Dissertationen zum Thema „Nonlinear internal waves“
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Fedorov, Alexey V. „Nonlinear effects in surface and internal waves /“. Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1997. http://wwwlib.umi.com/cr/ucsd/fullcit?p9737309.
Der volle Inhalt der QuelleDobra, Tom. „Nonlinear interactions of internal gravity waves“. Thesis, University of Bristol, 2019. http://hdl.handle.net/1983/4a3f99e2-5e73-4c7c-8d3d-e1141fb23dda.
Der volle Inhalt der QuelleZhao, Zhongxiang. „A study of nonlinear internal waves in the northeastern South China Sea“. Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file 11.38Mb, 181 p, 2005. http://wwwlib.umi.com/dissertations/fullcit/3157312.
Der volle Inhalt der QuelleYuan, Chunxin. „The evolution of oceanic nonlinear internal waves over variable topography“. Thesis, University College London (University of London), 2018. http://discovery.ucl.ac.uk/10053741/.
Der volle Inhalt der QuelleAlias, Azwani B. „Mathematical modelling of nonlinear internal waves in a rotating fluid“. Thesis, Loughborough University, 2014. https://dspace.lboro.ac.uk/2134/15861.
Der volle Inhalt der QuelleSmith, Sean Paul. „Laboratory Experiments on Colliding Nonresonant Internal Wave Beams“. BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3300.
Der volle Inhalt der QuelleStastna, Marek. „Large fully nonlinear solitary and solitary-like internal waves in the ocean“. Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/NQ65262.pdf.
Der volle Inhalt der QuelleLin, Duo-min Wu Theodore Y. T. Wu Theodore Y. T. „Run-up and nonlinear propagation of oceanic internal waves and their interactions /“. Diss., Pasadena, Calif. : California Institute of Technology, 1996. http://resolver.caltech.edu/CaltechETD:etd-12192007-084353.
Der volle Inhalt der QuelleKim, Won-Gyu 1962. „A Study of Nonlinear Dynamics in an Internal Water Wave Field in a Deep Ocean“. Thesis, University of North Texas, 1996. https://digital.library.unt.edu/ark:/67531/metadc278092/.
Der volle Inhalt der QuelleWang, Caixia. „Geophysical observations of nonlinear internal solitary-like waves in the Strait of Georgia“. Thesis, University of British Columbia, 2009. http://hdl.handle.net/2429/17468.
Der volle Inhalt der QuelleCeschini, Joseph J. „Modeling the effects of transbasin nonlinear internal waves through the South China Sea basin“. Monterey, California: Naval Postgraduate School, 2013. http://hdl.handle.net/10945/34641.
Der volle Inhalt der QuelleThe objective of this research is to model and study the effects of transbasin internal waves on low-frequency signal transmission through the South China Sea (SCS) basin. Specifically, the fluctuations in the multipath arrival structure of a 400-Hz acoustic pulse transmitted through a distance of 167-km in the SCS basin in the presence of an internal ocean soliton was modeled and examined. The modeling entailed the integration of a raytracing program with an eigenray search and arrival-structure calculation program, and the use of measured bathymetry and inferred bottom-loss characteristics from previous research. A range-dependent perturbation was added to a range-independent background sound-speed profile to model the varying sound-speed field as the nonlinear ocean internal soliton propagates along the transmission path. All cases studied, each simulating a soliton at a different location, had six distinct acoustic arrivals that suffered from large-amplitude fluctuations (~ 10 dB). The factors that affect the amplitude of the arrivals are changes: in the number of bottom interaction, in ray tube spreading, phase interference and in the number of eigenrays making up an arrival. The results also show that the closer the soliton to the receiver, the less impact the soliton has on the arrival structure.
Mueller, Martin Fritz. „Analytical investigation of internally resonant second harmonic lamb waves in nonlinear elastic isotropic plates“. Thesis, Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/31827.
Der volle Inhalt der QuelleCommittee Chair: Laurence J. Jacobs; Committee Member: Jianmin Qu; Committee Member: Jin-Yeon Kim. Part of the SMARTech Electronic Thesis and Dissertation Collection.
Tiron, Roxana Camassa Roberto. „Strongly nonlinear internal waves in near two-layer stratifications generation, propagation and self-induced shear instabilities /“. Chapel Hill, N.C. : University of North Carolina at Chapel Hill, 2009. http://dc.lib.unc.edu/u?/etd,2527.
Der volle Inhalt der QuelleTitle from electronic title page (viewed Oct. 5, 2009). "... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Mathematics." Discipline: Mathematics; Department/School: Mathematics.
Moncuquet, Adèle. „Coastal internal waves on the Bay of Biscay shelf and their impact on cross-shelf transport“. Electronic Thesis or Diss., Brest, 2024. http://www.theses.fr/2024BRES0010.
Der volle Inhalt der QuelleThe Bay of Biscay (BoB) is a hot spot for the generation of internal tides and nonlinear internal waves (NLIW). Previous studies have focused mainly on the seaward propagation of internal waves, and less on the shoreward propagation. The shelf region can be affected by internal tides and NLIW transport. The shelf is a complex hydrodynamical region and processes of different scales modify the background stratification and currents. Therefore, internal waves transform as they propagate across the shelf. Internal wave transformation on the shelf and the induced transport remain poorly described worldwide, especially on the BoB shelves. In this thesis, we describe the internal tide and NLIW from mooring observations on the BoB shelf and the induced cross-shelf transport. First, we describe the internal tide and NLIW on the Aquitaine shelf using 22 days of measurements (at 62 and 153 m depth). The results highlight the unexpected importance of the internal tide and NLIW during summer-time stratified conditions. NLIW of depression and elevation, with amplitude reaching up to 1/4th of the water depth and propagating shoreward with different speeds were observed. We observed conditions in which depression and elevation waves coexisted within the same internal tide phase, and could potentially interact. The second part of the work is dedicated to crossshelf net transport, associated with internal waves, or internal waves pumping (IWP) on both the Aquitaine and the Armorican shelf. On the Armorican shelf, IWP was the main driver of total transport near the boundaries and counterbalanced the subtidal dynamics in the middle of the water column. On the Aquitaine shelf, the total cross-shelf transport was a combination of subtidal transport and IWP
Renaud, Antoine. „On wave-mean flow interactions in stratified fluid“. Thesis, Lyon, 2018. http://www.theses.fr/2018LYSEN059/document.
Der volle Inhalt der QuelleThe dynamics of planetary-scale geophysical flows is strongly influenced by physicalprocesses, mostly unresolved by general circulation numerical models. To parametrisethe coupling between small and large scales, it is essential to understand the underlying physical mechanisms. In this thesis, we study an emblematic problem of interactions between waves and mean flows: the dynamics of zonal flows forced by internal gravity waves. A striking manifestation of these interactions is the quasi-biennial oscillation (QBO) of equatorial winds in the Earth’s atmosphere. First, we describe a transition to chaos in a classical quasilinear model of the QBO and show that these bifurcations persist in direct numerical simulations. Based on these results, we suggest an interpretation for the observation of the unexpected periodicity disruption of the QBO in 2016. The mechanism by which mean flows are generated by waves in stratified fluids requires the consideration of dissipative effects. This phenomenon is analogous to acoustic "streaming". In a second time, we exploit this analogy to study the generation of mean flows by internal gravity waves close to a wall, using multi-scale asymptotic approaches. Finally, we propose an inertial approach to describe the spontaneous emergence of vortical flows in the presence of waves: we apply the tools of statistical mechanics to calculate the partition of energy between small and large scales in the shallow-water model
Girard, Réjean. „Relativistic nonlinear wave equations with groups of internal symmetry“. Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=75688.
Der volle Inhalt der QuelleTabaei, Befrouei Ali 1974. „Theoretical and experimental study of nonlinear internal gravity wave beams“. Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/30193.
Der volle Inhalt der QuelleIncludes bibliographical references (leaves 121-124).
Continuously stratified fluids, like the atmosphere and the oceans, support internal gravity waves due to the effect of buoyancy. This type of wave motion is anisotropic since gravity provides a preferred direction. As a result, a localized source oscillating at a frequency below the buoyancy frequency in a uniformly stratified Boussinesq fluid, rather than cylindrical wavefronts, gives rise to elongated disturbances propagating along specific directions depending on the driving frequency. Such wave beams can be readily generated in the laboratory by oscillating a cylinder in a stratified fluid tank, and, according to recent numerical simulations and field observations, often arise in the atmosphere due to thunderstorms and may also be generated in the oceans by tidal flow over sea-floor topography. So far, internal wave beams have been studied mostly using the linearized equations of motion valid for small-amplitude disturbances. The present thesis examines theoretically and experimentally some aspects of non-linearity in the propagation, reflection and collision of internal gravity wave beams. An asymptotic theory is developed for the propagation of isolated two-dimensional or axisymmetric nonlinear beams, that also takes into account viscous as well as re- fraction effects due to the presence of a mean flow and non-uniform buoyancy frequency. In this instance, it turns out that non-linearity plays a secondary role even for a finite-amplitude beam, which explains why a linear approach has been useful in interpreting observations of isolated beams in the atmosphere. On the other hand, nonlinear effects play an important part in the reflection of wave beams from a sloping wall.
(cont.) Using small-amplitude expansions, it is shown that nonlinear interactions are confined solely in the vicinity of the sloping wall where the incident and reflected beams meet, and this overlap region acts as a source of additional reflected beams with higher-harmonic frequencies. In some flow geometries, higher-harmonic reflected beams are found on the opposite side to the vertical than the primary reflected beam. Similarly, when two obliquely propagating beams collide, nonlinear interactions in the overlap region induce secondary beams with frequencies equal to the sum and difference of those of the colliding beams, consistent with recent numerical simulations of oscillatory stratified flow of finite depth over a ridge. A singularity arises in the reflection of linear wave beams when the angle of incidence is close to the wall slope and the reflected beam propagates nearly parallel to the sloping wall. The near-critical reflection of weakly nonlinear wave beams is studied separately by a matched-asymptotics approach. Non-linearity alone is not capable of healing the singularity of linear theory, as the inviscid nonlinear response at the critical angle grows with time and most likely eventually overturns. Laboratory experiments are also performed for the reflection of two-dimensional wave beams from a sloping wall. Internal-wave disturbances are generated by oscillating a circular cylinder in salt-stratified water and visualized using the synthetic schlieren non-intrusive technique. Secondary reflected beams due to nonlinear effects can be quite strong under certain flow conditions, and are in excellent agreement with the theoretical predictions in regards to their propagation characteristics.
by Ali Tabaei Befrouei.
Ph.D.
Harris, Victoria Siân. „Creation of nonlinear density gradients for use in internal wave research“. Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/40437.
Der volle Inhalt der Quelle"June 2007."
Includes bibliographical references.
A method was developed to create a nonlinear density gradient in a tank of water. Such gradients are useful for studying internal waves, an ocean phenomenon that plays an important role in climate and ocean circulation. The method was developed by expanding on the two-tank system currently used to create linear density gradients. A mathematical model of the two-tank system was used and a Matlab script was written to solve the model for the required flow rates in the system given a desired density gradient. The method was tested by creating three different density gradients: a linear gradient, a hyperbolic gradient, and a two-layer gradient. It was discovered that for a two-layer gradient the flow rates for each layer must be calculated independently of each other, because of problems integrating over a density gradient with a non-continuous slope. It was also discovered that the system failed at very low flow rates; insufficient mixing in the two-tank system led to gradients weaker than expected. Overall, the measured gradients matched up well with the expected gradients, and it was concluded that the system can successfully produce nonlinear density gradients.
by Victoria Siân Harris.
S.B.
Patel, Rupa Ashyinkumar. „Theory and computation on nonlinear vortex/wave interactions in internal and external flows“. Thesis, Imperial College London, 1997. http://hdl.handle.net/10044/1/8597.
Der volle Inhalt der QuelleDosser, Hayley V. „Propagation and breaking of nonlinear internal gravity waves“. Master's thesis, 2010. http://hdl.handle.net/10048/878.
Der volle Inhalt der QuelleTitle from pdf file main screen (viewed on April 20, 2010). A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Master of Science, Department of Physics, University of Alberta. Includes bibliographical references.
Dorostkar, ABBAS. „Three-Dimensional Dynamics of Nonlinear Internal Waves“. Thesis, 2012. http://hdl.handle.net/1974/7693.
Der volle Inhalt der QuelleThesis (Ph.D, Civil Engineering) -- Queen's University, 2012-12-14 12:45:21.727
Kiss, Andrew Elek. „Nonlinear interactions of internal gravity waves in a continuously stratified fluid“. Thesis, 1995. http://hdl.handle.net/1885/240918.
Der volle Inhalt der QuelleChang, Ming-Huei, und 張明輝. „Study of Large-Amplitude Nonlinear Internal Waves in the South China Sea“. Thesis, 2008. http://ndltd.ncl.edu.tw/handle/86114265552616480614.
Der volle Inhalt der Quelle國立臺灣大學
海洋研究所
96
The study is focused on the large-amplitude nonlinear internal waves (NLIW) in the South China Sea (SCS): the propagation characteristics, the energy, energy flux and dissipation, and the relationship between the interior properties of NLIW and its surface scattering strength. Three sets of long-term ADCP measurements taken on the Dongsha plateau, integrating with both the shipboard measurement and the remote sensing data, are used to study the propagation characteristics of the NLIWs. The moorings were aligned along 21o05’N near the eastern edge of the Dongsha plateau. From east to west, the distances between the two successive moorings are ~8.5’ and ~17’, respectively. The NLIW propagating directions and speeds were computed by NLIW-induced current velocity and NLIW arrival time between two successive mooring stations, respectively. The averaged propagating direction of NLIW is 165o, which is northwestward. The averaged propagating speeds between two successive mooring stations are 1.83±0.38 m/s and 1.61±0.20 m/s from east to west. The above estimations are further verified by the observations of both shipboard marine radar and satellite images. The propagating directions reveal irregular variation. Nonetheless, the propagating speeds, which are higher in Aug.-Oct. and are slower in Jan.-Mar, reveal apparently seasonal variation. Such seasonal variation could relate with the typically seasonal stratification in the SCS, strong stratification in Aug.-Oct and weak stratification in Jan.-Mar. The linear phase speed, which is calculated using the climatological density profiles of Generalized Digital Environmental Model (GDEM) output, has good correlation with the measured NLIW propagating speed. Both the propagation direction and speed reveal daily inequality. Two types of NLIW appear reciprocally around the spring tide. One of them propagates faster and mainly northwestward and the other propagates slower and more northward than the previous one. It could be associated with the tidal current in the Luzon Strait. Three sets of ADCP measurements taken on the Dongsha plateau, on the shallow continental shelf, and on the steep continental slope in the northern South China Sea are analyzed. The data show strong divergences of energy and energy flux of nonlinear internal waves along and across waves’ prevailing westward propagation path. The NLIW energy flux is 8.5 kW m-1 on the plateau, only 0.25 kW m-1 on the continental shelf 220 km westward along the propagation path, and only 1 kW m-1 on the continental slope 120 km northward across the propagation path. Along the wave path on the plateau, the average energy flux divergence of NLIW is ~0.04 W m-2, which corresponds to a dissipation rate of O(10-7-10-6)Wkg-1. Combining the present with previous observations and model results, a scenario of NLIW energy flux in the SCS emerges. NLIWs are generated east of the plateau, propagate predominantly westward across the plateau along a beam of ~100 km width that is centered at ~210N, and dissipate nearly all their energy before reaching the continental shelf. Surface signatures and interior properties of NLIWs were measured during a period of weak northeast wind (~2 m s-1) using shipboard marine radar, ADCP, CTD, and echo sounder. The surface scattering strength measured by the marine radar is positively correlated with the local wind speed when NLIWs are absent. When NLIWs approach, the surface scattering strength within the convergence zone is enhanced. The sea surface scattering induced by NLIWs is equivalent to that of a ~6 m s-1 surface wind speed, i.e., three times greater than the actual surface wind speed. The horizontal spatial structure of the enhanced sea surface scattering strength predicts the horizontal spatial structure of the NLIW. The observed average half-amplitude full width of NLIWs is 1.09±0.2 km; the average half-amplitude full width of the enhanced scattering strength is ~0.57 . The average half-amplitude full width of the enhanced horizontal velocity convergence of NLIWs is approximately equal to . The peak of the enhanced surface scattering leads the center of NLIWs by ~0.46 . NLIW horizontal velocity convergence is positively correlated with the enhancement of the surface scattering strength. NLIW amplitude is positively correlated with the spatial integration of the enhancement of the surface scattering strength within the convergence zone of NLIWs. The analysis concludes that in low-wind conditions remote sensing measurements may provide useful predictions of horizontal velocity convergences, amplitudes, and spatial structures of NLIWs. Further applications and modification of our empirical formulas in different conditions of wind speed, surface waves, and NLIWs, or with other remote sensing methods are encouraged.
Lin, Duo-min. „Run-up and nonlinear propagation of oceanic internal waves and their interactions“. Thesis, 1996. https://thesis.library.caltech.edu/5066/1/Lin_dm_1996.pdf.
Der volle Inhalt der QuelleCAVALIERE, DAVIDE. „Investigation on internal solitary waves breaking for geophysical applications“. Doctoral thesis, 2020. http://hdl.handle.net/11573/1434133.
Der volle Inhalt der QuelleHu, Youna. „The Effects of the Earth's Rotation on Internal Wave Near-resonant Triads and Weakly Nonlinear Models“. Thesis, 2007. http://hdl.handle.net/10012/3180.
Der volle Inhalt der QuelleSagers, Jason Derek. „Predicting acoustic intensity fluctuations induced by nonlinear internal waves in a shallow water waveguide“. Thesis, 2012. http://hdl.handle.net/2152/ETD-UT-2012-08-6025.
Der volle Inhalt der Quelletext
Fu, Ke-Shian, und 傅科憲. „The effect of nonlinearity and mixed layer thickness on the propagation of nonlinear internal waves“. Thesis, 2007. http://ndltd.ncl.edu.tw/handle/z78s3z.
Der volle Inhalt der Quelle國立中山大學
海洋物理研究所
95
This thesis applies a numerical model to study the propagation of internal solitary wave based on a two-dimensional model developed by Lynett and Liu (2002) and modified by Cheng et al. (2005).The numerical model derived assumes weak nonlinearity and weak dispersion in a two-layer inviscid fluid system. The governing continuity and momentum equations are solved and the real topography is included in the wave model. In order to improve the accuracy of simulation, mixed-layer thickness is allowed to change from place to place. Initial conditions are modified so that wave forms of non-hyperbolic -secant functions and wave fronts taken by satellite can be used. The diffraction near the island of Dongsha is simulated, and results of both fixed and variable mixed-layer thickness are compared. Simulated waveform in MODIS images after 24 hours are compared with other wave fronts of the same image. Laterally, internal waves can become very wide when it is far away from its origin. The extra energy can be explained by nonlinear wave-wave interaction because the energy of large amplitude internal wave increases after interacting with smaller internal waves.
Soontiens, Nancy. „Stratified Flow Over Topography: Steady Nonlinear Waves, Boundary Layer Instabilities, and Crater Topography“. Thesis, 2013. http://hdl.handle.net/10012/8049.
Der volle Inhalt der QuelleShieh, Jih-hong, und 謝志宏. „A study of generation and evolution of nonlinear internal waves in the andaman sea by using SAR and MODIS images“. Thesis, 2004. http://ndltd.ncl.edu.tw/handle/81664695225580457037.
Der volle Inhalt der Quelle國立臺灣海洋大學
海洋科學系
92
The main research domain in the earlier articles about internal wave phenomenon in the Andaman Sea, like Osborne (1980) and Alpers (1997). From CRISP and MODIS websites, we searched more than 5000 SAR images during 1995 and 2003 that acquired by ERS-1/2 satellite, and some MODIS images acquired by Terra and Aqua satellite over the Andaman Sea. In order to study the generation and revolution of nonlinear internal wave in the Andaman Sea, we had composed some figures including SAR images and sea bottom topography. We had found another four generation areas of internal wave, one origin of reflection. Since the internal wave was produced, generally spread to the direction of the Malay Peninsula eastwards. The interaction of internal waves was obvious. While the wave packets were propagated onto to the continental shelf, such that the shoaling effect include refraction and breaking was obvious, too.
Wu, Chung-lin, und 吳承霖. „Simulation of nonlinear internal wave based on two-layer fluid model“. Thesis, 2011. http://ndltd.ncl.edu.tw/handle/83111631729069116253.
Der volle Inhalt der Quelle國立中山大學
海下科技暨應用海洋物理研究所
99
The main topic of this research is the simulation of internal wave interaction by a two-dimensional numerical model developed by Lynett & Liu (2002) of Cornell University, then modified by Cheng et al. (2005). The governing equation includes two-dimensional momentum and continuity equation. The model uses constant upper and lower layer densities; hence, these factors as well as the upper layer thickness. Should be determined before the simulation. This study discusses the interface depth and the density according to the buoyancy frequency distribution, the EOF, and the eigen-value based on the measured density profile. Besides, a method based on the two-layer KdV equation and the KdV of continuously-stratified fluid. By minimize the difference of linear celeriy, nonlinear and dispersion terms, the upper layer thicknes can also be determined. However, the interface will be much deeper than the depth of max temperature drop in the KdV method if the total water depth is bigger than 500 meters. Thus, the idealization buoyancy frequency formula proposed by Vlasenko et al. (2005) or Xie et al. (2010) are used to modify the buoyancy frequency. The internal wave in the Luzon Strait and the South China Sea are famous and deserves detailed study. We use the KdV method to find the parameters in the two fluid model to speed up the simulation of internal wave phenomena found in the satellite image.
Zhang, Zh-Wei, und 張志瑋. „Three Dimensional Variation of Underwater Acoustic Propagation due to Nonlinear Internal Wave“. Thesis, 2011. http://ndltd.ncl.edu.tw/handle/55924144831209462384.
Der volle Inhalt der Quelle國立臺灣大學
工程科學及海洋工程學研究所
99
There is a biggest internal wave in the South China Sea. The amplitude can more than one hundred meter and the vertical current velocity can large then 2.5 meters per second. The internal wave perturbs the water column dramatically which affect sound propagation greatly. This thesis is about the sound propagation’s variation in three dimensions due to internal waves. The acoustic and environment data are from the 2007 NLIWI experiment. We study both depression and elevation internal waves simulates KdV formula analysis the 3D effect on acoustic propagation using FOR3D model.
Lee, Chou-Heng, und 李周衡. „A Study of Generation and Evolution of Nonlinear Internal Wave in the Sulu Sea Using SAR“. Thesis, 2001. http://ndltd.ncl.edu.tw/handle/41353851416819992372.
Der volle Inhalt der Quelle國立海洋大學
海洋科學系
89
The large-scaled internal wave phenomenon in the Sulu Sea in Philippine is prominent. In the early research, only Apel et al. (1985) acquired numerous in-situ data in the Sulu Sea, analyzed less low-resolution visible-wavelength imagery and applied the KdV equation to carry out the numerical simulation. However, few papers had been published since then. Recently the spatial and temporal resolution of the spaceborn Synthetic Aperture Radar (SAR) have largely promoted. From Centre for Remote Imaging, Sensing and Processing (CRISP) web site, http://crisp.nus.edu.sg , we first searched about four hundred SAR images captured during 1996 and 2001 by the ERS-1/2 satellite over the Sulu Sea. In order to investigate the generation and evolution of nonlinear internal wave in the Sulu Sea in Philippine, we have plot some multi-layer synthetic figures including SAR images and sea bottom topography by seasons and months, so they are easy to study and reveal some features. It is found that most of the internal waves are generated from the Sulu archipelago in southeast of the Sulu Sea and travels toward the Palawan Island. Some sources are near the Pearl Bank and Doc Can Island instead of the underwater shallow sill between the two islands. Another source also have been found near the Pandu Can Island about sixty five kilometers northeast from the Doc Can Island. When the water depth becomes shallow to about two hundred meters, the refraction effect is significant.