Combining the logarithmic law with the Charnock relation yields a drag coefficient that is a function of wind speed with the Charnock coefficient as a parameter. It is found that the function is nearly linear within the typically measured range of the drag coefficient. The slope of the linear function is dominated by the Charnock coefficient. When the Charnock relation is extended to a wave age-dependent function, the drag coefficient remains a near-linear function of wind speed after invoking the 3/2 power law. The slope of the linear function is dominated by wave steepness.

The Princeton Ocean Model (POM) is widely used in both the research and real-time marine forecast communities. However, there is a single heavily criticized feature and shortcoming of POM, i.e., the pressure gradient (PG) error associated with sloping topography. To overcome this problem, in this paper we present an eta-coordinate POM (ECPOM). The eta-coordinate system was originally adopted in atmospheric numerical models and has proved to be effective in removing the large errors associated with the horizontal pressure gradient force and advection and diffusion terms along a steeply sloping topography. A familiar idealized seamount problem is used to test the PG error in the ECPOM in order to isolate errors from other sources, as is done in the literature. The model is set up so that, ideally, the ocean should be at rest forever; any development of circulation is regarded as numerically artificial. Results show that in ECPOM, errors are dramatically reduced by two orders of magnitude over a wide range of parameters. As a trade-off, the bottom boundary of the ECPOM is a stepwise instead of a continuous one, as in the sigma-coordinate POM (SCPOM). Modification of the SCPOM to the ECPOM is straightforward and minimal. Compared to the z-coordinate model, the ECPOM is numerically simpler since the eta-coordinate has a surface-followlng character.

In this paper the WAM model is improved by considering the radiation stresses due to wave-current interactions in the spectral transport equation. The improved wave model is applied to compute wind waves in the Rhone river mouth area in the Southern France under various steady and homogeneous wind conditions. The aim of this study is to determine the wave conditions involved in the long-term evolution of the shoreline. From the numerical computation results, we can conclude that even for obliquely offshore wind conditions, alongshore waves exist in nearshore area and that the current due to the Rhone discharge has very little effect on the wave characteristics in relatively deep water.

Based upon the nonlinear model of random sea waves, the statistical distribution of wave surface elevation exact to the fourth order is derived as the truncated Gram-Charlier series, by calculating directly each order moment. The phenomenon found by Huang et al. that the agreement between observed data and investigated series deteriorates much more when the series is kept to λ8 is explained, The effect of the appmximation order on the truncation of series and the determination of coefficients is investigated. For the mth order approximation, the derived series is truncated at H3m-3 with the absence of H3m-4, and the coefficients of H3m-3 and H3m-6 are connected by a simple algebraic relation.

Wen et al.'s method developed to obtain wind-wave frequeriacy spectrum in deep water was used to derive the spectrum in finite depth water. The spectrum S(ω) (ω being angular frequency) when normalized with the zeroth moment m0 and peak frequency ω0 contains in addition to the peakness factor P=ω0S(ω0)/mo, a depth pararmeter η=(2nmo)1/2/d (d being water depth), so the spectrum behavior can be studied for different wave growth stages and water depths.