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1.
The nonlinear interactions of waves with a double-peaked power spectrum have been studied in shallow water.The starting point is the prototypical equation for nonlinear unidirectional waves in shallow water,i.e.the Korteweg de Vries equation.By means of a multiple-scale technique two defocusing coupled Nonlinear Schrdinger equations are derived.It is found analytically that plane wave solutions of such a system are unstable for small perturbations,showing that the existence of a new energy exchange mechanism which can influence the behavior of ocean waves in shallow water. 相似文献
2.
In this study the evolution of internal solitary waves shoaling onto a shelf is considered. The results of high resolution two-dimensional numerical simulations of the incompressible Euler equations are compared with the predictions of several weakly-nonlinear shoaling models of the Korteweg–de Vries family including the Gardner equation and the cubic regularized long wave (or Benjamin–Bona–Mahoney) equation. Wave models in both physical x–t space and in s–x space are considered where s is a commonly used characteristic time variable. The effects of rotation, background currents and damping are ignored. The Boussinesq and rigid lid approximations are also used. The shoaling internal solitary waves generally fission into several waves. Reflected waves are negligible in the cases considered here. Several hyperbolic tangent stratifications are considered with and without a critical point. Among the equations in x–t space the cubic regularized long wave equation gives the best predictions. The Gardner equation in s–x space gives the best predictions of the shape of the leading waves on the shelf, but for many stratifications it predicts a propagation speed that is too large. 相似文献
3.
A numerical model which consists of the Korteweg-de Vries (KdV) equation, the action balance equation and the radar backscat- tering model is developed to simulate the frequency dependence of synthetic aperture radar (SAR) remote sensing of nonlinear o- cean internal waves. Muhifrequency data collected by NASA SIR - C SAR and NASA JPL AIRSAR are used as comparison. Case studies show that the results of simulation agree well with the results of SAR data. 相似文献
4.
Recent numerical studies (Hibiya et al., 1996, 1998, 2002) showed that the energy cascade across the internal wave spectrum down to small dissipation scales was
under strong control of parametric subharmonic instabilities (PSI) which transfer energy from low vertical mode double-inertial
frequency internal waves to high vertical mode near-inertial internal waves. To see whether or not the numerically-predicted
energy cascade process is actually dominant in the real deep ocean, we examine the temporal variability of vertical profiles
of horizontal velocity observed by deploying a number of expendable current profilers (XCPs) at one location near the Izu-Ogasawara
Ridge. By calculating EOFs, we find the observed velocity profiles are dominated by low mode semidiurnal (∼double-inertial
frequency) internal tides and high mode near-inertial internal waves. Furthermore, we find that the WKB-stretched vertical
scales of the near-inertial current shear are about 250 sm and 100 sm. The observed features are reasonably explained if the
energy cascade down to small dissipation scales is dominated by PSI. 相似文献
5.
南海北部2011年台风“纳沙”尾迹处近惯性内波特征的研究 总被引：5，自引：0，他引：5
In September 2011, Typhoon Nesat passed over a moored array of instruments recording current and temperature in the northern South China Sea（SCS）. A wake of baroclinic near-inertial waves（NIWs） commenced after Nesat passed the array. The associated near-inertial currents are surface-intensified and clockwise-polarized. The vertical range of NIWs reached 300 m, where the vertical range is defined as the maximum depth of the horizontal near-inertial velocity 5 cm/s. The current oscillations have a frequency of 0.709 9 cycles per day（cpd）, which is 0.025 f higher than the local inertial frequency. The NIWs have an e-folding time-scale of 10 d based on the evolution of the near-inertial kinetic energy. The depth-leading phase of near-inertial currents indicates downward group velocity and energy flux. The estimated vertical phase velocity and group velocity are 0.27 and 0.08 cm/s respectively, corresponding to a vertical wavelength of 329 m. A spectral analysis reveals that NIWs act as a crucial process to redistribute the energy injected by Typhoon Nesat. A normal mode and an empirical orthogonal function analysis indicate that the second mode has a dominant variance contribution of 81%, and the corresponding horizontal phase velocity and wavelength are 3.50 m/s and 420 km respectively. The remarkable large horizontal phase velocity is relevant to the rotation of the earth, and a quantitative analysis suggests that the phase velocity of the NIWs with a blue-shift of 0.025 f overwhelms that of internal gravity waves by a factor of 4.6. 相似文献
6.
7.
Using a two-dimensional primitive equation model, we examine nonlinear responses of a semidiurnal tidal flow impinging on
a seamount with a background Garrett-Munk-like (GM-like) internal wavefield. It is found that horizontally elongated pancake-like
structures of high vertical wavenumber near-inertial current shear are created both in the near-field (the region over the
slope of the seamount) and far-field (the region over the flat bottom of the ocean). An important distinction is that the
high vertical wavenumber near-inertial current shear is amplified only at mid-latitudes in the far-field (owing to a parametric
subharmonic instability (PSI)), whereas it is amplified both at mid-and high-latitudes (above the latitude where PSI can occur)
in the near-field. In order to clarify the generating mechanism for the strong shear in the near-field, additional numerical
experiments are carried out with the GM-like background internal waves removed. The experiments show that the strong shear
is also created, indicating that it is not caused by the interaction between the background GM-like internal waves and the
semidiurnal internal tides. One possible explanation is proposed for the amplification of high vertical wavenumber near-inertial
current shear in the near-field where tide residual flow resulting from tide-topography interaction plays an important role
in transferring energy from high-mode internal tides to near-inertial internal waves. 相似文献
8.
A new method to estimate phase speed and vertical velocity of internal solitary waves in the South China Sea 总被引：2，自引：0，他引：2
A new method of estimating the phase speed and vertical velocity of internal solitary waves (ISW) based on dynamic governing equations using Acoustic Doppler Current Profiler (ADCP) data was developed. This method was applied to a representative ISW case, which was captured in the South China Sea in the 2007 summer experiment. The result shows that this ISW had a phase speed of approximately 2.6?m?s?1. This method provides an excellent alternative in estimating the phase speed of ISWs, especially useful in the absence of vertical stratification needed in solving the Korteweg–de Vries (KdV)-type equation, e.g., long-term mooring observation. Analyses show that the new method is fairly self-consistent, and it can be applied when only a part of the ISW observations is available. The computed vertical velocity of the ISW using the new method has a good agreement with the ADCP observations both in magnitude and pattern. 相似文献
9.
Ping Chang 《Journal of Oceanography》1993,49(5):477-489
The effects of short waves on the propagration of velocity discontinuity along the interface of two uniform potential vorticity, zones on anf-plane is examined. It is shown, using a multiple scale analysis, that the dispersion introduced by the short waves can balance the nonlinear steepening effects predicted by the semigeostrophic theory. The time evolution of a shear disturbance along the front is governed by a Korteweg-de Vries equation. Numerical solutions of the solitary waves along the front are presented. 相似文献
10.
Toshio Yamagata 《Journal of Oceanography》1983,38(6):339-345
Long nonlinear topographic waves in a continuously stratified ocean with a linear bottom slope are investigated. It is shown that odd cross-channel modes are governed by the Korteweg-de Vries (K-dV) equation. The solitary waves are those of a low pressure type. The long waves are shown to be modulationally stable because of the nonlinear effect due to irrotational motion. All these results are missed if the conventional quasi-geostrophic approximation is adopted. 相似文献
12.
13.
Numerical study of the storm-induced circulation on the Scotian Shelf during Hurricane Juan using a nested-grid ocean model 总被引：2，自引：0，他引：2
A nested-grid ocean circulation modelling system is used to assess the upper ocean response of the Scotian Shelf and adjacent slope to Hurricane Juan in September 2003. The nested-grid system consists of a fine-grid inner model covering the Scotian Shelf/slope and a coarse-grid outer model covering the northwest Atlantic Ocean. The model-calculated upper ocean response to Hurricane Juan is characterized by large divergent surface currents forced by the local wind forcing under the storm, and intense near-inertial currents in the wake of the storm. The sea surface temperature (SST) cooling produced by the model is biased to the right of the storm track and agrees well with a satellite-derived analysis. Over the deep water, off the Scotian Shelf, some of the near-inertial energy input by the storm is advected eastward by the Gulf Stream away from the storm track. The hurricane also generates shelf waves that propagate equatorward with the coastline on their right. In comparison with the outer model results, the inner model captures more meso-scale structures, greater SST cooling and stronger near-inertial currents in the study region. 相似文献
14.
Shanwu Zhang Yun Qiu Hangyu Chen Junqiang Shen Junpeng Zhang Jing Cha Fuwen Qiu Chunsheng Jing 《海洋学报(英文版)》2021,40(11):1-10
Near-inertial motions contribute most of the velocity shear in the upper ocean. In the Bay of Bengal (BoB), the annual-mean energy flux from the wind to near-inertial motions in the mixed layer in 2013 is dominated by tropical cyclone (TC) processes. However, due to the lack of long-term observations of velocity profiles, our knowledge about interior near-inertial waves (NIWs) as well as their shear features is limited. In this study, we quantified the contribution of NIWs to shear by integrating the wavenumber-frequency spectra estimated from velocity profiles in the upper layers (40?440 m) of the southern BoB from April 2013 to May 2014. It is shown that the annual-mean proportion of near-inertial shear out of the total is approximately 50%, and the high contribution is mainly due to the enhancement of the TC processes during which the near-inertial shear accounts for nearly 80% of the total. In the steady monsoon seasons, the near-inertial shear is dominant to or at least comparable with the subinertial shear. The contribution of NIWs to the total shear is lower during the summer monsoon than during the winter monsoon owing to more active mesoscale eddies and higher subinertial shear during the summer monsoon. The Doppler shifting of the M2 internal tide has little effect on the main results since the proportion of shear from the tidal motions is much lower than that from the near-inertial and subinertial motions. 相似文献
15.
Using the reductive perturbation method, we investigate the small amplitude nonlinear acoustic wave in a collisional self-gravitating dusty plasma. The result shows that the small amplitude dust acoustic wave can be expressed by a modified Korteweg-de Vries equation, and the nonlinear wave is instable because of the collisions between the neutral gas molecules and the charged particles. 相似文献
16.
Based on the full water-wave equation,a second-order analytic solution for nonlinear interaction of short edge waves on a plane sloping bottom is presented in this paper.For special case of slope angle β=π/2,this solution can reduced to the same order solution of deep water gravity surface waves traveling along parallel coastline.Interactions between two edge waves including progressive,standing and partially reflected standing waves are also discussed.The unified analytic expressions with transfer functions for kinematic-dynamic elements of edge waves are also given.The random model of the unified wave motion processes for linear and nonlinear irregular edge waves is formulated,and the corresponding theoretical autocorrelation and spectral density functions of the first and the second orders are derived.The boundary conditions for the determination of the parameters of short edge wave are suggested,that may be seen as one special simple edge wave excitation mechanism and an extension to the sea wave refraction theory.Finally some computation results are demonstrated. 相似文献
17.
THE NONLINEAR INTERNAL GRAVITY WAVES IN STRATIFIED FLUID 总被引：1，自引：0，他引：1
In this paper, starting from the equations of the nonlinear internal gravity waves in stratified fluid, using the method of the Taylor expansion nearby the equilibrium point for the nonlinear terms, we find the analytical solutions for nonlinear internal gravity waves. The linear internal gravity waves and solitary waves are its special cases. The nonlinear internal gravity waves satisfy the well-known KdV (Karteweg-de Vries) equation. The nonlinear internal gravity waves are different from linear waves in character. The former dispersive relation contains the amplitude, but the latter does not. The larger the amplitude and the wavelength the faster are waves for the nonlinear internal gravity waves. The smaller the stability of the stratification, the larger is the wavelength (or the width). Some phenomena such as squall line, cumulus, turbulent mass structure in atmosphere, and thermocline in ocean have these natures. 相似文献
18.
The horizontally variable density stratification and background currents are taken into the variable-coefficent extended Korteweg-de Vries(evKdV) theory to obtain the geographical and seasonal distribution of kinematic parameters of internal solitary waves in the Andaman Sea(AS). The kinematic parameters include phase speed,dispersion parameter, quadratic and cubic nonlinear parameters. It shows that the phase speed and dispersion parameter are mainly determined by the topographic feature and ha... 相似文献
19.
Compared with solar and wind energy, wave energy is a kind of renewable resource which is enormous and still under development. In order to utilize the wave energy, various types of wave energy converters (WECs) have been proposed and studied. And oscillating-body WEC is widely used for offshore deployment. For this type of WEC, the oscillating motion of the floater is converted into electricity by the power take off (PTO) system, which is usually mathematically simplified as a linear spring and a damper. The linear PTO system is characteristic of frequency-dependent response and the energy absorption is less powerful for off resonance conditions. Thus a nonlinear snap through PTO system consisting of two symmetrically oblique springs and a linear damper is applied. A nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two oblique springs to the original length of both springs. JONSWAP spectrum is utilized to generate the time series of irregular waves. Time domain method is used to establish the motion equation of the oscillating-body WEC in irregular waves. And state space model is applied to replace the convolution term in the time domain motion equation. Based on the established motion equation, the motion response of both the linear and nonlinear WEC is numerically calculated using 4th Runge–Kutta method, after which the captured power can be obtained. Then the influences of wave parameters such as peak frequency, significant wave height, damping coefficient of the PTO system and the nonlinear parameter γ on the power capture performance of the nonlinear WEC is discussed in detail. Results show that compared with linear PTO system, the nonlinear snap through PTO system can increase the power captured by the oscillating body WEC in irregular waves. 相似文献
20.
Based on the full water-wave equation, a second-order analytic solution for nonlinear interaction of short edge waves on a constant plane sloping bottom is presented in this paper. For special case of slope angle b=p/2, this solution can be reduced to the same order solution of deep water gravity surface waves traveling along parallel coastline. Interactions between two edge waves including progressive, standing and partially reflected standing waves were also discussed. The unified analytic expressions with transfer functions for kinematic-dynamic elements of edge waves were also discussed. The random model of the unified wave motion processes for linear and nonlinear irregular edge waves is formulated, and the corresponding theoretical autocorrelation and spectral density functions of the first and second orders are derived. The boundary conditions for the determining determination of the parameters of short edge wave are suggested, that may be seen as one special simple edge wave excitation mechanism and an extension to the sea wave refraction theory. Finally some computation results are demonstrated. 相似文献