Empirical wave spectra

2 Empirical Wave Spectra The energy spectrum of the immature wind sea state (which is the matter in the Baltic Sea at wind speeds of more than 16 kn) is admittedly described by the JONSWAP spectrum (Hasselmann et al.,). 

Measurements in various sea areas and under a variety of conditions have shown that the peak enhancement factor y and the slope parameter a are variable quantities, but that they can be assumed to be constant for individual sea areas. 

A parameterization of the JONSWAP spectrum has been worked out by Houmb and Overvik (1976). This work gives recommended values of a, y, and f, when the significant wave height 77 and average zero crossing wave period are given (Table 7.6). 

The following relationship derived from the sea state statistics in Section 7.1.5 was used to calculate the zero crossing period. 

The peak enhancement factor y and the slope parameter a are calculated as follows  

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A procedure for empirical computation of significant wave height, mean wave period and wavelength, and an empirical energy spectrum of wind waves is introduced. 

Ultrasonic Spectroscopy. Information on size distribution maybe obtained from the attenuation of sound waves traveling through a particle dispersion. Two distinct approaches are being used to extract particle size data from the attenuation spectrum an empirical approach based on the Bouguer-Lambert-Beer law (63) and a more fundamental or first-principle approach (64—66). The first-principle approach impHes that no caHbration is requited, but certain physical constants of both phases, ie, speed of sound, density, thermal coefficient of expansion, heat capacity, thermal conductivity. 

To give an idea of its order of magnitude, it is sufficient to remark that the intensity maximum of the radiation from the sun, which radiates like a black body at the temperature T = 6000°, lies in the green region of the spectrum, i.e. at a wave-length of about 4500 A.) From these two empirically determined constants, h and h can be calculated the values so obtained agree very well with the correct ones. 

In order to define the dynamic characteristics of the foundation soils, in relation to the choice of an elastic site-compatible spectrum, it is advisable to evaluate the profile of the shear wave velocity. This profile should be determined on-site by down-hole geophysical tests. As an alternative, it can be defined with the aid of empirical correlations with the site penetration resistance (SPT, CPT) or with other geotechnical properties. For a more complete definition of the dynamical characteristics, it might be necessary to define shear wave velocity values compatible with the deformations induced in the ground by the passage of seismic waves. 

Although we have dealt here solely with predictions for ambient air fluidization, for which validation by means of the counterpart empirical relations may be readily confirmed, the procedures outlined are quite generally applicable. The immediate conclusion is that predicted e b values provide a continuous measure of fluidization quality across the whole spectrum of behaviour corresponding to the Geldart powder classification map. However, when it comes to the general situation of fluidization by any fluid, this measure turns out to be by no means complete. To appreciate this point it becomes necessary to examine in more detail the perturbation wave relations that delivered the Smb predictions in the first place. This will then lead to more comprehensive predictive criteria for fluidization quality in general. 

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