In the present study, the surface elevation of wind waves observed in laboratory and in the Bohai Sea are adopted for the estimation of the wind wave frequency spectrtm by use of the method of the arcsine law （MAL）. The traditional method uses the surface elevation to calculate the correlation and then estimate the frequency spectrum while the MAL, presented by Yu and l.an （1979）, uses the time sequence of zero-crossing points of surface elevation rather than directly the surface elevation to calculate the correlation. 66 sets of wind wave data obtained in laboratory and 420 sets of data observed in the Bohai Sea are adopted for the examination of the method introduced by Yu and Lan. Results show that the MAL can give reliable estimation of wind wave spectra. Correlation and form of spectra estimated by the MAL are similar to those estimated by the traditional method. The peak frequency and the spectral density in peak frequency by the MAL are close to those obtained by the traditional method.
The scattering process, which means the redistribution of energy fluy in modenumber space, is analyzed for internal waves propagating from the abyssal ocean onto a subcritical strait slope and then a shelf region. In light of Wunsch＇s work, the waves are analytically expressed as superimposition of eigensolutions distribution of energy flux in the shelf region： one is the ratio of water depth in and the other is the ratio of the slope of the internal tide rays to the topographic energy flux distribution： the energy flux is focused around one modenumber or case, the range of modenumbers where energy flux is distributed is narrow. Two parameters have evident effects on the the shelf region to that in the abyssal ocean slope. Generally, there are two patterns of focused around two modenumbers. In any case, the range of modenumbers where energy flux is distributed is narrow.
Laboratory experiments and field observations show that the equilibrium range of wind wave spectra presents a – 4 power law when it is scaled properly. This feature has been attributed to energy balance in spectral space by many researchers. In this paper we point out that white noise on an oscillation system can also lead to a similar inverse power law in the corresponding displacement spectrum, implying that the – 4 power law for the equilibrium range of wind wave spectra may probably only reflect the randomicity of the wind waves rather than any other dynamical processes in physical space. This explanation may shed light on the mechanism of other physical processes with spectra also showing an inverse power law, such as isotropic turbulence, internal waves, etc.
In a two-dimensional and linear framework, a transformation was developed to derive eigensolutions of internal waves over a subcritical hyperbolic slope and to approximate the continental slope and shelf. The transformation converts a hyperbolic slope in physical space into a flat bottom in transform space while the governing equations of internal waves remain hyperbolic. The eigensolutions are further used to study the evolution of linear internal waves as it propagates to subcritical continental slope and shelf. The stream function, velocity, and vertical shear of velocity induced by internal wave at the hyperbolic slope are analytically expressed by superposition of the obtained eigensolutions. The velocity and velocity shear increase as the internal wave propagates to a hyperbolic slope. They become very large especially when the slope of internal wave rays approaches the topographic slope, which is consistent with the previous studies.
