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Ray Q. Lin
and
Norden E. Huang

Abstract

To select a wind wave model as the basis for developing a coupled wind wave-current model for coastal dynamics, the numerical schemes used in state-of-the-art wind wave models are examined analytically. The schemes used in the existing models contain serious numerical aliases leading to dissipation and dispersion. These numerical aliases could mistakenly be interpreted as part of the physical phenomena. To alleviate these shortcomings, a fourth-order semi-implicit scheme for transport-type models and a second-order semi-implicit scheme with a gradient-dependent directional filter for the conservation-type models are proposed. The traditional difficulty of a hyperbolic conservation law is surmounted by this directional filter. These new schemes and the new filter are insensitive to the sizes of the time step and spatial grid and the magnitude of the group velocity; therefore, aliasing of the physical phenomena will not occur. Furthermore, the numerical dissipation and the dispersion of the new method are practically zero. Even though each computation step of these new schemes requires greater computing time, the total computing time is still considerably shorter than that in previous models because the time steps of the new schemes can be an order of magnitude greater than those used previously.

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Steven R. Long
and
Norden E. Huang

Abstract

Laboratory measurements utilizing a laser probe are made for the slopes of wind waves generated on both positive and negative currents at different values of fetch. The data are then processed electronically to yield an average wave-slope spectrum in frequency space with 128 degrees of freedom. These spectra are used to obtain the growth of the spectral components at various frequency bands for increasing wind and different values of fetch and current. The results indicate that the growth of these components is not monotonic with the frictional wind speed U *, but rather exhibits an “overshoot” phenomena at lower values of U *, and in addition, displays a significant effect due to current. The peak location and spectral intensity of the spectra also show strong influence by the current condition. This results in the rms surface slope value increasing with negative current and decreasing with positive current. The results agree qualitatively with some theoretical predictions. The potential use of the current-induced effects as a means for remote sensing of ocean current is also briefly discussed.

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Ray Q. Lin
and
Norden E. Huang

Abstract

A new coastal wave model is being developed to study air–sea interaction processes in the coastal region. The kinematics of this model, which govern the wave propagation, are reported. This new model is based on the action conservation equation rather than on the energy transport equation; it also employs the full nonlinear dispersion relationship in water of arbitrary depth. With these improvements, it includes nonstationary wave-current interaction processes and functions in coastal regions with variable finite water depths. Numerical results show that these changes cause significant differences between the new model and the WAM model when waves encounter any steady or unsteady current, and when waves propagate over changing bottom topography in a shallow water region. Such conditions are very common and should not be neglected in the coastal regions.

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Norden E. Huang
and
Chi-Chao Tung

Abstract

The influence of the directional distribution of wave energy on the dispersion relation is calculated numerically using various directional wave spectrum models. The results indicate that the dispersion relation varies both as a function of the directional energy distribution and the direction of propagation of the wave component under consideration. Furthermore, both the mean deviation and the random scatter from the linear approximation increase as the energy spreading decreases. Limited observational data are compared with the theoretical results. The agreement is favorable.

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Man Li C. Wu
,
Siegfried Schubert
, and
Norden E. Huang

Abstract

Fourteen years (1980–93) of National Aeronautics and Space Administration reanalysis data are used to document and study the variability in the development of the South Asian summer monsoon associated with the Intraseasonal Oscillation (ISO). The focus is on the coupling of the large-scale upper-level divergent circulation with the low-level southwesterlies and the associated developing regions of moisture convergence and precipitation, which serve to define the onset times of the various regions of the South Asian monsoon.

The impact of the ISO on the development of the low-level southwesterlies is both local and remote, and depends on the strength and phasing of the ISO with the seasonal cycle. Of the 14 yr examined here, 6 showed a strong contribution to the northeastward progression and onset of the monsoon rains over India. In these cases, the ISO is initially (about 2 weeks prior to onset of rains over India) out of phase with, and therefore suppresses, the seasonal development of the regions of large-scale rising and sinking motion. As the ISO moves to the northeast, the rising branch enters the Indian Ocean and acts to enhance the latent heating in the region of the emerging Somali jet. At low levels the response takes the form of an anticyclonic circulation anomaly over the Arabian Sea, and a cyclonic circulation anomaly to the south, which acts to inhibit the eastward progression of the Somali jet. As the ISO moves in phase with and enhances the seasonal mean upper-level divergent circulation, there is an abrupt and intense development of the southwesterly winds leading to an unusually rapid northeast shift and intensification of the monsoon rains over India and the Bay of Bengal. The general northeast progression of the anomalies may be viewed as an initial suppression and then acceleration of the “normal” seasonal cycle of the monsoon.

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Charles R. McClain
,
Norden E. Huang
, and
Leonard J. Pietrafesa

Abstract

The problem of a small-amplitude wave propagating over a flat porous bed is reanalyzed subject to the bottom boundary conditionwhere u represents the horizontal velocity in the fluid,ũ s represents the horizontal velocity within the bed as predicted by Darcey's law, K is the permeability and the subscript 0 denotes evaluation at the bottom (z=0). The term α is a constant whose value depends on the porosity of the bed at the interface and must be determined experimentally. The boundary condition is of the form of a “radiation-type” condition commonly encountered in heat conduction problems.

The important physical quantities (velocity, velocity potential, streamfunction, shear stress and energy dissipation) have been derived and are presented, subject to natural conditions. The bottom boundary layer is represented by the linearized Navier-Stokes equations under the usual boundary layer approximation. It is found that the boundary layer velocity distribution and shear stress can be greatly altered from impermeable bed predictions. Theoretical results for energy dissipation and shear stress are compared to existing data and are found to agree very well. The predictions of classical small-amplitude wave theory are not appreciably modified away from the boundary.

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Norden E. Huang
,
Steven R. Long
, and
L. F. Bliven

Abstract

The significant slope of a random wave field is found to be an important parameter in empirical wind-wave studies. This significant slope Ss is defined as Ss = ( ζ2 )½0, with ζ2 as the mean-square surface elevation and λ0 as the wavelength corresponding to the waves at the peak of the spectrum. With this parameter, the relationship between and ñ is reduced to an identity expressing a pure geometric measure of the sea state, because Ẽñ 4 = (2πSs )2. By applying the significant slope as a parameter explicitly, we proposed that the traditional empirical formulas relating the nondimensional energy , fetch and frequency ñ be combined into a single unified relationship as Ẽñ/ = (9/40)Ss 9/4 . This unified empirical formula governs the wind-wave data equally as well in the field as in the laboratory.

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Xianyao Chen
,
Meng Wang
,
Yuanling Zhang
,
Ying Feng
,
Zhaohua Wu
, and
Norden E. Huang

Abstract

Signal detection from noisy data by rejecting a noise null hypothesis depends critically on a priori assumptions regarding the background noise and the associated statistical methods. Rejecting one kind of noise null hypothesis cannot rule out the possibility that the detected oscillations are generated from the stochastic processes of another kind. This calls for an adaptive null hypothesis based on general characteristics of the noise that is present. In this paper, a new method is developed for identifying signals from data based on the finding that true physical signals in a well-sampled time series cannot be destroyed or eliminated by resampling the time series with fractional sampling rates through linear interpolation. Therefore, the significance of signals could be tested by checking whether the signals persist in the true time–frequency spectral representation during resampling. This hypothesis is based on the general characteristics of noise as revealed by empirical mode decomposition, an adaptive data analysis method without linear or stationary assumptions, and without any predefinition of the background noise. Applications of this method to synthetic time series, solar spot number, and sea surface temperature time series illustrate its power in identifying characteristics of background noise without any a priori knowledge.

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Norden E. Huang
,
Hsing H. Shih
,
Zheng Shen
,
Steven R. Long
, and
Kuang L. Fan

Abstract

Using a process denoted here as the empirical mode decomposition and the Hilbert spectral analysis, the ages of the seiches on the Caribbean coast of Puerto Rico are determined from their dispersion characteristics with respect to time. The ages deduced from this method are less than a day; therefore, the seiches could be locally generated.

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Norden E. Huang
,
Larry F. Bliven
,
Steven R. Long
, and
Chi-Chao Tung

Abstract

Using a threshold criterion governing the onset of wave breaking, we derived an analytical expression for the whitecap coverage of the ocean. This expression is a function of the wave steepness in terms of the significant slope and the ratio of the frictional velocity of the wind to the phase velocity of the energy-containing waves. Theoretically, this analytical expression works only for the narrowband wave field. However, the comparison with the field data of Snyder et al. suggests that the present model could be applied to fresh wind-wave fields. Since the present approach is based on the probability density function of wave breaking with or without wind stress, it is believed that this analytical expression will offer a more reliable answer than the traditional empirical formula.

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