Relative role of subinertial and superinertial modes in the coastal long wave response forced by the landfall of a tropical cyclone

A set of numerical experiments has been performed in order to analyze the long-wave response of the coastal ocean to a translating mesoscale atmospheric cyclone approaching the coastline at a normal angle. An idealized two-slope shelf topography is chosen. The model is forced by a radially symmetric atmospheric pressure perturbation with a corresponding gradient wind field. The cyclone's translation speed, radius, and the continental shelf width are considered as parameters whose impact on the long wave period, modal structure, and amplitude is studied. Subinertial continental shelf waves (CSW) dominate the response under typical forcing conditions and on the narrower shelves. They propagate in the downstream (in the sense of Kelvin wave propagation) direction. Superinertial edge wave modes have higher free surface amplitudes and faster phase speeds than the CSW modes. While potentially more dangerous, edge waves are not as common as subinertial shelf waves because their generation requires a wide, gently sloping shelf and a storm system translating at a relatively high (∼10 m s⁻¹ or faster) speed. A relatively smaller size of an atmospheric cyclone also favors edge wave generation. Edge waves with the highest amplitude (up to 60% of the forced storm surge) propagate upstream. They are produced by a storm system with an Eulerian time scale equal to the period of a zero-mode edge wave with the wavelength of the storm spatial scale. Large amplitude edge waves were generated during Hurricane Wilma's landfall (2005) on the West Florida shelf with particularly severe flooding occurring upstream of the landfall site.     

Generation of baroclinic topographic waves by a tropical cyclone impacting a low-latitude continental shelf

Numerical model experiments have been performed to analyze the low-latitude baroclinic continental shelf response to a tropical cyclone. The theory of coastally trapped waves suggests that, provided appropriate slope, latitude, stratification and wind stress, bottom-intensified topographic Rossby waves can be generated by the storm. Based on a scale analysis, the Nicaragua Shelf is chosen to study propagating topographic waves excited by a storm, and a model domain is configured with simplified but similar geometry. The model is forced with wind stress representative of a hurricane translating slowly over the region at 6 km h⁻¹. Scale analysis leads to the assumption that baroclinic Kelvin wave modes have minimal effect on the low-frequency wave motions along the slope, and coastal-trapped waves are restricted to topographic Rossby waves. Analysis of the simulated motions suggests that the shallow part of the continental slope is under the influence of barotropic topographic wave motions and at the deeper part of the slope baroclinic topographic Rossby waves dominate the low-frequency motions. Numerical solutions are in a good agreement with theoretical scale analysis. Characteristics of the simulated baroclinic waves are calculated based on linear theory of bottom-intensified topographic Rossby waves. Simulated waves have periods ranging from 153 to 203 h. The length scale of the waves is from 59 to 87 km. Analysis of energy fluxes for a fixed volume on the slope reveals predominantly along-isobath energy propagation in the direction of the group velocity of a topographic Rossby wave. Another model experiment forced with a faster translating hurricane demonstrates that fast moving tropical cyclones do not excite energetic baroclinic topographic Rossby waves. Instead, robust inertial oscillations are identified over the slope.     

Internal tides and waves near the continental shelf edge

Abstract

The subject is reviewed from the viewpoints of theory, internal tide and wave structure and their implications.

A wider theoretical context suggests scope for further investigation of natural or nearly-trapped forms above the inertial frequency.

Although internal tides in many locations are observed to have first-mode vertical structure, higher modes are seen offshore from shallow shelf-break forcing and for particular Froude numbers, and may be expected locally near generation. Bottom intensification is often observed where the sea floor matches the characteristic slope. Solitons form from internal tides of large amplitude or at large changes of depth.

Internal tides and solitons are observed also at many sills and in straits, and to intensify in canyons.

Non-linear effects of the waves, especially solitons, include the conveyance of water, nutrients, ‘‘mixing potential'’ etc. away from their source to other locations, and the generation of mean currents. The waves transfer energy and possibly heat between the ocean and shelf, may be a source of medium frequency waves on the shelf (periods of minutes) and can contribute to interior mixing and overturning, bottom stirring and sediment movement.     

Critical levels for forced Rossby and continental shelf waves

The generation of waves on a geostrophic shear flow by a travelling forcing pattern is considered. The model describes both atmospheric Rossby waves on a zonal shear flow and continental shelf waves on a boundary current. By means of the Laplace transform technique, the development of the solution in time is studied, starting from some initial instant when the forcing starts. The asymptotic form of the forced solution is shown to depend crucially upon whether the speed of the travelling forcing lies inside the range of the current or not. The possible application of the results to the Florida current is discussed.     

The evolution of an internal bore at the Malin shelf break

Observations of internal waves were made at the Malin shelf edge during SESAME (Shelf Edge Studies Acoustic Measurement Experiment), a part of the NERC LOIS-SES experiment, in August-September 1996. These measurements provide a high resolution dataset demonstrating internal wave generation and propagation. This note presents observations of the evolution of an internal bore. The process is shown clearly in a sequence of thermistor chain tows across the shelf break covering a complete tidal cycle, as the double-sided bore transforms into a group of undulations and eventually into more distinct solitary waveforms. Current structures associated with the bore and waves were also observed by ship-mounted ADCP. Analysis of the waveforms in terms of the linear modes and empirical orthogonal functions (EOFs) indicate the dominance of the first mode, which is typical of a shallow water seasonal thermocline environment. Determination of the phase speed of the waves from the consecutive ship surveys enabled the Doppler shift in the towed data to be removed, allowing analysis of the real length scales of the waves. The bore evolution has been modelled using a first order non-linear KdV model for the first mode, initialised with the waveform in the first survey. Comparison of the model and the observations show close agreement in the amplitudes, length scales, phase speeds and separations of the leading internal waves as they evolve. Finally, analysis of the observed internal wave shapes indicates that, within the uncertainties of measurement, the wave-lengths lie between those predicted by first and second order soliton theory.     

Numerical experiments on the generation of long ocean waves in coastal waters of the Buenos Aires province,Argentina

A numerical model (two horizontal dimensions, vertically integrated) is used to investigate the generation of long ocean waves, ranging from 20 min to almost 2 h, at Buenos Aires continental shelf. The domain includes the Río de la Plata estuary and the continental shelf together and extends from 33.5° to 40.5°S latitude, and from 51° to 63°W longitude. Sea-level oscillations are modeled by forcing with passage of atmospheric cold fronts and atmospheric gravity waves. Both forcing mechanisms, which have been present during high activity lapses of long ocean waves, are mathematically implemented. After several numerical simulations, it is concluded that the pressure and wind fields associated to cold fronts do not generate long ocean waves in the area, though they do produce disturbances with periods longer than the tidal ones. On the other hand, it is so concluded that atmospheric gravity waves are an effective mechanism to force long ocean waves. Results obtained show that generation of long ocean waves is highly sensitive depending on the propagation direction and the phase speed of the atmospheric gravity waves. The long ocean wave event detected during the large-amplitude gravity-wave event of 13 October 1985 is successfully simulated. Finally, all our results suggest that atmospheric gravity waves are a highly effective mechanism forcing for the generation of long ocean waves in Buenos Aires coastal waters.     

On the completeness of inertial wave modes in rotating annular channels

An important unanswered mathematical question in the theory of rotating fluids has been the completeness of the inviscid eigenfunctions which are usually referred to as inertial waves or inertial modes. We provide for the first time a mathematical proof for the completeness of the inertial modes in a rotating annular channel by establishing the completeness relation, or Parseval’s equality, for any piecewise continuous, differentiable velocity of an incompressible fluid.     

Study on rupture zone of the M=8.1 Kunlun Mountain earthquake using fault-zone trapped waves

Introduction The study on deep crustal faults has been one of the most vigorous subjects in seismology. In the past, 3-D deep seismic sounding and 3-D seismic tomography were usually used for this pur-pose. But it is difficult to obtain the fine structures of the faults in deep crust by these methods. Recently, seismologists in the world pay more attention to the fault zone trapped waves. Since the fault-zone trapped waves arise from coherent multiple reflections at two boundaries of the fau…     

利用断层围陷波研究昆仑山口西8.1级地震破裂面

利用横跨地表破裂带的小点距的地震测线, 对2001年11月14日昆仑山口西8.1级地震进行了断层围陷波的观测实验. 经过数字滤波和频谱分析等技术, 由地震记录图中分离出了断层围陷波. 资料处理结果表明: ① 无论是人工地震震源还是天然地震震源, 只要位于断层带内或紧靠断层带, 均能激发断层围陷波; ② 断层围陷波的能量主要集中于断层带内, 其振幅随测点与断层带距离的增加而急剧衰减; ③ 断层围陷波的优势频率与断层的宽度及断层带内介质的速度有关, 断层带越宽, 或断层带内部介质速度越低, 则观测到的断层围陷波的优势频率越低; ④ 断层围陷波存在着频散现象; ⑤ 根据昆仑山口西地震测线断层围陷波的观测结果, 可推断该处破裂面宽度为300 m左右, 远远大于地表破裂带的宽度.      

Continental shelf wave scattering by a semi-infinite coastline; partial removal of the “rigid lid”

Abstract

By relaxing the rigid-lid approximation in the ocean, significant improvements are made to the mathematical and physical aspects of a previously presented model. The difficulties associated with |κ| in wavenumber space are eliminated and the velocities remain bounded at the coastal tip. The method of solution has significant changes but the well-known shelf waves are essentially unaltered and the overall conclusions are similar.     

A coupled tide-wave model for the NW European shelf seas

Understanding the interaction of tides and waves is essential in many studies, including marine renewable energy, sediment transport, long-term seabed morphodynamics, storm surges and the impacts of climate change. In the present research, a COAWST model of the NW European shelf seas has been developed and applied to a number of physical processes. Although many aspects of wave–current interaction can be investigated by this model, our focus is on the interaction of barotropic tides and waves at shelf scale. While the COWAST model was about five times more computationally expensive than running decoupled ROMS (ocean model) and SWAN (wave model), it provided an integrated modelling system which could incorporate many wave–tide interaction processes, and produce the tide and wave parameters in a unified file system with a convenient post-processing capacity. Some applications of the model such as the effect of tides on quantifying the wave energy resource, which exceeded 10% in parts of the region, and the effect of waves on the calculation of the bottom stress, which was dominant in parts of the North Sea and Scotland, during an energetic wave period are presented, and some challenges are discussed. It was also shown that the model performance in the prediction of the wave parameters can improve by 25% in some places where the wave-tide interaction is significant.     

松软覆盖层对隐伏断层带围陷波的影响研究

利用二维非均匀介质地震波传播的伪谱和有限差分混合方法,通过数值计算,讨论了松软覆盖层对隐伏断层带围陷波特征的影响.在没有覆盖层的情况下,围陷波振幅和围岩上相比明显增加,持续时间变长.覆盖层造成围岩上地面运动振幅增大,围陷波的部分能量传播到覆盖层中,使得围陷波的能量变小.随着覆盖层厚度增加,围陷波的振幅越来越小,和围岩上...     

Study on rupture zone of the M =8.1 Kunlun Mountain earthquake using fault-zone trapped waves

The observation of the fault-zone trapped waves was conducted using a seismic line with dense receivers across surface rupture zone of the M=8.1 Kunlun Mountain earthquake. The fault zone trapped waves were separated from seismograms by numerical filtering and spectral analyzing. The results show that: a) Both explosion and earthquake sources can excite fault-zone trapped waves, as long as they locate in or near the fault zone; b) Most energy of the fault-zone trapped waves concentrates in the fault zone and the amplitudes strongly decay with the distance from observation point to the fault zone; c) Dominant frequencies of the fault-zone trapped waves are related to the width of the fault zone and the velocity of the media in it. The wider the fault zone or the lower the velocity is, the lower the dominant frequencies are; d) For fault zone trapped waves, there exist dispersions; e) Based on the fault zone trapped waves observed in Kunlun Mountain Pass region, the width of the rupture plane is deduced to be about 300 m and is greater than that on the surface. Foundation item: Joint Earthquake Science Foundation of China (201001). Contribution No. RCEG200305, Research Center of Exploration Geophysics, China Earthquake Administration.     

Modelling the Quaternary evolution of shore platforms and erosional continental shelves

A mathematical model was used to investigate the effect of glacially induced fluctuations in sea level on the evolution of wave‐cut shore platforms and erosional continental shelves during the Quaternary. The model used two deep‐water wave sets, which were used to calculate breaker height and depth, and the force of the waves at the waterline, according to the width and bottom roughness of the surf zone and the gradient of the submarine slope. The model also incorporated an erosional threshold related to the strength of the rocks, the number of hours each year in which the water level is at each intertidal elevation and the amount and persistence of the debris at the cliff foot. Most runs were made using a sea level model that consisted of 26 glacial cycles from 2 million to 0·9 million years ago, and nine, of approximately twice the amplitude and wavelength, in the last 0·9 million years. The model emphasized the dynamic association between the contemporary intertidal platform and the continental shelf. Both surfaces trend towards a state of static equilibrium under oscillating sea level conditions, when attenuated waves are unable to continue eroding the rock. If there has not been enough time to reduce the gradient of the shallower portions of the continental shelf, however, intertidal shore platforms can be in a temporary, though possibly long‐lasting, state of dynamic equilibrium. The model suggests that most platforms are, at least in part, inherited from one, or in many cases more, interglacial stages when sea level was similar to today's. Copyright © 2001 John Wiley & Sons, Ltd.     

Edge wave and non-trapped modes of the 25 april 1992 Cape Mendocino tsunami

The 25 April 1992 Cape Mendocino earthquake generated a tsunami characterized by both coastal trapped edge wave and non-trapped tsunami modes that propagated north and south along the U.S. West Coast. Both observed and synthetic time series at Crescent City and North Spit are consistent with the zero-order edge wave mode solution for a semi-infinite sloping beach depth profile. Wave amplitudes at Crescent City were about twice that observed at North Spit, in spite of the fact that the source region was three times farther from Crescent City than North Spit. The largest observed amplitude was due to an edge wave which arrived almost three hours after the initial onset of the tsunami; since such waves are highly localized nearshore, this suggests that the enhanced responsiveness at Crescent City is at least partly due to local dynamic processes. Furthermore, the substantially delayed arrival of this wave, which was generated at the southern end of the Cascadia Subduction Zone, has significant implications for hazard mitigation efforts along the entire U.S. West Coast. Specifically, this study demonstrates that slow-moving but very energetic edge wave modes could be generated by future large tsunamigenic earthquakes in the CSZ, and that these might arrive unexpectedly at coastal communities several hours after the initial tsunami waves have subsided.     

极区中层尘埃等离子体中的尘埃声波研究

基于统计方法的自洽场理论,考虑了带电粒子与中性分子的碰撞以及对尘埃粒子的充电过程,建立了弱电离尘埃等离子体的纵波色散关系.分析了极区中层大气80~90 km高度范围内的尘埃声波的不稳定性.研究表明,极区中层大气中的尘埃声波有不稳定的模式,不稳定的波模对进一步解释极区中层尘埃等离子体的分层结构可能有重要意义.     

Simulation of irregular waves in an offshore wind farm with a spectral wave model

A numerical study of irregular waves in the Norwegian continental shelf wind farm (HAVSUL-II) was conducted using 3rd generation spectral wave models. The study was composed of two parts: the study of the effect of a single windmill monopile in the local incoming wave field using an empirical JONSWAP spectrum, and a wave hindcast study in the wind farm area using realistic incoming wave spectra obtained from large scale simulations for the 1991-1992 winter period. In the single windmill monopile study the SWAN wave model was used, while the hindcast study was conducted by successively nesting from a coarse grid using the WAM model up to a high-resolution (56 m) grid covering 26.2 km² of the HAVSUL-II windmill farm using the SWAN model. The effect of a single monopile on incident waves with realistic spectra was also studied. In the single windmill study the monopile was represented as a closed circular obstacle and in the hindcast study it was represented as a dry grid point. The results showed that the single windmill monopile creates a shadow zone in the down wave region with lower significant wave height (H_s) values and a slight increase of H_s in the up wave region. The effects of the windmill monopile on the wave field were found to be dependent on the directional distribution of the incoming wave spectrum and also on the wave diffraction and reflection. The hindcast study showed that the group of windmill monopiles may contribute to the reduction of the wave energy inside the offshore wind farm and that once the waves enter into the offshore wind farm they experience modifications due to the presence of the windmill monopiles, which cause a blocking of the wave energy propagation resulting in an altered distribution of the H_s field.     

Fast accurate computation of shelf waves for arbitrary depth profiles

A simple fast and straightforward, accurate numerical method is proposed for calculating barotropic non-divergent continental shelf waves, above general shelf profiles. The problem is reduced to a linear eigenvalue problem for the along-stream wavenumber k, that can be solved directly with exponential accuracy, using any standard linear eigenvalue package.     

汤西断裂的断层围陷波初步研究

作为断层围陷波方法在城市活断层探测中的首次尝试,我们针对太行山山前断裂带南段的汤西断裂开展了爆炸震源的观测试验。运用数字滤波和频谱分析等技术,由地震记录图分离出了断层围陷波。根据2横测线的观测结果,可确定断层的位置,并可推测断层在该处宽度为200～300m。破裂面较宽,可能与其张性特征有关。分频道地震图显示,断层围陷波具有正频散现象,其低频分量传播较快。这表明断层围陷波是一种面波,可利用其频散规律研究断裂带内介质的物理性质。这次的观测结果也表明,断层围陷波并不局限于新破裂带,在老断层中也能形成和传播。事实上,只要断层带内外的介质在物理性质上有较大的差异,均能产生沿断层传播的围陷波。在城市活断层探测中,断层围陷波的方法具有非常独特的优越性     

A note on edge waves on a flat shelf

Abstract

A variational approximation to the dispersion relation for trapped waves on a flat shelf of depth h ₁, bounded internally by a vertical coast and externally by a semi-infinite ocean of depth h ₂>h ₁, is obtained through an integral-equation formulation that accounts for all of the non-propagated modes that are excited at the discontinuity in depth (the conventional formulation of the edge-wave problem allows only for the propagated mode on the shelf and the dominant, non-propagated mode in the deep water). Coriolis effects are neglected. The exact result in the limit ω² h ₂/g↓0 (ω = angular frequency) is obtained by conformal mapping and compared with the variational approximation, which proves to be quite accurate over the entire range 1>h ₂/h ₁>x. The effects of the higher-order, non-propagated modes are found to be small for the long waves observed over the Southern California shelf by Snodgrass, Munk and Miller (1962).