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Stokes Expansion
In fluid dynamics, a Stokes wave is a nonlinear and periodic surface wave on an inviscid fluid layer of constant mean depth. This type of modelling has its origins in the mid 19th century when Sir George Stokes – using a perturbation series approach, now known as the Stokes expansion – obtained approximate solutions for nonlinear wave motion. Stokes's wave theory is of direct practical use for waves on intermediate and deep water. It is used in the design of coastal and offshore structures, in order to determine the wave kinematics (free surface elevation and flow velocities). The wave kinematics are subsequently needed in the design process to determine the wave loads on a structure. For long waves (as compared to depth) – and using only a few terms in the Stokes expansion – its applicability is limited to waves of small amplitude. In such shallow water, a cnoidal wave theory often provides better periodic-wave approximations. While, in the strict sense, ''Stokes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amplitude
The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplitude (see below), which are all functions of the magnitude of the differences between the variable's extreme values. In older texts, the phase of a periodic function is sometimes called the amplitude. Definitions Peak amplitude and semi-amplitude For symmetric periodic waves, like sine waves or triangle waves, ''peak amplitude'' and ''semi amplitude'' are the same. Peak amplitude In audio system measurements, telecommunications and others where the measurand is a signal that swings above and below a reference value but is not sinusoidal, peak amplitude is often used. If the reference is zero, this is the maximum absolute value of the signal; if the reference is a mean value ( DC component), the peak amplitude is the maximum ab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Wavenumber
In the physical sciences, the wavenumber (or wave number), also known as repetency, is the spatial frequency of a wave. Ordinary wavenumber is defined as the number of wave cycles divided by length; it is a physical quantity with dimension of reciprocal length, expressed in SI units of cycles per metre or reciprocal metre (m−1). Angular wavenumber, defined as the wave phase divided by time, is a quantity with dimension of angle per length and SI units of radians per metre. They are analogous to temporal frequency, respectively the '' ordinary frequency'', defined as the number of wave cycles divided by time (in cycles per second or reciprocal seconds), and the ''angular frequency'', defined as the phase angle divided by time (in radians per second). In multidimensional systems, the wavenumber is the magnitude of the ''wave vector''. The space of wave vectors is called ''reciprocal space''. Wave numbers and wave vectors play an essential role in optics and the physics of w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Average
In colloquial, ordinary language, an average is a single number or value that best represents a set of data. The type of average taken as most typically representative of a list of numbers is the arithmetic mean the sum of the numbers divided by how many numbers are in the list. For example, the mean or average of the numbers 2, 3, 4, 7, and 9 (summing to 25) is 5. Depending on the context, the most representative statistics, statistic to be taken as the average might be another measure of central tendency, such as the mid-range, median, Mode (statistics), mode or geometric mean. For example, the average income, personal income is often given as the median the number below which are 50% of personal incomes and above which are 50% of personal incomes because the mean would be higher by including personal incomes from a few billionaires. General properties If all numbers in a list are the same number, then their average is also equal to this number. This property is shared by each o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Earth's Gravity
The gravity of Earth, denoted by , is the net acceleration that is imparted to objects due to the combined effect of gravitation (from mass distribution within Earth) and the centrifugal force (from the Earth's rotation). It is a vector quantity, whose direction coincides with a plumb bob and strength or magnitude is given by the norm g=\, \mathit\, . In SI units, this acceleration is expressed in metres per second squared (in symbols, m/ s2 or m·s−2) or equivalently in newtons per kilogram (N/kg or N·kg−1). Near Earth's surface, the acceleration due to gravity, accurate to 2 significant figures, is . This means that, ignoring the effects of air resistance, the speed of an object falling freely will increase by about every second. The precise strength of Earth's gravity varies with location. The agreed-upon value for is by definition. This quantity is denoted variously as , (though this sometimes means the normal gravity at the equator, ), , or simply ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Gravity Wave
In fluid dynamics, gravity waves are waves in a fluid medium or at the interface between two media when the force of gravity or buoyancy tries to restore equilibrium. An example of such an interface is that between the atmosphere and the ocean, which gives rise to wind waves. A gravity wave results when fluid is displaced from a position of equilibrium. The restoration of the fluid to equilibrium will produce a movement of the fluid back and forth, called a ''wave orbit''. Gravity waves on an air–sea interface of the ocean are called surface gravity waves (a type of surface wave), while gravity waves that are the body of the water (such as between parts of different densities) are called '' internal waves''. Wind-generated waves on the water surface are examples of gravity waves, as are tsunamis, ocean tides, and the wakes of surface vessels. The period of wind-generated gravity waves on the free surface of the Earth's ponds, lakes, seas and oceans are predominantly be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wave Propagation
In physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. '' Periodic waves'' oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in one direction, it is said to be a travelling wave; by contrast, a pair of superimposed periodic waves traveling in opposite directions makes a '' standing wave''. In a standing wave, the amplitude of vibration has nulls at some positions where the wave amplitude appears smaller or even zero. There are two types of waves that are most commonly studied in classical physics: mechanical waves and electromagnetic waves. In a mechanical wave, stress and strain fields oscillate about a mechanical equilibrium. A mechanical wave is a local deformation (strain) in some physical medium that propagates from particle to particle by creating local stresses that cause strain in neighboring particles too ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase (waves)
In physics and mathematics, the phase (symbol φ or ϕ) of a wave or other periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is expressed in such a scale that it varies by one full turn as the variable t goes through each period (and F(t) goes through each complete cycle). It may be measured in any angular unit such as degrees or radians, thus increasing by 360° or 2\pi as the variable t completes a full period. This convention is especially appropriate for a sinusoidal function, since its value at any argument t then can be expressed as \varphi(t), the sine of the phase, multiplied by some factor (the amplitude of the sinusoid). (The cosine may be used instead of sine, depending on where one considers each period to start.) Usually, whole turns are ignored when expressing the phase; so that \varphi(t) is also a periodic function, with the same period as F, that repeatedly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phase Speed
The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity. The phase velocity is given in terms of the wavelength (lambda) and time period as :v_\mathrm = \frac. Equivalently, in terms of the wave's angular frequency , which specifies angular change per unit of time, and wavenumber (or angular wave number) , which represent the angular change per unit of space, :v_\mathrm = \frac. To gain some basic intuition for this equation, we consider a propagating (cosine) wave . We want to see how fast a particular phase of the wave travels. For example, we can choose , the phase of the first crest. This implies , and so . Formally, we let the phase and see immediately that and . So, it immediately follows that : \frac = -\frac \frac = \fra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Velocity Potential
A velocity potential is a scalar potential used in potential flow theory. It was introduced by Joseph-Louis Lagrange in 1788. It is used in continuum mechanics, when a continuum occupies a simply-connected region and is irrotational. In such a case, \nabla \times \mathbf =0 \,, where denotes the flow velocity. As a result, can be represented as the gradient of a scalar function : \mathbf = \nabla \varphi\ = \frac \mathbf + \frac \mathbf + \frac \mathbf \,. is known as a velocity potential for . A velocity potential is not unique. If is a velocity potential, then is also a velocity potential for , where is a scalar function of time and can be constant. Velocity potentials are unique up to a constant, or a function solely of the temporal variable. The Laplacian of a velocity potential is equal to the divergence of the corresponding flow. Hence if a velocity potential satisfies Laplace equation, the flow is incompressible. Unlike a stream function, a velocity potential ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
