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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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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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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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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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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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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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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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Man-Li C. Wu
,
Siegfried D. Schubert
,
Max J. Suarez
, and
Norden E. Huang

Abstract

This study examines the nature of episodes of enhanced warm-season moisture flux into the Gulf of California. Both spatial structure and primary time scales of the fluxes are examined using the 40-yr ECMWF Re-Analysis data for the period 1980–2001. The analysis approach consists of a compositing technique that is keyed on the low-level moisture fluxes into the Gulf of California. The results show that the fluxes have a rich spectrum of temporal variability, with periods of enhanced transport over the gulf linked to African easterly waves on subweekly (3–8 day) time scales, the Madden–Julian oscillation (MJO) at intraseasonal time scales (20–90 day), and intermediate (10–15 day) time-scale disturbances that appear to originate primarily in the Caribbean Sea–western Atlantic Ocean.

In the case of the MJO, enhanced low-level westerlies and large-scale rising motion provide an environment that favors large-scale cyclonic development near the west coast of Central America that, over the course of about 2 weeks, expands northward along the coast eventually reaching the mouth of the Gulf of California where it acts to enhance the southerly moisture flux in that region. On a larger scale, the development includes a northward shift in the eastern Pacific ITCZ, enhanced precipitation over much of Mexico and the southwestern United States, and enhanced southerly/southeasterly fluxes from the Gulf of Mexico into Mexico and the southwestern and central United States. In the case of the easterly waves, the systems that reach Mexico appear to redevelop/reorganize on the Pacific coast and then move rapidly to the northwest to contribute to the moisture flux into the Gulf of California. The most intense fluxes into the gulf on these time scales appear to be synchronized with a midlatitude short-wave trough over the U.S. West Coast and enhanced low-level southerly fluxes over the U.S. Great Plains. The intermediate (10–15 day) time-scale systems have zonal wavelengths roughly twice that of the easterly waves, and their initiation appears to be linked to an extratropical U.S. East Coast ridge and associated northeasterly winds that extend well into the Caribbean Sea during their development phase. The short (3–8 day) and, to a lesser extent, the intermediate (10–15 day) time-scale fluxes tend to be enhanced when the convectively active phase of the MJO is situated over the Americas.

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Norden E. Huang
,
Davidson T. Chen
,
Chi-Chao Tung
, and
James R. Smith

Abstract

Interactions between steady non-uniform currents and gravity waves are generalized to include the case of a random gravity wave field. The Kitaigorodskii-Pierson-Moskowitz frequency spectrum is used as the basic spectral form for zero current condition. Modified spectral functions in both wavenumber and frequency spaces under the influence of current are found by using energy conservation and kinematic wave conservation laws. The relative importance of the current-wave interaction was measured by the nondimensional parameter U/C 0, with U as the current speed and C 0 the phase speed of a wave under no current. As a result of the current-wave interaction, the magnitude and the location of the energy peak in the spectrum is altered.

Since the phase speed of gravity waves is a monotonically decreasing function of wavenumber and frequency, the influence of current will be predominant at the higher wavenumber range. Furthermore, the contribution from the higher wavenumber range dominates the surface slope spectrum; the current conditions changes the surface slope pattern drastically. This phenomenon is studied by use of Phillips' equilibrium range spectrum in wavenumber space. It was found that the rms surface slope is extremely sensitive to the change of current conditions especially for the case of adverse current, but eventually becomes saturated at a high positive value. The surface slope data together with a generalized dispersion relation offer a possible current measurement technique which appears ideally suited for remote sensing devices such as stereoscopic photography and radar scattering.

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