• Journal of Korean Society of Coastal and Ocean Engineers
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• v.5 no.2
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• pp.76-83
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• 1993

In this study, an approximate method for calculating the directional spectrum of waves encountering a current in shallow water is developed. The wave trains in tile directional spectrum are assumed to be linear and Gaussian; development of the spectrum requires that the waves also be short crested. The Miche's breaking criterion is imposed to determine the upper limit of wave height and to establish an expression for the breaking wave elevation in terms of the ideal wave's elevation and the second time derivative of wave elevation. Two examples are given; one for a Wallops directional spectrum encountering a shear current and another with an upwelling current.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.31 no.5
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• pp.278-293
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• 2019

The joint distribution of wave height and period has been maltreated despite of its great engineering value due to the absence of any analytical model for wave period, and as a result, no consensus has been reached about the effect of nonlinearity on these joint distribution. On the other hand, there was a great deal of efforts to study the effects of non-linearity on the wave height distribution over the last decades, and big strides has been made. However, these achievements has not been extended to the joint distribution of wave height and period. In this rationale, we first express the joint distribution of wave height and period as the product of the marginal distribution of wave heights with the conditional distribution of associated periods, and proceed to derive the joint distribution of wave heights and periods utilizing the models of Longuet-Higgins (1975, 1983), and Cavanie et al. (1976) for conditional distribution of wave periods, and height distribution derived in this study. The verification was carried out using numerically simulated data based on the Wallops spectrum, and the nonlinear wave data obtained via the numerical simulation of random waves approaching toward the uniform beach of 1:15 slope. It turns out that the joint distribution based on the height distribution for finite banded nonlinear waves, and Cavanie et al.'s model (1976) is most promising.