects and the closer they are, the higher the gravitational potential energy. This potential energy is a scalar quantity, meaning it only has magnitude and no direction.The formula to calculate the gravitational potential energy between two objects is given by the equation:PE = -G * (m1 * m2) / rWhere PE represents the gravitational potential energy, G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass.From an astrophysical perspective, the concept of gravitational potential energy is crucial in understanding the formation and evolution of celestial bodies. During the formation of stars, for example, gravitational potential energy plays a significant role in the collapse of interstellar gas and dust clouds, leading to the formation of protostars. As the protostar continues to accrete mass, the gravitational potential energy increases, and this energy is eventually converted into thermal energy, powering the star's nuclear fusion processes.In cosmology, gravitational potential energy is also important in understanding the large-scale structure of the universe. The distribution of matter and energy in the universe is influenced by the gravitational potentialenergy between galaxies, galaxy clusters, and even larger cosmic structures. The gravitational potential energy acts as a driving force for the formation of cosmic filaments, voids, and superclusters, shaping the overall structure of the universe.Moreover, gravitational potential energy is intimately connected to the concept of escape velocity. Escapevelocity is the minimum velocity an object needs to escape the gravitational pull of a celestial body. It is directly related to the gravitational potential energy of the object. By calculating the escape velocity, scientists candetermine whether an object, such as a spacecraft or a planet, can overcome the gravitational pull and leave the vicinity of a celestial body.Furthermore, the concept of gravitational potential energy is closely related to the principle of conservationof energy. In a closed system, the total energy, including the gravitational potential energy, remains constant. This principle allows scientists to study the interplay between different forms of energy, such as kinetic energy and gravitational potential energy, in various astrophysical phenomena.In conclusion, the gravitational potential energy between celestial bodies is a fundamental concept in physics that has wide-ranging implications in astrophysics and cosmology. It is defined as the energy possessed by objects due to their positions in a gravitational field and can be calculated using the gravitational potential energy formula. This concept is crucial in understanding the formation and evolution of celestial bodies, the large-scale structure of the universe, escape velocity, and the conservation of energy. By studying gravitational potential energy, scientists can gain valuable insights into the dynamics and behavior of the universe at both small and large scales.。
动力学斜面问题总结
动力学斜面问题总结英文回答：Introduction:In this summary, I will discuss the dynamics ofinclined planes. The study of dynamics involves understanding the motion of objects and the forces acting upon them. Inclined planes are a common example used to illustrate the principles of dynamics. By analyzing the forces at play on an object on an inclined plane, we can determine its acceleration and other relevant parameters.Explanation of Forces:When an object is placed on an inclined plane, there are two main forces acting upon it: gravity and the normal force. Gravity is the force that pulls the object downward, while the normal force is the force exerted by the plane perpendicular to the object's surface. These two forces arecrucial in determining the object's motion along the inclined plane.Example: Imagine a box placed on a ramp that isinclined at an angle of 30 degrees. The force of gravity is pulling the box downwards, while the normal force is acting perpendicular to the ramp's surface. The component of the force of gravity parallel to the ramp, known as the gravitational force component, is responsible for the box's acceleration along the ramp.Calculation of Acceleration:To calculate the acceleration of an object on an inclined plane, we need to consider the forces acting upon it. The gravitational force component can be determined using the formula F = mg sinθ, where F is thegravitational force component, m is the mass of the object, g is the acceleration due to gravity, and θ is the angle of inclination. The normal force can be calculated using the formula N = mg cosθ.Example: Let's say the box on the ramp has a mass of 5 kg. Using the given angle of 30 degrees, we can calculate the gravitational force component as F = (5 kg)(9.8 m/s^2) sin(30 degrees) = 24.5 N. The normal force can be calculated as N = (5 kg)(9.8 m/s^2) cos(30 degrees) = 42.4 N. By applying Newton's second law (F = ma), we can determine the acceleration of the box along the ramp.Frictional Force:In addition to gravity and the normal force, frictional force also plays a role in the dynamics of objects on inclined planes. Friction opposes the motion of the object and can be either static or kinetic, depending on whether the object is at rest or in motion.Example: If the box on the ramp is not moving, the frictional force acting upon it is the static friction. Once the applied force exceeds the maximum static friction, the object will start moving, and the frictional force becomes kinetic friction. The coefficient of friction, denoted as μ, is a measure of the frictional force'sstrength.Conclusion:Understanding the dynamics of inclined planes is essential in various fields, including physics and engineering. By analyzing the forces acting upon objects on inclined planes, we can determine their motion and acceleration. The gravitational force component, normal force, and frictional force are all factors to consider when studying the dynamics of inclined planes.中文回答：介绍：在这个总结中，我将讨论斜面的动力学问题。
物理英语作文
物理英语作文Title: The Wonders of Physics: Exploring the Universe。
Physics, the fundamental science that seeks to understand the behavior of matter and energy in the universe, encompasses a vast array of phenomena, from the tiniest subatomic particles to the largest celestial bodies. In this essay, we delve into the marvels of physics, exploring its profound implications and the mysteries it continues to unravel.At the heart of physics lies the quest to uncover the underlying principles governing the universe. Through empirical observation, experimentation, and mathematical modeling, physicists strive to elucidate the laws that govern the motion, forces, and interactions of all physical entities. These laws, such as Newton's laws of motion and Einstein's theory of relativity, provide the framework for understanding the dynamics of the cosmos.One of the most fascinating realms of physics is the study of particle physics, which delves into the fundamental constituents of matter and the forces that govern their interactions. The Standard Model of particle physics has successfully elucidated the properties of quarks, leptons, and gauge bosons, forming the basis of our understanding of the subatomic world. Yet, the quest for deeper insights continues, with experiments at particle accelerators such as the Large Hadron Collider probing the frontiers of particle physics and seeking to unravel the mysteries of dark matter, supersymmetry, and beyond.In addition to the microcosm of particle physics, physics also explores the macrocosm of the cosmos itself. Astrophysics and cosmology endeavor to unravel the mysteries of the universe on the largest scales, from the formation of galaxies and stars to the evolution of the cosmos as a whole. Through observations using telescopes and space probes, physicists have gained remarkableinsights into the structure, composition, and dynamics of the universe, revealing its astonishing complexity and beauty.The theory of general relativity, formulated by Albert Einstein, revolutionized our understanding of gravity and the fabric of spacetime. This theory has profound implications for cosmology, providing the theoretical framework for understanding the expanding universe, the nature of black holes, and the origin of gravitational waves. Recent discoveries, such as the detection of gravitational waves by the LIGO and Virgo collaborations, have opened new windows onto the universe, allowing us to explore phenomena previously beyond our reach.Moreover, the field of quantum mechanics challenges our intuitions about the nature of reality, revealing a realm of phenomena governed by probability and uncertainty. Quantum mechanics underpins modern technology, from transistors and lasers to quantum computers and encryption protocols. Yet, its philosophical implications continue to spark debate and intrigue, raising profound questions about the nature of observation, measurement, and the fundamental structure of the universe.Furthermore, physics intersects with numerous other disciplines, from chemistry and biology to engineering and medicine. The insights gleaned from physics research have led to transformative advances in fields such as materials science, renewable energy, and medical imaging, improving the quality of life for people around the globe.In conclusion, physics stands as a cornerstone of scientific inquiry, offering profound insights into the nature of reality and the workings of the universe. From the microscopic realm of particle physics to the cosmic expanse of astrophysics, physics continues to push the boundaries of human knowledge, revealing the wonders of the universe in all its splendor. As we continue to unravel the mysteries of the cosmos, the journey of discovery promises to be both thrilling and enlightening, enriching our understanding of the world and our place within it.。
气科院大气物理面试英语专业词汇[1]
![气科院大气物理面试英语专业词汇[1]](https://img.taocdn.com/s3/m/ebc29b211611cc7931b765ce050876323012747d.png)
大气科学系微机应用基础Primer of microcomputer applicationFORTRAN77程序设计FORTRAN77 Program Design大气科学概论An Introduction to Atmospheric Science大气探测学基础Atmospheric Sounding流体力学Fluid Dynamics天气学Synoptic Meteorology天气分析预报实验Forecast and Synoptic analysis生产实习Daily weather forecasting现代气候学基础An introduction to modern climatology卫星气象学Satellite meteorologyC语言程序设计 C Programming大气探测实验Experiment on Atmospheric Detective Technique云雾物理学Physics of Clouds and fogs动力气象学Dynamic Meteorology计算方法Calculation Method诊断分析Diagnostic Analysis中尺度气象学Meso-Microscale Synoptic Meteorology边界层气象学Boundary Layer Meteorology雷达气象学Radar Meteorology数值天气预报Numerical Weather Prediction气象统计预报Meteorological Statical Prediction大气科学中的数学方法Mathematical Methods in Atmospheric Sciences专题讲座Seminar专业英语English for Meteorological Field of Study计算机图形基础Basic of computer graphics气象业务自动化Automatic Weather Service空气污染预测与防治Prediction and Control for Air Pollution现代大气探测Advanced Atmospheric Sounding数字电子技术基础Basic of Digital Electronic Techniqul大气遥感Remote Sensing of Atmosphere模拟电子技术基础Analog Electron Technical Base大气化学Atmospheric Chemistry航空气象学Areameteorology计算机程序设计Computer Program Design数值预报模式与数值模拟Numerical Model and Numerical Simulation接口技术在大气科学中的应用Technology of Interface in Atmosphere Sciences Application海洋气象学Oceanic Meteorology现代实时天气预报技术（MICAPS系统）Advanced Short-range Weather Forecasting Technique(MICAPS system)1) atmospheric precipitation大气降水2) atmosphere science大气科学3) atmosphere大气1.The monitoring and study of atmosphere characteristics in near space as an environment forspace weapon equipments and system have been regarded more important for battle support.随着临近空间飞行器的不断发展和运用,作为武器装备和系统环境的临近空间大气特性成为作战保障的重要条件。
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Dynamics of the internal gravity waves in the heterogeneous and nonstationarystratified mediumsVitaly V. Bulatov and Yuriy V. VladimirovInstitute for Problems in MechanicsRussian Academy of SciencesPr.Vernadskogo 101-1, 117526 Moscow, Russiabulatov@index-xx.ruAbstractIn the present paper in the assumption of the slowness of variation of thevertically stratified medium parameters in the horizontal direction within the timewe have analyzed the evolution of the non-harmonic wave trains of the internalgravity waves. The particular form of the wave train can be expressed throughsome special functions, for example, Airy functions, Fresnel integrals, Pearsyintegrals, etc., and is determined by the local behavior of the dispersion curves ofthe separate modes near to the corresponding singular points. The solution of thisprob lem is possib le using the modified version of the space-time ray-tracingmethod offered b y the authors (the method of the ray optics), the fundamentaldifference of which consists, that the asymptotic notation of such a solutionshould be searched for in the form of the series using the non-integral degrees ofsome small parameter, the asymptotic forms of the solution at analysis ofevolution of the non-harmonic wave trains present in the stratified non-stationaryhorizontally-non-uniform mediums is searched in the form of the series using thenon-integral degrees of some small parameter, at that the exponent depends onthe concrete type of the wave train notation. The particular form of the notation isdetermined from the asymptotical b ehavior of the solution in the stationaryhorizontally-homogeneous event. The phase of the wave train will be determinedfrom the corresponding eikonal equation, which can be solved numerically usingthe characteristics (rays). The amplitude of the wave train is determined fromsome law of preservation along the characteristics (rays).IntroductionAs is well known, the horizontal inhomogeneity and nonstationarity exert influence on the stratified natural mediums (the ocean, the atmosphere). To the number of the most specific typical horizontal inhomogeneities of the real ocean it is possible to refer the variations of the shape of the bottom, inhomogeneity of the field of density and changeability of the average flows. The precise value of the analytical solution of the obtained problem, for example by the method of separation of variables, may be gained only in the event, if the density distribution and the shape of the bottom are described by the simple enough model functions. When the shape of the bottom and stratification are arbitrary, then it is possible only to build the asymptotic notation of the solution of the problemin the near and far zones, however for description of the field of the internal waves between these zones it is necessary to have the precise numerical solution of the problem.If the depth of the ocean and its density varies slowly, as compared with the characteristic length of the internal waves, that is rather well fulfilled at the real ocean, then at searching the solution of the problem of propagation of the internal waves above the variable shape of the bottom it is possible to use the method of geometrical optics. In the present paper the uniform asymptotic forms of the far (distant) field of the internal waves for the case of the constant depth have been developed. It was demonstrated, that the far field represents the sum of the modes, each of which is inside the Mach cone and the asymptotics of each mode is expressed through Airy functions (Airy waves) or Fresnel integrals ( Fresnel waves).In the present paper in the assumption of the slowness of variation of the vertically stratified medium parameters in the horizontal direction within the time we have analyzed the evolution of the non-harmonic wave trains of the internal gravity waves. The particular form of the wave train can be expressed through some special functions, for example, Airy functions, Fresnel integrals, Pearsy integrals, etc., and is determined by the local behavior of the dispersion curves of the separate modes near to the corresponding singular points.The solution of this problem is possible using the modified version of the space-time ray-tracing method offered by the authors (the method of the ray optics), the fundamental difference of which consists, that the asymptotic notation of such a solution should be searched for in the form of the series using the non-integral degrees of some small parameter, the asymptotic forms of the solution at analysis of evolution of the non-harmonic wave trains present in the stratified non-stationary horizontally-non-uniform mediums is searched in the form of the series using the non-integral degrees of some small parameter, at that the exponent depends on the concrete type of the wave train notation.The particular form of the notation is determined from the asymptotical behavior of the solution in the stationary horizontally-homogeneous event. The phase of the wave train will be determined from the corresponding eikonal equation, which can be solved numerically using the characteristics (rays). The amplitude of the wave train is determined from some law of preservation along the characteristics (rays).At analysis of the wave trains of the internal waves in the stratified mediums with the slow-changing parameters usually it is supposed, that such a wave train is locally harmonic. Unlike the majority of the publications devoted to this problem study, the modified method of the ray optics developed by the authors in the form of some special functions expansion enables to describe the structure of the wave fields near to and far from the wavefronts. The problems concerning the evolution of the non-harmonic wave trains of the internal gravity waves in the layer of the arbitrarily stratified medium of the variable depth with the non-stationary and non-uniform in the horizontal direction density.Using the asymptotic notations of the wave field at the great spacing intervals from the source for the event of the constant bottom, the problem to construct the uniform asymptotics of the far field for the case of the slow-varying bottom is solved by one of the modified method of the ray optics - by the method of " the vertical modes - the horizontal rays " (within the given method of the slowness, the variations in the vertical direction are not supposed).The gained solutions represent expansions of the special type waves - Airy or Fresnel waves, and describe not only the evolution of these non-harmonic wave trains at their propagation above the slow-varying bottom, but also the structure of the wave field of each separate mode both near and far from the wavefronts of the separate modes.The independent variable of Airy or Fresnel waves is determined from the solution of the corresponding eikonal equation. The amplitude of the wave field at that is determined from the law of conservation of energy along the ray tube.For the model distributions of the shape of the bottom and stratification describing the typical structure of the ocean shelf we have developed the exact analytical expressions for the rays and the analyzed singularities of the phase structure of the wave field. In particular it was shown, that depending on the path of the source motion, the shape of the bottom, and stratifications there may appear the different singularities of the structure of the wave fields. We have analyzed the effect of the spatial " shutting " concerning the low-frequency components of the wave field, which is generated at the source movement at supercritical speed along the ocean shore.Similarly we have built the asymptotic notations of the solutions on propagation of the non-harmonic wave trains in the heterogeneous in the horizontal direction medium and in the non-stationary density. The conducted.numerical calculations for the typical oceanic parameters indicate the essential influence of the factors of the non-stationarity and the horizontal heterogeneity of the natural parameters on the real dynamics of the internal gravity waves [1-31].1. Basic concepts of the method of the geometric opticsThe present section presents the basic provisions of the method of the geometric optics or Wentzel-Kramers-Brillouin (WKB) approximations with consideration of the specificity of the internal gravitational waves. If to consider the internal waves for the case, when the undisturbed field of density )y ,x ,z (0U depends not only on the depth z , but also on the horizontal coordinates x and y , then, generally speaking, if the undisturbed density is the function of the horizontal coordinates, then such a density distribution forms some field of the horizontal flows. H owever these flows are rather slow and as a first approximation they can be neglected, and so it is usually considered, that the field )y ,x ,z (0U is set a priori and thereby one may suppose the presence of some exterior sources, or the non-conservatism of the system under analysis. It is also quite evident, that, if the internal waves are propagated above the irregular bottom, then such problem does not originate, because the system “the internal wave – the irregular bottom” is conservative and there is no inflow of the energy from the outside. Let’s further consider the linearized system of the equations of hydrodynamics: x p t U ~10w w w w U y p t U ~20w w w w U U w w w w U g z p t W ~0 (1.1) 0zW ~y U ~x U ~21 w w w w w w 0z W ~y U ~x U ~t 00201 w U w w U w w U w w U w Here )W ~,U ~,U ~(21 are the vectors of velocity of the internal gravitational waves, p and U are disturbances of the pressure and density, g - an acceleration of gravity (z -axis is directed downwards).Using Boissinesq approximation, which means, that the density )y ,x ,z (0U in the first three equations of the system (1.1) is considered as a constant value, with the help of the crossover differentiation we shall re-arrange the system (1.1) into: 0)z W ~y U ~x U ~(g t W ~t z W ~00201022224 w U w w U w w U w 'U w w ' w w w 0)xz W ~U ~(t 21 w w w 'w w (1.2)0)yz W ~U ~(t 22 w w w 'w w where 2222y /x /w w w w '.As the boundary conditions we shall use the condition of "the solid cover"0W atH ,0z . (1.3) Let’s consider the harmonic waves )W ,U ,U (e )W ~,U ~,U ~(21t i 21Z and introduce the dimensionless variables in the formulas,hz z ,L y y ,L x xwhere L is the characteristic scale of variation of 0U in the horizontal direction, h is the characteristic scale of variation of 0U in the vertical direction (for example, the width of the thermocline).In the dimensionless coordinates (1.2) we shall have the following view (the character further down is omitted):,0)z W y U x U (g )W zW (002010122222 w U w w U w H w U w H U H 'H w w Z 0xz W U 21 w w w 'H ,0y z W U 22 w w w 'H , (1.4) where 1Lh H ,h g g 1 . The asymptotic solution of (1.4) we shall express in the form, which is typical for the method of the geometrical optics:H f ¦Hi )y ,x (S m 0m m e )y ,x ,z ()i ()y ,x ,z (V V , (1.5)where ))y ,x ,z (W ),y ,x ,z (U ),y ,x ,z (U ()y ,x ,z (21 V . Functions )y ,x (S and ,...1.0, m m V are the subject for determination. Later on we shall confine to the search only for the major member of the expansion (1.5) for the vertical component of the velocity )y ,x ,z (W 0. At that from the two last equations of (1.4) we shall have:z W Sx /S i U 0210w w w w , (1.6) z W Sy /S i U 0220w w w w Where: 22y S x S S ¸¸¹·¨¨©§w w ¸¹·¨©§w w . Insert (1.5) into the first equation of the system (1.4) and equate the terms of O (1) order:,0W 1)y ,x ,z (N S z W 0222202 ¸¸¹·¨¨©§ Z w w (1.7) ,0)y ,x ,H (W )y ,x ,0(W 00 where zg )y ,x ,z (N 0012w U w U - Brunt-Väisälä frequency depending on the horizontal coordinates For the function )y ,x (S we shall have the eikonal equation:)y ,x (K y S x S 222 ¸¸¹·¨¨©§w w ¸¹·¨©§w w (1.8) The initial conditions for S eikonal equation for a planar case are set on the link: )(y ),(x :00D D L )(S )y ,x (S 0D L .For the solution of the eikonal equation it is necessary to plot the rays, i.e. the characteristics of the equation (1.8))y ,x (K p d dx V ,x)y ,x (K d dp w w V , (1.9) )y ,x (K q d dy V ,y)y ,x (K d dq w w Vwhere V w w w w d ,y /S q ,x /S p - a ray length element .The initial conditions 0p and 0q we shall determine from the system of the equations (1.9)Dw w D w w D w w 00000S y q x p ))(y ),(x (K q p 0022020D D and the initial conditions )(q ),(p ),(y ),(x 0000D D D D shall determine the ray ),(y y ),,(x x D V D V . After determination of the beams the eikonal S is being determined by integration over the be ³VV D V D V D 00d )),(y ),,(x (K )(S S(1.10)Now we shall move to determination of the eigenfunction )y ,x ,z (W 0. We would like to underline, that from (1.7) it is possible to determine only the vertical dependence of the eigenfunction )y ,x ,z (W 0. In other words, the eigenfunction 0W may be determined with the accuracy up to the multiplication by the arbitrary function )y ,x (A 0. Now we shall determine 0W in the form of)y ,x ,z (Wˆ)y ,x (A )y ,x ,z (W 000 (1.11), where )y ,x ,z (Wˆ0 is the solution of the problem (1.7) normalized to the following view ³ Z H20221dz )y ,x ,z (W ˆ))y ,x ,z (N (. (1.12) Let’s equate the terms of )(O H order after substituting (1.5) into (1.4). 020001002212222122W )S N (2z W )S (g )S W S W 2)(N (W 1)y ,x ,z (N K z W w w U U ' Z ¸¸¹·¨¨©§¸¸¹·¨¨©§ Z w w Z ,)y ,x ,H (W )y ,x ,0(W 11 .(1.13) Further we shall take advantage of the condition of orthogonality of the right part of the equation (1.13) to the function )y ,x ,z (W 0. Multiplying (1.13) by 0W and integrating by z from 0 up to H , we shall receive:³³³ w w U Z H 0202H 0200H0120220dz W )S )y ,x ,z (N (2dz )z W )(ln S (2g dz )S W ())y ,x ,z (N (. (1.14)Transform the second item in (1.14) using integration by parts and the zero boundary conditions for 0W :³³ w w U H 0202H 02001dz W N 2S dz )z W )(ln S (2g .(1.15)Transform the first item of (1.14) considering (1.12):³³ Z H0202H 0202022dz W )N S ()S A (dz )S W ()N (.(1.16)To transform the third item of (1.14), we shall apply the operator of the gradient to the equation (3.1.7), considering 0W Y :01)y ,x ,z (N )y ,x (K W 1)y ,x ,z (N )y ,x (K z )y ,x ,z (222022222 »»¼º««¬ª¸¸¹·¨¨©§ Z ¸¸¹·¨¨©§ Z w w Y Y . (1.17).Multiplying (1.17) by 0W and integrating by z from 0 up to H and considering (1.12), we shall receive:)y ,x (K ln )y ,x (A 2dz )y ,x ,z (N W H020220 ³. (1.18)Finally, we shall rewrite the equation (1.14) using (1.15), (1.16) and (1.18)0K ln S 3S A S A 2020 ' .(1.19) The transport equation (1.19) we shall solve using characteristics of the eikonal equation (1.9). Using expression for S ' along the beams)JK (d d J 1S V',where: )y ,x (J is the geometrical divergence of the beams. Then we shall transform the transport equation (1.19) to the following law of energy conservation along the rays:0)y ,x (K )y ,x (J )y ,x (A ln d d 220 ¸¸¹·¨¨©§V . (1.20) The law of the energy conservation (1.20) can be recorded also in the form suitable for finding 0A function:))(y ),(x (a d ))(y ),(x (K ))(y ),(x (A )),(y ),,(x (a d )),(y ),,(x (K )),(y ),,(x (A 000020020220D D D D D D D V D V D V D V D V D V (1.21),where: D D V D V D V D V d )),(y ),,(x (J )),(y ),,(x (a d is the width of an elementary ray tube. Weshall mark, that the current of the wave energy is proportional to da K A 120 , so the (1.21) shows,that in this case the value equal to the current of the wave energy divided by the modulus of the wave vector is kept safe.For transition to the study of the problem of the non-harmonic wave packet s in the smoothly heterogenous in horizontal direction and the non-stationary stratified medium before selection of ansatzs (Anzatz (german.) - a kind of solution), describing propagation of Airy and Fresnel subsurface waves, let’s first consider some leading considerations.Airy surface wave. Inject the slow variables t t ,y y ,x x H H H (for z - slowness the variations are not supposed, the character further is neglected), where 1L / O H is the small parameter characterizing the smoothness of the medium variation in the horizontal direction (O - the characteristic length of the wave, L - the scale of the horizontal heterogeneity). Then the system (1.2) with the slow variables will look like this:0)z W y U x U (g t W t z W 002010222224 w U w w U w H w U w H 'U w w H w w w (1.22) 0x z W U 21 w w w 'H 0yz W U 22 w w w 'H . Further, we shall consider the superposition of the cosine waves (with the slow variables t ,y ,x ):>@Z Z H Z Z Z H f ³¦d e )y ,x ,z ,(W )i (W )y ,x ,(S t i 0m m m m .(3.1.23) Concerning functions )y ,x ,(S m Z it is supposed, that they are odd for Z and their Z w w Z /S min isreached at 0 Z (for all x and y ).Substituting (1.23) in (1.22) it will easy to demonstrate, that the function )y ,x ,z ,(W m Z at 0 Z has a pole of m-th order. Therefore the model integrals )(V m R for the separate units in (1.23) will be the following expressions:Z ZZ S V VZ d e i R i m m ¸¸¸¹·¨¨¨©§ f f ³¸¹·¨©§ 31321)(,where the contour of the integration bends around the dot 0 Z from above, that ensures the exponential fading of the functions )(V m R at 1 V . Functions )(V m R possess the following property:)()(1V VV m m R d R d ,At that )()(0V V i A R c ,)()(1V V Ai R ,du u Ai R ³fV V )()(2 etc.It is obvious, that proceeding from the corresponding properties of Airy integrals, the )(V m R functions are connected to each other by the following ratios:)()(11 V V V R R 0)()(2)(1203 V V V V R R R .Fresnel wave. As the model integrals )(V m R describing propagation of Fresnel waves, proceeding from the structure of the solution for the elevation in the horizontally homogeneous case following expressions are used:)()(Re 2exp Re )(*020V V V V ){){¸¸¹·¨¨©§ ³f dt t i it R It quite evident, that function )(*V )possesses the following property:³)f dt i it it d d t )21exp()(20*V V V )(1)21exp()21()21exp(*20220V V V V V V ) ³³f f i dt t i it i t i it d i it t whence, for example, it is possible to obtain:V V V V V V V d d i d d i d d )(2)()(*2*23*3))) or (in terms of functions )(V m R ):0)()(01 V V V R i R 0)()(2)(213 V V V V R i R i R .Proceeding from the above-stated, and also from the structure of the first item of the uniform asymptotics of Airy and the Fresnel waves in the horizontally uniform medium, the solution of the system (1.22), for example, it is possible to find in the form of (for the separately taken mode n W n U with the following exclusion of “n ”index):. )(),,,()(),,,()(),,,(22211000V H V H V H R t y x z W R t y x z W R t y x z W W a a (1.24). )(),,,()(),,,()(),,,(32121101V H V H V H R t y x z R t y x z R t y x z a a U U U U ,where: argument a at y x S a ¸¹·¨©§ H V ),,(1.is considered of the order of unity. Expansion (1.24) will be in accord with the general approach of the ray optics method and the space-time ray-tracing method.Let us also to note, that from the similar structure of the solution follows, that in the heterogeneous in horizontal direction and the non-stationary medium the solution depends both on the "fast" (the vertical coordinate), and the "slow" (the time and horizontal coordinates) variables. Further we shall look for the solution, as a rule, in the "slow" variables. At that those structural members of the solution, which depends on the "fast" variables, are received in the form of the integrals from some slowly-variable functions along the time-space beams. The given method of the solution allows to present the uniform asymptotes of the fields of the internal gravitational waves propagating in the stratified mediums with the slowly-variable parameters, which is true both in the close vicinity and at the far distance from the wave fronts of a separate wave mode. If it is necessary to describe the behavior of the field only near to the wave front, it is possible to use one of the methods of the ray optics – the method of "traveling wave", and also the low-dispersive approximation in the form of the corresponding local asymptotes and to look for presentation for the argument of the phase functions V in the form of the separate wave mode: H H D V a t y x t S y x t )),,()(,,(,where the function ),,(y x t S presents the wave front position and is determined from the solution of the eikonal equation),,(22t y x c S where ),,(y x t c - the maximum group velocity of the corresponding mode, that is the first term of expansion of the dispersing curve in zero. The function ),,(y x t D (the second term of the expansion of the dispersing curve) describes space-time evolution of the pulse width of Airy and Fresnel waves and then will be determined from some energy conservation laws along the characteristics of an eikonal equation, which concrete composition is determined by the physical conditions of the problem.2. Uniform asymptotics of the far field of the internal gravity waves in the layer of thestratified medium with the smoothly varying bottomIn this section we present the built uniform asymptotics of the far field of the internal gravity waves during motion of the point source of mass of the single intensity in the layer of the random stratified liquid with the slowly varying ocean bottom. The gained solutions describe the far field both near to the wave fronts of each separate mode, and far from wave fronts and represent expansions into Airy waves and Fresnel waves, which argument is determined from the solution of the applicable equation of the eikonal. The amplitude of the wave field is determined from the energy conservation law along the ray tube. For the model distributions of the form of the bottom and the stratification, there have been gained the exact analytical notations for rays are gained and the wave field phase structure features have been analyzed.Formulation of the problem and selection of the kind of the solution.Let the point source of mass moves in the layer 0z )y ,x (H H H (H - the small argument) of the stratified liquid with Brunt-Väisälä frequency )z (N 2. It is assumed, that the velocity V of the source movement along x axis exceeds the maximal group velocity of propagation of the internal waves, that is the source is moving with the supercritical velocity.From linearized system of equations of hydrodynamics in Boissinesq approximation we have (see Chapter 1-2))z z ()y ()Vt x (w )z (N w z t 0tt 22222 G c G G c c ' ¸¸¹·¨¨©§w w 'w w ))y ()Vt x (()z z (zw 0G G G w w ' u (2.1) 2222yx w w w w ',¸¸¹·¨¨©§w w w w y ,x Where )u ,u (21 u - the vector of the horizontal velocities, w - the vertical component of velocity, 0z - depth of the source motion.As the boundary conditions on the surface the “solid cover” condition is used, at the bottom )y ,x (H z H H we have the non-flow conditionz ,0w ),y ,x (H w H H u )y ,x (H z H H . (2.2) Solution of the problem (2.1) - (2.2) we shall look for proceeding from the structure of the uniform asymptotics for const )y ,x (H , in the form of the sum of modes, each of which is propagating independently from each other (“adiabatic approximation”} and can be presented in the form of the following asimptotic series:. V H H H H V H H H )(R )t ,z ,y ,x (B )(R )t ,z ,y ,x (A w 1a 0(2.3) . H V H H H 1a 10)(R )t ,z ,y ,x (u u (2.4))(R )(R i 1i V V c ,aa )t ,y ,x (S ¸¹·¨©§H H H H {V Functions )t ,y ,x (S H H H , )t ,z ,y ,x (A H H H , )t ,z ,y ,x (0H H H u in (2.3), (2.4) are the subject to determiation. The argument )t ,y ,x (V is of the order of a unit. The function )(R 0V depending on presence of the homogeneous (non-stratified) sublayer is expressed through Airy function (Airy wave) or through Fresnel integrals (Fresnel wave). Later on without any limitation of generality we shall consider, for example, propagations of Fresnel wave elevation )t /w (w K w K ),()(Re 2exp Re )(*020V V V V ){){¸¸¹·¨¨©§ ³fdt t i it R 21a meeting the following ratios:)(1)(**V V V V ) )i d d V V V V V V V d d i d d i d d )(2)()(*2*23*3) ) )Eikonal equation and characteristics. Geometry of the wave field phase structure.Now we shall transfer to determination of S function. Substituting (2.3), (2.4) in (2.1) with accuracy up to the terms of the order23H it is possible to gain)(O y S x S SS 2A 2322z 0H ¸¸¹·¨¨©§¸¸¹·¨¨©§w w ¸¹·¨©§w w H c u (2.5)Having substituted (2.3), (2.5) in (2.1), (2.2) and having equated the terms at the equal degreesH , we shall gain at 21H0A 1)z (N z A 22222 ¸¸¹·¨¨©§ Z w w k (2.6))y ,x (H ,0z ,0A t/S ,S (p,q)w w Z { k The dispersion dependence designated further through )y ,x ,(K Z , is determined from the solution of the vertical spectral problem (2.6), Z - the spectral parameter. Then for determination of function S we have the eikonal equation)y ,x ,(K y S x S 222Z ¸¸¹·¨¨©§w w ¸¹·¨©§w w (2.7)The equation (2.7) is H amilton-Jacobi equation with the Hamiltonian )y ,x ,(K 22Z k and the characteristic system of this equation looks like0d d ,)y ,x ,(K )y ,x ,(K d dq ,)y ,x ,(K )y ,x ,(K d dp )y ,x ,(K )y ,x ,(K q d dy ,)y ,x ,(K )y ,x ,(K p d dx ''y ''x '' W Z Z Z W Z Z W Z Z W Z Z W Z Z Z Z (2.8)Having solved the characteristic system (2.8) with the corresponding initial conditions, we gain the two-parameter set of the time-space rays depending on the ray coordinates. At that the choice of the initial conditions and the ray coordinates is determined by the particular kind of the being solved problem. Then the eikonal expressed in ray coordinates )t ,y ,x (S )m ,l (S { can be determined by integration along these rays.As the model instance enabling the analytical solution of the system (2.8) and at the same time qualitatively truly describing the real bottom configuration, we shall consider the following example. Let Brunt-Väisälä frequency is constant const N )z (N and the depth of the bottom depends only on one coordinate y linearly y )y (H E . Now we shall introduce the coordinate system with x -axis going along the shore 0y .Let the point source of mass moves from the right to the left in the negative direction of the x axis at the velocity V at the distance 0y offshore and at that in each moment of time t generates the waves of all frequencies within the range N 0 Z . We shall consider the first mode. Further at const )z (N from (2.6) we shall have22222N )y (H )y ,(K ),y ,(K q p Z SZ Z Z As function )y ,(K Z does not depend on x , then from (2.8) we shall gain222V)y ,(K q ,const V p ,0d dp Z Z r Z WThen the characteristic system and the initial conditions for the eikonal equation will look likeS E J Z D DJ J D r W J D W N ,N1t t ,y y ,t t ,Vt x V y 1y d dy ,y Vd dx 220000222232222 (2.9)。