Physics
Water Wave
A water wave is a disturbance that travels through water, transferring energy from one place to another. It is characterized by the oscillation of water particles, causing the surface of the water to rise and fall. Water waves can be created by wind, seismic activity, or the motion of an object through the water.
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12 Key excerpts on "Water Wave"
eBook - PDF- Birendra Nath Mandal, Soumen De(Authors)
- 2015(Publication Date)
- CRC Press(Publisher)
CHAPTER I Introduction When a particle in a continuous medium is slightly disturbed from its position of rest then the disturbance is transferred to the neighboring particles and these particles disturb further particles. In this manner the disturbance thus created travels with a de fi nite velocity throughout the medium. This is generally referred to as wave motion. Thus a wave may be regarded as a progressive disturbance propagating from point to point in a continuous medium without displacement of the points. Waves are encountered in almost all branches of mathematical physics such as continuum mechanics, quantum mechanics, acoustics, electromagnetic theory, etc. A wave may be intuitively de fi ned as a recognizable signal that is transferred from one part of a medium to another part, and the signal may be any feature of disturbance which is clearly recognizable and its location at any time can be determined. Ever science waves were studied Water Waves have served the scientists as models since these can be viewed by the naked eye. Waves are generated due to the existence of some kind of restoring force that tends to bring the system back to its undisturbed state and some kind of inertia that causes the system to overshoot after the system returned to the undisturbed state. One of the common wave motions with which we are most familiar is that of waves occurring at free surface of the liquid with gravity playing the role of the restoring force. These waves are called surface gravity waves. Water Waves are such waves. The various wave phenomena in water with a free surface and under gravity have attracted the attention of many famous physicists and mathematician from the eighteenth century. An incomplete list of them includes A.L. Cauchy (1758–1857), S.D. Poisson (1781–1840), J.L. Lagrange (1736–1813), G.B. Airy (1801–1892), G.G. Stokes (1819–1903), Lord Kelvin (Sir William Thompson) (1824–1907), J.H.
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
The buoy survived the difficult ocean environment, including operation off the New Jersey coast through Hurricane Irene in 2011. The concepts presented in this chapter will be the foundation for many interesting topics, from the transmission of information to the concepts of quantum mechanics. Chapter 16 | Waves 795 16.1 | Traveling Waves Learning Objectives By the end of this section, you will be able to: • Describe the basic characteristics of wave motion • Define the terms wavelength, amplitude, period, frequency, and wave speed • Explain the difference between longitudinal and transverse waves, and give examples of each type • List the different types of waves We saw in Oscillations that oscillatory motion is an important type of behavior that can be used to model a wide range of physical phenomena. Oscillatory motion is also important because oscillations can generate waves, which are of fundamental importance in physics. Many of the terms and equations we studied in the chapter on oscillations apply equally well to wave motion (Figure 16.2). Figure 16.2 An ocean wave is probably the first picture that comes to mind when you hear the word “wave.” Although this breaking wave, and ocean waves in general, have apparent similarities to the basic wave characteristics we will discuss, the mechanisms driving ocean waves are highly complex and beyond the scope of this chapter. It may seem natural, and even advantageous, to apply the concepts in this chapter to ocean waves, but ocean waves are nonlinear, and the simple models presented in this chapter do not fully explain them. (credit: Steve Jurvetson) Types of Waves A wave is a disturbance that propagates, or moves from the place it was created. There are three basic types of waves: mechanical waves, electromagnetic waves, and matter waves. Basic mechanical waves are governed by Newton’s laws and require a medium.
eBook - PDFWaves, Tides and Shallow-Water Processes
Waves, Tides and Shallow-Water Processes
- Open Open University, Joan Brown, Gerry Bearman(Authors)
- 2013(Publication Date)
- Butterworth-Heinemann(Publisher)
Waves that are caused by periodic forces, such as the effect of the Sun and Moon causing the tides, will have periods coinciding with the causative forces. This aspect is considered in more detail in Chapter 2. Most other waves, however, result from a non-periodic disturbance of the water. The water particles are displaced from an equilibrium position, and to regain that position require a restoring force. In the case of Water Waves, the particle motion resulting from the restoring force acting upon one wave cycle provides the displacing force acting upon the next cycle. Such alternate displacements and restorations establish a characteristic oscillatory 'wave motion', which in its simplest form has sinusoidal characteristics (Figures 1.1 and 1.6), and is sometimes referred to as simple harmonic motion. In the case of surface waves on water, there are two such restoring forces which maintain wave progress: 1 The gravitational force exerted by the Earth. 2 Surface tension, which is the tendency of water molecules to stick together and present the smallest possible surface to the air. So far as the effect on Water Waves is concerned, it is as if a weak elastic skin were stretched over the water surface. Water Waves are affected by both of these forces. In the case of waves with wavelengths less than about 1.7cm, the principal maintaining force is surface tension, and such waves are known as capillary waves. Capillary waves are important in the context of remote sensing of the oceans (Section 1.6.1). However, the main interest of oceanographers lies with surface waves of wavelengths greater than 1.7cm, and the principal maintaining force for such waves is gravity; hence they are known as gravity waves. Figure 1.2 summarizes some wave types and their causes. Not all waves are displaced in a vertical plane. Because atmosphere and oceans are on a rotating Earth, variation of planetary vorticity with latitude causes deflection of atmospheric and oceanic currents, and
eBook - PDFEnvironmental Oceanography
An Introduction to the Behaviour of Coastal Waters
- Tom Beer(Author)
- 2013(Publication Date)
- Pergamon(Publisher)
C H A P T E R 3 Waves We are all familiar with the concept of a Water Wave. A sugar cube dropped into a cup of tea will generate waves that travel radially outwards; a breeze blowing over a river will produce waves that will move in the direction of the wind on the surface of the river, even though the current may be flowing in some other direction. These examples of wave motions in a liquid have two properties in common with all other types of waves: firstly, energy is being propagated from one point to another; secondly, the disturbance travels through the medium without giving the medium as a whole any permanent displacement. Follow the motion of a cork floating on the water surface as waves pass; the cork rises and falls and at the same time moves back and forth, describing a circular motion whose diameter is the wave height. The cork makes very little nett advance in the direction of wave motion, illustrating that the water itself does not move along with the wave form. The period of a wave is the time for successive crests to arrive at the cork and it is an easily measured quantity, provided that you are equipped with a watch. Waves on the surface of the sea can be conveniently grouped in terms of their period as shown in Table 3.1. TABLE 3.1. Surface Wave Types Period (T) Wave type Commonly seen as < 1 s capillary waves ripples ~ 1 s wind waves (chop) cat's paws ~ 10 s swell breakers minutes seiches harbour oscillations hours tides tides The wind is responsible for generating both wind waves and swell. Wind waves, or chop, are the short, bumpy, sharp crested waves that appear in windy condi-tions. Swell is the slow, gently rolling waves that impinge on an exposed shore-line even on calm days. Swell is produced by storms a long way away from the point of observation. Typically, the swell on the Californian coast is a product of storms near New Zealand. On the other hand, choppy seas due to strong wind conditions are the result of local wind generation.
eBook - PDFFly by Night Physics
How Physicists Use the Backs of Envelopes
- Anthony Zee, A. Zee(Authors)
- 2020(Publication Date)
- Princeton University Press(Publisher)
Part VIII From surfing to tsunamis, from dripping faucets to mammalian lungs VIII.1 C H A P T E R Water Waves Water Waves are awesome I am guessing that in your daily life, you have seen Water Waves (on the surface of a pond, for example) a lot more often than falling apples or colliding billiard balls. You also appreciate that Water Waves display a bewildering variety of behavior, from soothing ripples to pounding surfs. Waves and dispersion Let us start by reviewing some basic concepts about waves in general, not restricted to Water Waves. A wave is characterized by its period T and wavelength λ , namely, its variations in time and space, respectively. As in chapter I.1, introduce circular frequency 1 ω ≡ 2 π/ T . Also, recall the wave num-ber vector k , defined to point in the direction that the wave is propagating, with magnitude k ≡ 2 π/λ = | k | . Then the wave can be written variously as cos (ω t − k · x ) , sin (ω t − k · x ) , or in complex notation, ∗ e i (ω t − k · x ) . Often, it is convenient to simply write k for k . The context should make things clear. We will also refer to ω simply as frequency. Much of this has already been discussed in connection with electromagnetic waves in part II. You understand that the vector k is a more basic concept than the ele-mentary wavelength λ , which does not transform naturally under rotations. However, our brains evolved to perceive period and wavelength more directly than frequency and wave number. (Recall the remark about x versus 1 / x in ∗ As usual, it is understood that either the real or imaginary part is taken. 270 Chapter VIII.1 chapter III.5.) Thus, we will often end up interchanging these two reciprocal sets of variables. Dispersion relation: group versus phase speed How the frequency ω = ω( k ) depends on k is known as a dispersion relation. Perhaps you are already familiar with the concepts of phase velocity and group velocity. I review these in appendix Grp for those readers who are not.
eBook - PDF- Tsutomu Kambe(Author)
- 2007(Publication Date)
- World Scientific(Publisher)
Chapter 6 Water Waves and sound waves Fluid motions are characterized by two different elements, i.e. vor-tices and waves . In this chapter, we consider Water Waves and sound waves. There exists a fundamental difference in character between the two waves from a physical point of view. The vortices will be considered in the next chapter. A liquid at rest in a gravitational field is in general bounded above by a free surface. Once this free surface experiences some disturbance, it is deformed from its equilibrium state, generating fluid motion. Then, the deformation propagates over the surface as a wave. Waves are observed on water almost at any time and are called Water Waves which are sometimes called a surface wave . The surface wave is a kind of dispersive waves whose phase velocity depends on its wave length. On the other hand, a sound wave is nondispersive and the phase velocity of different wave lengths take the same value. This results in a remarkable consequence, i.e. invariance of wave form during propagation. 6.1. Hydrostatic pressure Suppose that water of uniform density ρ is at rest in a uniform field of gravity. Then, setting v = 0 and f = g = (0 , 0 , − g ) in (5.2), with respect to the ( x, y, z )-cartesian frame, the z axis taken verti-cally upward (where g is a constant of gravitational acceleration), 115 116 Water Waves and sound waves the Euler equation of motion reduces to grad p = ρ g , = ρ (0 , 0 , − g ) . (6.1) Horizontal x and y components and vertical z component of this equation are ∂p ∂x = 0 , ∂p ∂y = 0 , ∂p ∂z = − ρg. Since the density ρ is a constant, we obtain p = p ( z ) := − ρgz + const . Provided that the pressure on the surface is equal to the uniform value p 0 (the atmospheric pressure) at every point, the surface is given by z = const . , called the horizontal plane . Since the surface is determined by the pressure solely without any other constraint, it is also called a free surface .
eBook - PDFOceanography
An Invitation to Marine Science
- Tom Garrison(Author)
- 2015(Publication Date)
- Cengage Learning EMEA(Publisher)
Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. WAVES 285 uniform circular movement of water molecules in one direction as the waves pass. Figure 10.4 indicates that water molecules in the crest of a passing wave move in the same direction as the wave, but mol-ecules in the trough move in the opposite direction. If particle speed decreases with depth, molecules in the top half of the orbit will move farther forward in the direction the wave is moving than molecules in the bottom half of the orbit will move back-ward (Figure 10.5) . This flow, known as Stokes drift , is important in driving the ocean surface currents you studied in Chapter 9. C O N C E P T C H E C K Before going on to the next section, check your understanding of some of the important ideas presented so far: We wrote that an ocean wave is, in a sense, an illusion. What’s actually moving in an ocean wave? Draw an ocean wave and label its parts. Include a definition of wave period. 10.2 Waves Are Classified by Their Physical Characteristics Ocean waves are classified by the disturbing force that creates them, the extent to which the disturbing force continues to influence the waves once they are formed, the restoring force that tries to flatten them, and their wavelength. (Wave height is not often used for classification because it varies greatly depending on water depth, interference between waves, and other factors.) Ocean Waves Are Formed by a Disturbing Force Energy that causes ocean waves to form is called a disturbing force . Wind blowing across the ocean surface provides the dis-turbing force for capillary waves and wind waves. The arrival of a storm surge or seismic sea wave in an enclosed harbor or bay, or a sudden change in atmospheric pressure, is the disturbing force for the resonant rocking of water known as a seiche.
eBook - PDFElementary Classical Hydrodynamics
The Commonwealth and International Library: Mathematics Division
- B. H. Chirgwin, C. Plumpton, W. J. Langford, E. A. Maxwell, C. Plumpton(Authors)
- 2013(Publication Date)
- Pergamon(Publisher)
CHAPTER 5 WAVES IN LIQUIDS 5.1. Fundamental concepts In this chapter we consider the effect of small disturbances from the equilibrium state upon a uniform inviscid, incompressible liquid which has a free surface and upon which the only body force acting is uniform gravity. From the results of § 1.6 it follows that, in equilibrium, the free surface is a horizontal plane. A fun-damental assumption of the theory is that all disturbances are due to movements of the boundaries, e.g. movements due to variable wind pressure on the free surface, so that (cf. § 3.4) the motion is irrotational, being derived from a velocity potential cj) where v = grad
eBook - PDF- John Kimball(Author)
- 2015(Publication Date)
- CRC Press(Publisher)
147 5 W AVES 5.1 Introduction Waves are everywhere. Sound waves, radio waves, and light waves are as much a part of the world we know as solids, liquids, and gasses. After an overview of general wave properties with some examples, the descriptions emphasize sound and light waves because without these waves we would be lost. Two of our five senses, vision and hearing, interpret light and sound waves and tell us almost every-thing we know. 5.2 Common Features of Waves The geometries of sound and light waves are suggested by the Water Waves (gravity waves) that can be seen on the surface of a lake or a bathtub. But, the analogy should be approached with caution. In many ways, sound and light are simpler than both Water Waves and the wave function of quantum mechanics (Chapter 6). The Water Waves in Figure 5.1 spread out in circles. A long way from the center, the wave peaks and valleys are nearly straight lines. The waves become nearly “plane waves” with a shape that varies only in the direction pointed away from the wave source. Far from the source, light and sound waves also approach plane wave shape. 5.2.1 Wavelength, Frequency, Speed, Amplitude, and Energy The simplest wave geometry is the plane wave. The simplest plane wave shape is the “sine wave” shown in Figure 5.2. Any wave shape can be constructed by adding together various sine waves, so the sine wave building blocks of all waves deserve special attention. 148 PHYSICS CURIOSITIES, ODDITIES, AND NOVELTIES Sine waves are characterized by three quantities: wavelength, fre-quency, and amplitude. The wavelength is the distance between wave peaks. The frequency is the number of times a wave oscillates up and down each second. The amplitude is the height of the wave. The speed of a wave is the distance one of the wave peaks moves in 1 second. It is related to wavelength and frequency by an impor-tant equation.
eBook - PDF- Mitsuhiro Tanaka(Author)
- 2022(Publication Date)
- Springer(Publisher)
This is because the degree of penetration of motion in the direction toward the bottom changes depending on the wavelength, and also because the ratio of kinetic energy in the hori- 11 For a general theory of small oscillation around an equilibrium, see, for example, Chapter 6 of Goldstein [2]. 56 3. BASICS OF LINEAR Water WaveS zontal direction to that in the vertical direction changes depending on the wavelength. It can be said that this wavelength dependence of “inertia” produces the wavelength dependence of the frequency, that is, the dispersion of Water Waves. 3.3.3 ENERGY FLUX AND VELOCITY OF ENERGY PROPAGATION Next, let us consider the energy flux and energy propagation velocity associated with the linear sinusoidal wave (3.46). The energy flux, that is, the flow of energy F x in the positive x direc- tion per unit time, which crosses a vertical cross section perpendicular to the wave propagation directions, is composed of two parts: (1) by a portion of water with energy crossing the section; and (2) by the excess pressure generated by the wave doing work. If the wave amplitude is denoted as a, the energy density is O.a 2 / and the flow velocity is O.a/, so the part (1) is a quantity of O.a 3 /. On the other hand, in the part (2), the excess pressure by the wave is O.a/, and the displacement per unit time, that is, the flow velocity is O.a/, so the magnitude of its contribution is of O.a 2 /. Therefore, in linear theory where a is very small, the part (1) can be ignored compared to the part (2). Linearizing the Euler equation 12 which is an equation of motion for an inviscid fluid, and write its x component we get @u @t D 1 @p @x : (3.66) By using u D @ =@x here, we obtain p D @ @t D c @ @x : (3.67) Here, for the second equal sign, we have used the fact that @ @t D c @ @x holds because the sinu- soidal wave translates at a speed c .
eBook - PDF- Murry L. Salby(Author)
- 2012(Publication Date)
- Cambridge University Press(Publisher)
CHAPTER FOURTEEN Wave propagation The governing equations support several forms of wave motion. Atmospheric waves are excited when air is disturbed from equilibrium (e.g., mechanically when air is dis-placed over elevated terrain or thermally when air is heated inside convection). By transferring momentum, wave motions convey the influence of one region to another. This mechanism of interaction enables tropical convection to influence the extratrop-ical circulation. It also enables the troposphere to perturb the stratosphere, driving it out of radiative equilibrium (Fig. 8.27). 14.1 DESCRIPTION OF WAVE PROPAGATION Wave motion is possible in the presence of a positive restoring force. By opposing disturbances from equilibrium, the latter supports local oscillations in field properties. Under stable stratification, buoyancy provides such a restoring force (Sec. 7.3). The compressibility of air provides another. The variation with latitude of the Coriolis force provides yet another restoring force. It will be seen to support large-scale atmospheric disturbances. 14.1.1 Surface Water Waves The description of wave motion is illustrated with an example under nonrotat-ing conditions, which will serve as a model of buoyancy oscillations in the atmo-sphere. Consider disturbances to a layer of incompressible fluid of uniform density ρ and depth H (Fig. 14.1). The layer is bounded below by a rigid surface. It is bounded above by a free surface , namely, one that adjusts position to relieve any stress. Motion 416 14.1 Description of wave propagation 417 0 H z η ' Figure 14.1 A layer of incompressible fluid of uniform density ρ and depth H . The layer is bounded below by a rigid surface and above by a free surface that has displacement η from its mean elevation. The profile of horizontal motion for surface Water Waves is indicated.
eBook - PDF- Pengzhi Lin(Author)
- 2008(Publication Date)
- CRC Press(Publisher)
In Water Wave theory, it refers to a similar process except that the “medium” is replaced by “local water depth” that affects wave speed. For this argument, wave refraction will occur only for waves in shallow and intermediate water depths. 3.10.1 Conservation equation of waves Consider a steady linear wave train propagating over a changing topography (see Figure 3.18 for definition). The free surface displacement of the waves can be described by the real part of the following expression: x y t = ax y e i Sxyt = ax y e i k x x + k y y − t (3.131) where Sx y t is the phase function and k = k x 2 + k y 2 is the wave number with the local wave propagation angle = tan − 1 k y /k x . The relationship among k x and k y and k is k x = k cos and k y = k sin . The phase function is a scalar whose time derivative gives angular frequency, i.e., S/t = − , and whose spatial gradient gives the wave number vector, i.e.: S = k x x x i + ( k y x ) y j = k x i + k y j = k (3.132) By substituting Sx y t = k · x − t into the trivial identity S /t + − S/t = 0, we have: k t + = 0 ⇔ k i t + x i = 0 (3.133) The above equation is called the conservation equation of waves (or wave number). This equation describes the kinematics of wave propagation, during which the change rate of the wave number with time must be balanced x y Wave propagation direction k = k x i + k y j θ Figure 3.18 A steady linear wave train propagating over a changing topo-graphy. 72 Water Wave theories and wave phenomena by the spatial variation of wave angular frequency. For a steady wave field without current, the wave frequency is uniform in space and thus the wave number at a particular location is a constant.
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