共查询到20条相似文献，搜索用时 31 毫秒
1.
S. C. Martha 《地球物理与天体物理流体动力学》2013,107(2):65-80
The problem of oblique water wave diffraction by small undulation of the bottom of a laterally unbounded ocean is considered using linear water wave theory. A perturbation analysis is employed to obtain the velocity potential, the reflection and the transmission coefficients up to the first order in terms of integrals involving the shape functions c(x) representing the bottom undulation. Finite cosine transform is used to find the first order potential, and this potential is utilised in obtaining the first order reflection and transmission coefficients. Some particular forms of the shape function representing an exponentially damped undulation, a single hump and a patch of sinusoidal ripples are considered and the integrals for the reflection and transmission coefficients are evaluated. For the exponentially damped undulation, it is observed that the reflection ceases much before transmission while for the single hump, reflection and transmission go hand in hand up to a certain value of the wavenumber, after which they vanish. For the patch of sinusoidal ripples having the same wavenumber, the reflection coefficient up to the first order is found to be an oscillatory function in the quotient of twice the component of the wavenumber along x-axis and the ripple wavenumber. When this quotient becomes one, the theory predicts a resonant interaction between the bed and free surface, and the reflection coefficient becomes a multiple of the number of ripples. High reflection of the incident wave energy occurs if this number is large. Also, when a patch of ripples having different wavenumbers is considered the same result follows. Known results for the normal incidence are recovered as special cases for the patch of sinusoidal ripples. The theoretical observations are shown computationally. 相似文献
2.
S. Mohapatra 《地球物理与天体物理流体动力学》2013,107(5):347-374
Scattering of oblique incident waves by small bottom undulation in a two-layer fluid, where the upper layer has a thin ice-cover while the lower one has the undulation, is investigated within the framework of linearized water wave theory. The ice-cover is being modeled as an elastic plate of very small thickness. There exist two modes of time-harmonic waves–one with lower wave number propagating along the ice-cover (ice-cover mode) and the other with higher wave number along the interface (interfacial mode). A perturbation analysis is employed to solve the corresponding boundary value problem governed by modified Helmholtz equation and thereby evaluating the reflection and transmission coefficients approximately up to first order for both modes. A patch of sinusoidal ripples, having two different wave numbers over two consecutive stretches, is considered as an example and the related coefficients are determined. It is observed that when the wave is incident on the ice-cover surface we always find energy transfer to the interface, but for interfacial incident waves there are parameter ranges for which no energy transfer to the ice-cover surface is possible. Also it is observed that for small angles of incidence, the reflected energy is more as compared to the other angles of incidence. These results are demonstrated in graphical form. From the derived results, the solutions for problems with free surface can be obtained as particular cases. 相似文献
3.
Oblique wave scattering by undulating porous bottom in a two-layer fluid: Fourier transform approach
Srikumar Panda 《地球物理与天体物理流体动力学》2014,108(6):587-614
The problem involving scattering of oblique waves by small undulation on the porous ocean bed in a two-layer fluid is investigated within the framework of linearised theory of water waves where the upper layer is free to the atmosphere. In such a two-layer fluid, there exist waves with two different wave numbers (modes): wave with lower wave number propagates along the free surface whilst that with higher wave number propagates along the interface. When an oblique incident wave of a particular mode encounters the undulating bottom, it gets reflected and transmitted into waves of both modes so that some of the wave energy transferred from one mode to another mode. Perturbation analysis in conjunction with Fourier transform technique is used to derive the first-order corrections of velocity potentials, reflection and transmission coefficients at both modes due to oblique incident waves of both modes. One special type of undulating bottom topography is considered as an example to evaluate the related coefficients in detail. These coefficients are shown in graphical forms to demonstrate the transformation of water wave energy between the two modes. Comparisons between the present results with those in the literature are made for particular cases and the agreements are found to be satisfactory. In addition, energy identity, an important relation in the study of water wave theory, is derived with the help of the Green’s integral theorem. 相似文献
4.
A wave‐?ume experiment was conducted to examine the formative condition for three types of distinctive bedforms that emerged through deformation of existing ripples due to waning wave power. They were ripple marks with: (1) a single secondary crest, (2) double secondary crests, and (3) a rounded crest. Data were analysed using two parameters, kh and d0/λ*, where k is the wave number, h is the water depth, d0 is the near‐bottom orbital diameter, and λ* is the spacing of existing ripples. The former quantity, kh, was employed as a surrogate for the degree of ?ow asymmetry. The result showed that ripples with secondary crests developed under a rather symmetrical ?ow ?eld with kh ? 0·7, if d0/λ* ? 1·2, whereas rounded‐crest ripples emerged under asymmetrical ?ow ?eld with kh ? 0·7, if d0/λ* ? ?2·9 kh + 3·2. The number of secondary crests, which initially occurred in each trough, was single if d0/λ* ? 0·8, or double if d0/λ* ? 0·8. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
5.
Atsushi Kubokawa 《地球物理与天体物理流体动力学》2013,107(2):119-137
Although the study of topographic effects on the Rossby waves in a stratified ocean has a long history, the wave property over a periodic bottom topography whose lateral scale is comparable to the wavelength is still not clear. The present paper treats this problem in a two-layer ocean with one-dimensional periodic bottom topography by a simple numerical method, in which no restriction on the wavelength and/or the horizontal scale of the topography is required. The dispersion diagram is obtained for a wavenumber range of [?π/L b , π/L b ], where L b is the periodic length of the topography. When the topographic?β?is not negligible compared to the planetary β, the Rossby wave solutions around the wavenumbers which satisfy the resonant condition among the waves and topography disappear and separate into an infinite number of discrete modes. For convenience, each mode is numbered in order of frequency. As topographic height is increased, the high frequency barotropic Rossby wave (mode 1) becomes a topographic mode which can exist even on the f plane, and the highfrequency baroclinic mode (mode 2) becomes a surface intensified mode. Behaviors of low frequency modes are somewhat complicated. When the topographic amplitude is small, the low frequency baroclinic modes tend to be bottom trapped and the low frequency barotropic modes tend to be surface intensified. As topographic amplitude further increases, the relation between the mode number and vertical structure changes. This change can be attributed to the increase of the frequency of the topographic mode with the topographic amplitude. 相似文献
6.
Field measurements of wave ripples and megaripples were made with a Sand Ripple Profiler in the surf and shoaling zones of a sandy macrotidal dissipative beach at Perranporth, UK in depths 1–6 m and significant wave heights up to 2.2 m. A frequency domain partitioning approach allowed quantification of height (η), length (λ) and migration rate of ripples and megaripples. Wave ripples with heights up to 2 cm and wavelengths ～20 cm developed in low orbital velocity conditions (u m?<?0.65 m/s) with mobility number ψ?<?25. Wave ripple heights decreased with increasing orbital velocity and were flattened when mean currents were >0.1 m/s. Wave ripples were superimposed on top of megaripples (η?=?10 cm, λ?=?1 m) and contributed up to 35 % of the total bed roughness. Large megaripples with heights up to 30 cm and lengths 1–1.8 m developed when the orbital velocity was 0.5–0.8 m/s, corresponding to mobility numbers 25–50. Megaripple heights and wavelengths increased with orbital velocity but reduced when mean current strengths were >0.15 m/s. Wave ripple and megaripple migrations were generally onshore directed in the shoaling and surf zones. Onshore ripple migration rates increased with onshore-directed (+ve) incident wave skewness. The onshore migration rate reduced as offshore-directed mean flows (undertow) increased in strength and reached zero when the offshore-directed mean flow was >0.15 m/s. The migration pattern was therefore linked to cross-shore position relative to the surf zone, controlled by competition between onshore-directed velocity skewness and offshore-directed mean flow. 相似文献
7.
A.G. Davies 《Continental Shelf Research》1985,4(5):553-580
The results of two field experiments are described, both of which were carried out at Blackpool Sands, Start Bay. In the first experiment in 1978, observations were made of the near-bed flow, and of the movement of coarse sand on the bed, beneath progressive swell waves in shallow water. In the second experiment in 1980, similar observations were made, but for a bed comprising medium to fine sand, and for a more varied range of wave periods. In addition, a number of observations were made of the formation of ripples on an initially flat sand bed. For the naturally rippled beds, critical conditions for the onset of vortex formation and shedding have been established, and reasonable agreement with previous laboratory results has been found. In particular, it has been shown that vortex formation occurs above the lee slopes of ripples only if the near-bed orbital excursion exceeds the ripple wavelength. Prior to certain experimental runs, the area of the seabed in the vicinity of the bottom rig was flattened by divers, and an (equilibrium) ripple pattern was allowed to develop. The wavelengths of the ripples which formed have been found to be in close agreement with the field results of previous workers. To examine in detail some of the properties of separating flow above a rippled bed, an irrotational standing vortex model is presented. 相似文献
8.
与平面波反射系数相比,球面波反射系数可以更精确地描述实际地震波的反射特征.近些年关于球面波的研究主要聚焦于球面波反射系数随入射角的变化规律,很少对球面波反射系数随频率的变化(频变)做详细研究.为了更全面地了解球面波的反射机制,本文研究了两层弹性介质中球面波PP反射系数(幅值和相位)的频变规律.文中基于经典的Sommerfeld积分构造球面波PP反射系数,通过自适应的Gauss-Kronrod求积算法对其进行稳定的数值计算.数值试验发现,对于不同的介质参数,球面波反射系数表现出了复杂的频变规律.尤其是当平面波反射系数为零时,对应的球面波反射系数是非零的,且球面波反射系数的相位随频率增加在高频趋近于90°或-90°,即此时球面反射波相对于入射波会有90°的相位旋转.对四类AVO模型的测试表明,球面波反射系数与平面波反射系数在临界角附近和低频时差异很大. 相似文献
9.
Anatoliy Filonov 《Ocean Dynamics》2011,61(7):917-931
The dynamics of a semidiurnal internal tidal wave at a narrow Mexican Pacific shelf is discussed using the data of temperature
obtained by an anchored instrument and data of field surveys. The internal tide on the shelf is dominated by an inclined wave,
which propagates upward and onshore along a continental slope. Despite its reflection from the bottom and from the surface
of the ocean, they remain inclined and totally destroyed over the course of one wavelength. Due to wave reflection from the
inclined bottom, the horizontal and vertical wave number increase threefold when the wave goes into shallow waters. The wave
undergoes nonlinear transformation and overturns forming several homogeneous temperature layers up to 20 m thick. The most
intense disturbances of water layers are observed near the bottom, where the slope angle approaches its critical value. Because
of nonlinear effects, the wave carries cool deep water out to the shallow depth and causes coastal upwelling. Intense solar
warming together with vertical mixing results in a rapid rise of temperature in the 130-m water column that was observed. 相似文献
10.
11.
光滑处理使得单界面成为非均匀薄层,界面反射转变为层反射.为了探讨光滑处理的影响,以平面波作为入射波场,首先利用过渡层反射系数推导了反射信号的理论公式,然后就非均匀薄层下反射系数的计算问题,给出了具体的实现算法,并通过与经典Epstein过渡层反射系数解析结果的对比说明了算法的精度.最后在单界面及其被光滑后界面的对比分析中,得出了几点重要结论：随着光滑次数的增加,反射信号的到时基本保持不变,而反射信号的主频与能量呈减少趋势,其中信号能量在低光滑次数的衰减速率明显大于高光滑次数. 相似文献
12.
The bottom simulating reflector （BSR） in gas hydrate-bearing sediments is a physical interface which is composed of solid, gas, and liquid and is influenced by temperature and pressure. Deep sea floor sediment is a porous, unconsolidated, fluid saturated media. Therefore, the reflection and transmission coefficients computed by the Zoeppritz equation based on elastic media do not match reality. In this paper, a two-phase media model is applied to study the reflection and transmission at the bottom simulating reflector in order to find an accurate wave propagation energy distribution and the relationship between reflection and transmission and fluid saturation on the BSR. The numerical experiments show that the type I compressional （fast） and shear waves are not sensitive to frequency variation and the velocities change slowly over the whole frequency range. However, type II compressional （slow） waves are more sensitive to frequency variation and the velocities change over a large range. We find that reflection and transmission coefficients change with the amount of hydrate and free gas. Frequency, pore fluid saturation, and incident angle have different impacts on the reflection and transmission coefficients. We can use these characteristics to estimate gas hydrate saturation or detect lithological variations in the gas hydrate-bearing sediments. 相似文献
13.
Previous studies have shown that the Pacific geoid and gravity fields exhibit lineated anomalies, trending approximately in the direction of absolute plate motion over the underlying mantle. Because the undulations obliquely cross fracture zones they have often been attributed a convective origin. Recently, lithospheric boudinage caused by diffuse extension has been proposed as a possible mechanism. We have examined the undulations in the free-air anomalies, geoid and bathymetry over a portion of the Pacific Plate to determine quantitatively how the undulations are related to plate motion. We compare the observed data to an axisymmetric, sinusoidal undulation defined in an arbitrary frame of reference; in particular, we seek the north pole of this reference frame that maximizes the correlation between data and model. Poles that are close to the Pacific hotspot pole represent copolar undulations possibly related to plate motion. The distance between the best-fitting poles and the hotspot pole is determined as a function of undulation wavelength and reveals several minima (with distance < 10°) for discrete geoid wavebands centered on wavelengths of 160 km, 225 km, 287 km, 400 km, 660 km, 850 km, 1000 km and 1400 km. Bathymetry data have copolar bathymetric expressions as well, giving an implied admittance of 2–3 m/km. The most co-polar geoid/bathymetry undulations (with poles within 2–3° of the average Pacific Euler pole) have wavelengths of 280 km and 1050 km, respectively. The latter could have a convective origin or be related to the spacing of hotspot swells. The former may reflect lithospheric boudinage formed in response to diffuse extension, but could also have a dynamic origin since flexural dampening may only have attenuated the bathymetric amplitude by 50% or less. Radiometric dating of volcanic ridges found in the troughs of prominent gravity lineations gives ages that correlate well with documented changes in Pacific and Indo/Australian Plate motion, suggesting the ridges formed in response to intermittent plate boundary stresses and not as a direct consequence of small-scale convection or diffuse extension. 相似文献
14.
消除海底起伏影响的海洋地震波场正反向延拓 总被引：1，自引：0，他引：1
为了解决海底起伏变化对地震波场的影响问题,本文提出将（x-z）域中的曲网格映射成（ξ,η）域中的矩形网格,推导出（ξ,η）域中的二维标量声波方程,根据推导出来的波动方程采用逆时有限差分法将海面上采集到的地震波场在（ξ,η）域中向下延拓至海底面,延拓时采用海水的速度,然后采用顺时有限差分法将延拓后的地震波场再反延拓到海面上,延拓时采用海底面以下地层的速度,从而消除了海底起伏带来的负面影响。模型及实际地震资料的计算分析表明该方法不但能够校正由于海底起伏所引起的海底面下地层反射波场的不连续性还能够校正由于海底起伏所引起的地震波的动力学特征的变化。对延拓前后的地震波场进行速度反演,延拓后反演的地层速度比延拓前反演的地层速度的精度提高很多,延拓前后地震波场的叠加剖面对比表明该延拓方法能够明显提高地震波场的成像质量。 相似文献
15.
Dirk Goossens 《地球表面变化过程与地形》1991,16(8):689-699
The effect of a change of wind direction on the orientation (and some other morphometric characteristics) of aeolian dust ripples is investigated. Ripple formation is simulated in a wind tunnel on surfaces that are already characterized by a previously established rippling. The effect of a wind rotation of 45 degrees, 90 degrees, and 180 degrees is examined. It is found that wind rotations of 45 and 180 degrees will lead towards a ripple alignment perpendicular to the last air flow. A wind rotation of 90 degrees, however, leads towards a ripple alignment perpendicular to the resultant wind direction. The faster the wind blows, the more this effect is expressed. No distinct relationship exists between the asymmetry of a dust ripple (and a dust ripple field) and the direction of the wind blowing as the ripples formed. As the orientation and asymmetry of aeolian dust ripples do not necessarily reflect the air flow direction during which the ripples formed, great care should be taken when reconstructing wind directions from such aeolian ripples. 相似文献
16.
Barchans, isolated crescent‐shaped bedforms, are believed to be formed under almost unidirectional wind or water ?ows and limited sand supply. The formation of barchan morphologies under the action of purely oscillatory wave motion has not yet been fully investigated. The present study attempted to form barchan topography in a wave ?ume and to compare this with barchans in the ?eld. Barchan morphologies of ripple size, called the barchan ripples, were generated from a ?at bed by the action of waves. The horn width, the distance between horn tips, of the barchan ripples increased linearly with an increase in the total length, the overall length projected on the centre line of the barchan, with a coef?cient common to barchan dunes in deserts. The ratio of horn length to horn width of the barchan ripples was smaller than that of barchan dunes, but similar to that of subaqueous barchans in the ?eld. The longer the wave period was, the larger the ratio of the body length to horn width became. Most subaqueous barchans formed under waves (in the laboratory) and unidirectional ?ows (in the ?eld) had blunter horns than subaerial barchans. The shape of the barchan ripples changed with wave period. The outer rim became rounder with increasing wave period. The relationship between the base area and the height of barchan morphologies seems to be linear, with a constant coef?cient for the scale from ripples to dunes. The barchan ripples showed a linear relationship between the height and the horn width, similar to that for barchan dunes. The migration speed of the barchan ripples was proportional to the cube of the ?ow velocity and was inversely proportional to height. The same relation with a different value of the coef?cient was obtained for barchan dunes. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
17.
J. Guilln S. Soriano M. Demestre A. Falqus A. Palanques P. Puig 《Continental Shelf Research》2008,28(17):41
This work deals with the potential influence of benthic communities on the sediment dynamics of the coastal zone, and specifically with the modifications to bottom roughness caused by communities and their effects on wave propagation across the coastal profile. Time-series of video observations of the sea bottom on the Ebro delta coast were analysed in order to estimate the bottom roughness associated with physical and biological morphological components and the sediment reworking rates caused by epifaunal organisms. Biological roughness was mainly caused by ophiuroids and tanatocenosis of bivalve and gastropod shells, which changed their abundance during the study period. The total biological roughness (Kbio) ranged between 0.27 and 0.81 cm and represented a significant part (<20%) of the total form drag roughness. Flattening of ripples caused by bioturbation was observed under low-energy conditions. Surface sediment perturbation and bioturbation rates were also estimated. Based on these observations a wave propagation model was applied in order to carry out a sensitivity analysis of the significance of biological roughness on wave dissipation in the study area under different wave conditions. 相似文献
18.
Most amplitude versus offset (AVO) analysis and inversion techniques are based on the Zoeppritz equations for plane‐wave reflection coefficients or their approximations. Real seismic surveys use localized sources that produce spherical waves, rather than plane waves. In the far‐field, the AVO response for a spherical wave reflected from a plane interface can be well approximated by a plane‐wave response. However this approximation breaks down in the vicinity of the critical angle. Conventional AVO analysis ignores this problem and always utilizes the plane‐wave response. This approach is sufficiently accurate as long as the angles of incidence are much smaller than the critical angle. Such moderate angles are more than sufficient for the standard estimation of the AVO intercept and gradient. However, when independent estimation of the formation density is required, it may be important to use large incidence angles close to the critical angle, where spherical wave effects become important. For the amplitude of a spherical wave reflected from a plane fluid‐fluid interface, an analytical approximation is known, which provides a correction to the plane‐wave reflection coefficients for all angles. For the amplitude of a spherical wave reflected from a solid/solid interface, we propose a formula that combines this analytical approximation with the linearized plane‐wave AVO equation. The proposed approximation shows reasonable agreement with numerical simulations for a range of frequencies. Using this solution, we constructed a two‐layer three‐parameter least‐squares inversion algorithm. Application of this algorithm to synthetic data for a single plane interface shows an improvement compared to the use of plane‐wave reflection coefficients. 相似文献
19.
We characterize the seismic response of Lake Vostok, an Antarctic subglacial lake located at nearly 4 km depth below the ice sheet. This study is relevant for the determination of the location and morphology of subglacial lakes. The characterization requires the design of a methodology based on rock physics and numerical modelling of wave propagation. The methodology involves rock-physics models of the shallow layer (firn), the ice sheet and the lake sediments, numerical simulation of synthetic seismograms, ray tracing, τ–p transforms, and AVA analysis, based on the theoretical reflection coefficients. The modelled reflection seismograms show a set of straight events (refractions through the firn and top-ice layer) and the two reflection events associated with the top and bottom of the lake. Theoretical AVA analysis of these reflections indicates that, at near offsets, the PP-wave anomaly is negative for the ice/water interface and constant for the water/sediment interface. This behaviour is shown by AVA analysis of the synthetic data set. This study shows that subglacial lakes can be identified by using seismic methods. Moreover, the methodology provides a tool for designing suitable seismic surveys. 相似文献
20.
Chung-Muh Tang 《Pure and Applied Geophysics》1972,99(1):150-155
Summary It is shown that in laterally bounded two-layer models of the atmosphere the only permissible meridional variation of the wave solutions is of the form sin(/D) whereD is the lateral width. 相似文献