A joint probability density is derived for wavelengths and wave heights. It is asymmetric and depends only on the spectral bandwidth epsilon defined by Cartwright and Longuet-Higgins (1956). After that a theoretical probability density for wave steepness is obtained. It tends to Rayleigh distribution as epsilon --> 0. A comparison between theoretical steepness distribution and laboratory experiment result shows good agreement.
A joint probability density function (PDF) for surface slopes in two arbitrary directions is derived on the basis of Longuet Higgins's linear model for three-dimensionol (3-D) random wave field. and the correlation moments of surface slopes. as parameters in the PDF, are expressed in terms of directional spectrum of ocean waves. So long as the directional spectrum model is given, these parameters are determined. Since the directional spectrum models proposed so far are mostly parameterized by the wind speed and fetch, this allows for substituting these parameters with thc wind speed and fetch. As an example, the wind speed and fetch are taken to be 14 m ' s and 200 km, and the Hasselmann and Donclan directional spectra are, respectively, use to compute these parameters. Some novel results a reobtained. One of the increasing interesting results is that the variances of surface slope in downwind and cross-wind directions determined by the Donclan directional spectra are close to those measured by Cox and Munk (1954). Some discussions are made on these results.
The intertidal flats are classified as 'attached bar', 'spit' and 'isolated bar' in relation to the land, and 'broad flat', 'sharp bank' and 'eroded cliff' according to the shape of the cross-shore profile. Tidal currents on the flat are basically back and forth along the river channel banks but gyratory on the seaward side of the Chongming Island. The flow velocity on the intertidal flat is gradually reduced with increasing elevation. The river discharge strengthens ebb flows and modifies current asymmetry especially on the lower flat in neap tide, although hydrodynamics over the tidal flat is tide-dominated. The wave height on the tidal flat is normally limited to a few decimeters although it changes with water depth, slope and wind. Suspended sediment concentration over the tidal flat is typically hundreds to thousands of mg / 1. Although the delta has grown rapidly in history, the rate of growth is different in different periods. A maximum advancing rate of 330 m / a was recently found in the central part of the river month towards the sea. In view of the natural conditions, reclamation of higher intertidal flat (above the mean tidal level) in advancing coasts is suggested, which would leave broad wetlands for wild lives. In addition, some possible influences of coastal engineering projects and the future natural backgrounds of engineering under reduction in riverine sediment supply and sea level rise are addressed.
In Light of the analysis of the physical implication and underlying assumption of the bandwidth parameter epsilon of wave spectrum, a time-averaging method is used to evaluate epsilon of the JONSWAP spectrum for different sea states. The resulting values of epsilon, which vary from 0.44 to 0.53 depending on the dimensionless fetch, are physically meaningful and reasonable. The same method is also used to compute epsilon from wind-wave records measured in a flume under different wind speeds at different fetches. The computed values of epsilon, which vary with wind fetches and speeds too, are compared with those evaluated for the JONSWAP spectrum.
