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Ursell Parameter
In fluid dynamics, the Ursell number indicates the nonlinearity of long surface gravity waves on a fluid layer. This dimensionless parameter is named after Fritz Ursell, who discussed its significance in 1953. The Ursell number is derived from the Stokes wave expansion, a perturbation series for nonlinear periodic waves, in the long-wave limit of shallow water – when the wavelength is much larger than the water depth. Then the Ursell number ''U'' is defined as: :U = \frac \left(\frac\right)^2\, =\, \frac, which is, apart from a constant 3 / (32 π2), the ratio of the amplitudes of the second-order to the first-order term in the free surface elevation. The used parameters are: * ''H'' : the wave height, ''i.e.'' the difference between the elevations of the wave crest and trough, * ''h'' : the mean water depth, and * ''λ'' : the wavelength, which has to be large compared to the depth, ''λ'' ≫ ''h''. So the Ursell parameter ''U'' is the relative wave height ''H'' / ''h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sine Wave Amplitude
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle \theta, the sine and cosine functions are denoted as \sin(\theta) and \cos(\theta). The definitions of sine and cosine have been extended to any real number, real value in terms of the lengths of certain line segments in a unit circle. More modern definitions express the sine and cosine as Series (mathematics), infinite series, or as the solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers. The sine and cosine functions are commonly used to model periodic function, periodic pheno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
