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A tidal bore is a natural phenomenon usually occur in bays with large tidal waves. Sometimes this large tidal inflow are channeled deep into a river. In Indonesia, this natural phenomenon is found in the Kampar River, which is known as the tidal bore Bono. Sometimes, these tidal bore phenomena disappear, as happened to the Mascaret, tidal bore on the River Seine France. Through an understanding of the formation of tidal bore mechanism, there is hope that the tidal bore Bono in Kampar River can be preserved. In this paper, the occurrence of tidal bore Bono is simulated using the non-hydrostatic Saint-Venant equation under a staggered grid formulation. To test the accuracy of the implementation, several scenarios of hydraulic jumps were simulated first. The numerical results have shown to quantitatively confirm the analytical formula of bore height and velocity, two parameters that are important to characterize a bore wave. Further, by adopting a model that incorporates the non-hydrostatic pressure, our simulation shows the appearance of an undular bore accompanying the shock front. Finally, by using tidal current data measured along Kampar River estuary, our simulation that employs the actual river topography can show the appearance of tidal bore Bono. Our simulations were shown to be in fair agreement with the measurement.

The transformation of long waves&mdash, such as tsunamis and storm surges&mdash, evolving over a continental shelf is investigated. We approach this problem numerically using a pseudo-spectral method for a higher-order Euler formulation. Solitary waves and undular bores are considered as models for the long waves. The bathymetry possesses a periodic ridge-valley configuration in the alongshore direction which facilitates a means by which we may observe the effects of refraction, diffraction, focusing, and shoaling. In this scenario, the effects of wave focusing and shoaling enhance the wave amplitude and phase speed in the shallower regions of the domain. The combination of these effects leads to a wave pattern that is atypical of the usual behavior seen in linear shallow-water theory. A reciprocating behavior in the amplitude on the ridge and valley for the wave propagation causes wave radiation behind the leading waves, hence, the amplitude approaches a smaller asymptotic value than the equivalent case with no lateral variation. For an undular bore propagating in one dimension over a smooth step, we find that the water surface resolves into five different mean water levels. The physical mechanisms for this phenomenon are provided.

The tidal bore of the Garonne River (France) was investigated on 29 August, 31 August and 27 October 2015, during which instantaneous velocity measurements were performed continuously at high-frequency (200 Hz). The tidal bore occurrence had a marked effect on the flow field and turbulent Reynolds stress data, indicating large shear stresses, together with large and rapid fluctuations, during the bore passage and the early flood tide. Like many natural process flows, the tidal bore flow motion was dominated by coherent structure activities and turbulent events, with significant impact on the natural systems including in terms of sediment processes. Herein a new turbulent event analysis was developed for the highly-unsteady rapidly-varied tidal bore flow. The analysis was based upon basic concepts, in which turbulent bursting events were defined in terms of the instantaneous relative turbulent flux, and the method was extended to the rapidly-varied, highly-unsteady tidal bore motion. The turbulent event data showed relatively close results for most fluxes during the tidal bores. The event duration showed some tidal trend, with longer turbulent events immediately after the tidal bore passage, occurring simultaneously with major sediment erosion processes. The field data set and analyses suggested that a turbulent event analysis may be applicable to highly-unsteady rapidly-varied flows, providing quantitative details into the turbulent bursts that are responsible for major mixing and sedimentary processes.

When tsunami waves propagate into shallow and gentle continental shelves, the effects of submarine topography and wave dispersion lead to the appearance of undular bore. This kind of wave is quite different from the initial tsunami wave in the waveform, and its amplitude is enhanced significantly. The undular bore will cause great and repeated runups on the beach, which brings larger destruction to the coastal region. In order to investigate the characteristics of the propagation of undular bore, this paper simulates the evolution from the sinusoidal long wave to the undular bore and analyzes the influencing factors. The beach slope has an important effect on the development of undular bores in terms of the undulation form, amplitude, wave length and occurrence time. The influence of bottom friction and submarine topography on the undulations and soliton fissions are discussed. These bottom conditions will lead to great change of the waveform and amplitude of undular bores.

International audience; This paper reports a combined observational and numerical study of wave transformation over barrier reefs. The field instrumentation, which consists in a cross-shore network of pressure sensors and one high resolution velocity profiler, has been deployed for more than two months over the Ouano reef barrier, New Caledonia. The combined analysis of observations and numerical simulations shows that the reef barrier acts as an efficient, but depth-dependent, filter for incoming wave energy. The data analysis reveals the presence of very low frequency standing wave patterns due to reflection either at the reef barrier inner boundary or at the lagoon shore. Another striking feature is the development of undular bore trains over the reef flat.

[Departement_IRSTEA]Eaux [TR1_IRSTEA]RIVAGE; International audience; In this paper, a detailed analysis of undular bore dynamics in channels of variable cross-section is presented. Two undular bore regimes, LowFroude Number (LFN) and High Froude Number (HFN), are simulated with a Serre-Green-Naghdi model, and the results are compared with theexperiments by Treske. We show that contrary to Favre waves and HFN bores, which are controlled by dispersive non-hydrostatic mechanisms, LFN bores correspond to a hydrostatic phenomenon. The dispersive-like properties of the LFN bores is related to wave refraction on the banks in a way similar to that of edge waves in the nearshore. A fully hydrostatic asymptotic model for these dispersive-like bores is derived and compared to the observations, confirming our claim

This paper presents numerical simulations of the propagation, shoaling and run-up of full-scale tsunami waves. The simulations are performed with a model solving Reynolds-averaged Navier-Stokes equations with k-ω turbulence closure, and is one of very few studies involving CFD simulations at full tsunami scale, involving full resolution of small scale dispersive effects as well as wave breaking. It is demonstrated that a combination of previous analytical and empirical expressions for run-up heights and inundation speeds match those simulated well. This indicates that these are reasonable first approximation even in cases where the underlying assumption of linearity of the incoming tsunami is violated, as well as in cases where breaking occurs, though they generally slightly underestimate both run-up height and inundation speed. It is shown that the run-up of tsunamis can manifest in different ways depending on the initial wave shape and slope of the coast, and three qualitative run-up types previously identified in the literature are described in detail. It is further shown that the shorter waves of an undular bore, which appear during lengthy propagation in shallow water, can either maintain their shape the entire distance to shore, or break far offshore creating a breaking bore. It is demonstrated the front of the breaking bore will not appear as steep for N-waves as single waves because these need to re-wet the drawn-down region before reaching the original shoreline. Finally, the importance of shorter waves riding on the front of the tsunami is discussed. It is shown that they have little impact on the run-up height and inundation speed, but are important in terms of local flow velocities. The results presented here are Part 1 of a larger study, where Part 2 involves details of the tsunami-induced boundary layer dynamics, bed shear stresses and implication for sediment transport.

Laboratory experiments are reported where the analogue of a tidal bore is generated with a centimeter-scale local tidal range in a water channel. A discussion of the hydraulic regimes allows to set the experimental conditions to observe the bore. Temporal measurements of the free surface deformation with an acoustic sensor display an analogue of the tidal asymmetry met in nature between the ebb and the flood. Spatial measurements of the free surface deformation are performed with a laser sheet which delineates the interface thanks to the fluorescent re-emission of fluoresceine diluted in water. Afterwards, a parameter space is provided for the observation of a mini-bore with different hydrodynamical regimes (undular, undular–breaking, breaking) by showing the influence of the analogue local tidal range on the shape of the tidal wave. Finally, flow visualizations reveal the inner structure of the velocity profile of the mini-bore in the undular–breaking regime characterized by flow reversals.

A detailed field study was carried out on a tidal bore to document the turbulent processes and sediment entrainment which occurred. The measured bore, within the Arcins Channel of the Garonne River ( France), was undular in nature and was followed by well-defined secondary wave motion. Due to the local river geometry a collision between the Arcins channel tidal bore and the bore which formed within the main Garonne River channel was observed about 800m upstream of the sampling site. This bore collision generated a transient standing wave with a black water mixing zone. Following this collision the bore from the main Garonne River channel propagated 'backward' to the downstream end of the Arcins channel. Velocity measurements with a fine temporal resolution were complemented by measurements of the sediment concentration and river level. The instantaneous velocity data indicated large and rapid fluctuations of all velocity components during the tidal bore. Large Reynolds shear stresses were observed during and after the tidal bore passage, including during the 'backward' bore propagation. Large suspended sediment concentration estimates were recorded and the suspended sediment flux data showed some substantial sediment motion, consistent with the murky appearance of the flood tide waters. Copyright (C) 2015 John Wiley & Sons, Ltd.

A tidal bore is an unsteady rapidly-varied open channel flow generated by the swift advance of the early flood tide in a funnel-shaped river estuary when the tidal range exceeds 4.5 to 6 m. This contribution presents a detailed field investigation conducted on the tidal bore of the Garonne River (France). The bore was undular and the bore's leading edge was followed by well-defined secondary waves, or whelps. The instantaneous ADV velocity data indicated large and rapid fluctuations of all velocity components during the tidal bore. Large Reynolds shear stresses were observed during and after the tidal bore passage. The investigation characterized some unusual transient turbulence caused by the bore propagation in a large river system, and the results suggested the advection of large-scale eddies in the wake of the bore front. The present study highlighted the need for detailed field measurements with fine temporal resolution, to characterize the highly unsteady rapidly-varied nature of tidal bore ...

The formation and dynamics of tidal bores in funnel-shaped estuaries is investigated from both a global tidal wave scaling analysis and new quantitative field observations. We show that tidal bore occurrence in convergent estuaries can be estimated from a dimensionless scaling parameter characterizing the relative intensity of nonlinear friction versus local inertia in the momentum equation. A detailed analysis of tidal bore formation and secondary wave structure is presented from a unique long-term database (observations of more than 200 tides) acquired during four campaigns in the two main French tidal-bore estuaries: the Seine and Gironde/Garonne estuaries. We describe the effect of freshwater discharge on the global tidal wave transformation at the estuarine scale and on local tidal bore occurrence in the upper estuary. Our field data suggest that the tidal bore intensity is mainly governed by the dimensionless tidal range, which characterizes the local tidal wave nonlinearity. We also show that the secondary wavefield associated with tidal bore propagating in natural estuaries differs significantly from those associated to undular bores in rectangular channels. In particular, we observe an abrupt decrease of the whelp steepness when the Froude number goes below 1.1. This secondary field transition can explain why tidal bore occurrence in worldwide estuaries is certainly underestimated.

The secondary wave field associated with undular tidal bores (known as whelps) has been barely studied in field conditions: the wave field can be strongly non-hydrostatic, and the turbidity is generally high. In situ measurements based on pressure or acoustic signals can therefore be limited or inadequate. The intermittent nature of this process in the field and the complications encountered in the downscaling to laboratory conditions also render its study difficult. Here, we present a new methodology based on LiDAR technology to provide high spatial and temporal resolution measurements of the free surface of an undular tidal bore. A wave-by-wave analysis is performed on the whelps, and comparisons between LiDAR, acoustic and pressure-derived measurements are used to quantify the non-hydrostatic nature of this phenomenon. A correction based on linear wave theory applied on individual wave properties improves the results from the pressure transducer (Root mean square error, R M S E of 0 . 19 m against 0 . 38 m); however, more robust data is obtained from an upwards-looking acoustic sensor despite high turbidity during the passage of the whelps ( R M S E of 0 . 05 m). Finally, the LiDAR scanner provides the unique possibility to study the wave geometry: the distribution of measured wave height, period, celerity, steepness and wavelength are presented. It is found that the highest wave from the whelps can be steeper than the bore front, explaining why breaking events are sometimes observed in the secondary wave field of undular tidal bores.

In some tsunami waves travelling over the ocean, such as the one approaching the eastern coast of Japan in 2011, the sea surface of the ocean is depressed by a small metre-scale displacement over a multi-kilometre horizontal length scale, lying in front of a positive elevation of comparable magnitude and length, which together constitute a down-up wave. Shallow water theory shows that the latter travels faster than the former, leading to an interaction, whose description is the issue addressed in this paper, using model equations of the Korteweg–de Vries type. First, we re-examine the undular bore solutions of the Korteweg–de Vries equation which describe how an initial depression wave deforms into a depression rarefaction wave followed by an undular bore of large elevation waves riding on this depression. Then we develop a new extended Korteweg–de Vries equation some of whose solutions can be used to describe the interaction of an elevation wave chasing a depression wave. These show that the two waves coincide at a given position and time producing a maximum elevation. Typically this amplitude is larger than the initial displacement magnitude by a factor which can be as large as two, which may explain anomalous elevations of tsunamis at particular positions along their trajectories. It is physically significant that for these small amplitude waves, no wave breaking occurs and there is no excess dissipation. Then, following the transition, the elevation wave moves ahead of the depression wave and the distance between them increases either linearly or logarithmically with time. The implications for how these down-up tsunami waves reach the shoreline are considered.

The paper presented a smoothed particle hydrodynamics (SPH) method to study the three-dimensional (3D) tidal bore scenarios. The SPH method is a mesh-free particle modeling technique that can track the large deformation of free surfaces in a straightforward and accurate way. Two benchmark cases of the tidal bore propagation were computed and compared with the experimental results. The first one is related to the undular and breaking bores in a regular open channel, and the second one considers the undular bore passing through the contraction of bridge piers. Physical laboratory experiments have also been carried out to validate the numerical investigations. The comparisons of both the free surface profile and velocity field demonstrated that the SPH technique could provide a very promising tool to simulate tidal bore phenomena in engineering practice. The work is the first to systematically explore the potentials of mesh-free SPH modeling approach in predicting the tidal bore features under 3D flow conditions.

A tidal bore is a series of waves propagating upstream as the tidal flow turns to rising, and the bore front corresponds to the leading edge of the tidal wave in a funnel shaped estuarine zone with macro-tidal conditions. Some field observations were conducted in the tidal bore of the Garonne River on 7 June 2012 in the Arcins channel, a few weeks after a major flood. The tidal bore was a flat undular bore with a Froude number close to unity: Fr1 = 1.02 and 1.19 (morning and afternoon respectively). A key feature of the study was the simultaneous recording of the water elevation, instantaneous velocity components and suspended sediment concentration (SSC) estimates, together with a detailed characterisation of the sediment bed materials. The sediment was some silty material (d50 ≈ 13 μm) which exhibited some non-Newtonion thixotropic behaviour. The velocity and SSC estimate were recorded simultaneously at high frequency, enabling a quantitative estimate of the suspended sediment flux at the end of the ebb tide and during the early flood tide. The net sediment flux per unit area was directed upstream after the bore, and its magnitude was much larger than that at end of ebb tide. The field observations highlighted a number of unusual features on the morning of 7 June 2012. These included (a) a slight rise in water elevation starting about 70 s prior to the front, (b) a delayed flow reversal about 50 s after the bore front, (c) some large fluctuations in suspended sediment concentration (SSC) about 100 s after the bore front and (d) a transient water elevation lowering about 10 min after the bore front passage. The measurements of water temperature and salinity showed nearly identical results before and after the tidal bore, with no evidence of saline and thermal front during the study.

To study the hydrodynamics of tidal bore, a physical modeling study is carried out in a rectangular flume with considerations of the tidal bore heights, the propagation speeds, the tidal current velocities, the front steepness, and the bore shapes. After the validation with the field observations, the experimental results are analyzed, and it is shown that: (1) the greater initial ebb velocity or the larger initial water depth impedes the tidal bore propagation, (2) the maximum bore height appears at an initial ebb velocity in the range of 0.5 m/s-1.5 m/s, (3) when the Froude number exceeds 1.2, an undular bore appears, after it exceeds 1.3, a breaking bore occurs, and after it exceeds 1.7, the bore is broken.

This paper carries out the numerical simulation of tsunami propagation based on the fully nonlinear and highly dispersive Boussinesq model. The numerical results indicate that the waveforms of a tsunami are quite different on steeply and mildly sloping beaches, which cannot be predicted by the analytical solution of the nonlinear shallow water equations. Long wave trains form on the steeply sloping beaches while undular bores emerge on the mildly sloping beaches. The simulation of hypothesized tsunamis in the China Seas provide different wave patterns in the near shore regions, including long wave trains, undular bores, and solitons. In order to study the propagation and run-up of undular bores, a series of undular bores is proposed by sinusoidal and attenuation functions. The properties of the run-up and energy budget of these undular bores are investigated.

A tidal bore is a surge of waters propagating upstream in an estuary as the tidal flow turns to rising and the flood tide propagates into a funnel-shaped system. Large tidal bores have a marked breaking roller. The sounds generated by breaking tidal bores were herein investigated in the field (Qiantang River) and in laboratory. The sound pressure record showed two dominant periods, with some similarity with an earlier study [Chanson (2009). J. Acoust. Soc. Am. 125(6), 3561–3568]. The two distinct phases were the incoming tidal bore when the sound amplitude increased with the approaching bore, and the passage of the tidal bore in front of the microphone when loud and powerful noises were heard. The dominant frequency ranged from 57 to 131 Hz in the Qiantang River bore. A comparison between laboratory and prototype tidal bores illustrated both common features and differences. The low pitch sound of the breaking bore had a dominant frequency close to the collective oscillations of bubble clouds, which could be modeled with a bubble cloud model using a transverse dimension of the bore roller. The findings suggest that this model might be over simplistic in the case of a powerful breaking bore, like that of the Qiantang River.

A tidal bore is a positive surge taking place during the flood tide with a large tidal range and the bore corresponds to the leading edge of the tidal wave propagating upstream. In this study, some physical modelling was performed to investigate the upstream bore propagation over fixed and movable gravel beds. Both undular and breaking bores were tested. The free-surface and velocity measurements were complemented by some observations of particle motion beneath the bore front. In the initially-steady flow and beneath undular bores, no sediment motion was observed for the experimental set-up. Beneath breaking bores, on the other hand, some upstream gravel bed load motion was observed behind the bore. The gravel bed particles were de-stabilized by the roller toe passage and advected upstream. The unsteady velocity data showed some damping of the transient recirculation on the movable gravel bed.

The process of tidal bore passing through bridge piers is numerically simulated in an open channel using a pure Lagrangian method, i.e. Smooth Particle Hydrodynamics (SPH). Due to its “gridless” feature, SPH is intrinsically well-suited for the complex hydrodynamic simulation when the fluid encounters a structure. The behavior of bores propagation along the channel is illustrated herein and includes the bore's free surface properties and flow field, and in particular, the intricate behavior of unsteady flow during the passage of tidal bore. The generation of shock waves between the structures can be clearly observed in the numerical experiment. Intense vortical structures behind the bore front are generated as the bore propagate through the constriction.

A tidal bore is a wave propagating upstream as the tidal flow turns to rising. It forms during spring tide conditions when the flood tide is confined to a narrow funneled channel. To date, theoretical and numerical studies rely upon physical experiments to validate the developments, but the experimental data are limited mostly to visual observations and sometimes free-surface measurements. Herein turbulent velocity measurements were obtained in a large-size laboratory facility with a fine spatial and temporal resolution. The instantaneous velocity measurements showed rapid flow deceleration at all vertical elevations, and large fluctuations of all velocity components were recorded beneath the bore and secondary waves. A comparison between undular (nonbreaking) and breaking bores suggested some basic differences. In an undular bore, large velocity fluctuations were recorded beneath the first wave crest and the secondary waves showing a long-lasting effect after the bore passage. In a breaking bore, some la...

A tidal bore may occur in a macro-tidal estuary when the tidal range exceeds 4.5–6 m and the estuary bathymetry amplifies the tidal wave. Its upstream propagation induces a strong mixing of the estuarine waters. The propagation of undular tidal bores was investigated herein to study the effect of bridge piers on the bore propagation and characteristics. Both the tidal bore profile and the turbulence generated by the bore were recorded. The free-surface undulation profiles exhibited a quasi-periodic shape, and the potential energy of the undulations represented up to 30% of the potential energy of the tidal bore. The presence of the channel constriction had a major impact on the free-surface properties. The undular tidal bore lost nearly one third of its potential energy per surface area as it propagated through the channel constriction. The detailed instantaneous velocity measurements showed a marked effect of the tidal bore passage suggesting the upstream advection of energetic events and vorticity “clouds” behind the bore front in both channel configurations: prismatic and with constriction. The turbulence patches were linked to some secondary motions and the proposed mechanisms were consistent with some field observations in the Daly River tidal bore. The findings emphasise the strong mixing induced by the tidal bore processes, and the impact of bridge structures on the phenomenon.

The time-dependent response of upstream undular bores and internal hydraulic jumps from initial formation to eventual release is documented. Two events, characterized by qualitatively different responses, are discussed. In the first case, an undular bore develops upstream of the sill crest. This disturbance remains upstream through the ebb tidal flow but is transformed to a hydraulic jump as its amplitude increases. Toward the end of ebb tide, it is released and subsequently disperses into a group of solitary-like waves. During the second event, an upstream jump also develops at an early stage of the tide. However, it is subsequently swept downstream by the tidal flow such that the upstream region then appears featureless. Approaching slack tide, as an exchange flow becomes established, a large bore or gravity current is emitted. The different responses seen in these two events are interpreted in terms of the Froude number associated with the near-surface stratification.

A tidal bore is a natural and fragile phenomenon, which is of great importance for the ecology of an estuary. The bore development is closely linked with the tidal range and the river mouth shape, and its existence is sensitive to any small change in boundary conditions. Despite their ecological and cultural value, little is known on the flow field, turbulent mixing and sediment motion beneath tidal bores. Indeed, some striking features can be highlighted in two-dimensional simulations, such as large velocity fluctuations and flow recirculation structures. Using Large Eddy Simulation method, the numerical results emphasised the complicated turbulent structures and their unsteadiness under a tidal bore.

In macrotidal estuaries, a tidal bore may form during spring tide conditions when the flood tide is confined to a narrow channel. Most field occurrences showed well-defined undulations behind the leading wave, that is, an undular bore process. Herein, detailed free-surface and turbulence measurements were performed beneath undular bore fronts using side-looking acoustic Doppler velocimetry and nonintrusive free-surface measurement devices in a laboratory channel. Undular bores were observed for Froude numbers less than 1.7, which compared favourably with past studies. Velocity measurements with a temporal resolution of 50 Hz showed a marked effect of the bore passage. Longitudinal velocities were characterised by rapid flow deceleration at all vertical elevations, while large fluctuations of transverse velocities were recorded beneath the front. Turbulent Reynolds stress data highlighted high levels in the lower flow region, including next to the bed. Maximum normal and tangential turbulent stres...

In stratified tidal flow over a sill, the character of the upstream response is determined by a Froude number Fs based on the stratification near the surface. This is distinguished from the Froude number governing the response in the neighborhood of the sill crest, which is based on the weak density step associated with a flow bifurcation. For moderate values of Fs, the upstream response consists of nonlinear waves or a weak undular bore. For larger values of Fs, a strong, quasi-stationary, internal hydraulic jump dominates the upstream response. At sufficiently large values of Fs, the upstream bore is swept downstream and lost. Acoustic backscatter and velocity data are presented for the case of a strong internal bore or gravity current in a tidally modulated sill flow. Numerical simulations with varying near-surface stratification are presented to illustrate the upstream responses at different values of Fs. The theory of two-layer hydraulic flows is invoked to account for the development of the upstream jump.

A tidal bore may form in a converging channel with a funnel shape when the tidal range exceeds 6-9 m. The advancing surge has a major impact on the estuarine ecosystem. Physical modelling of an undular bore has been conducted based upon a quasi-steady flow analogy. The experimental data highlight rapid flow redistributions between successive wave troughs and crests as well as large bottom shear stress variations. The results suggest a sediment transport process combining scour beneath wave troughs associated with upward matter dispersion between a trough and the following wave crest. The process is repeated at each trough and significant sediment transport takes place with deposition in upstream intertidal zones. The conceptual model is supported by field observations showing murky waters after the bore passage and long-lasting chaotic waves.

Trains of quasi-periodic high-frequency internal waves (IWs) of large amplitude are common in the upper thermocline of the ocean. Sources for these waves may be different ones but it is not always possible to experimentally establish them for certain. We analyzed results of many IW experiments carried out in different representative regions of the World Ocean, including continental margins in the Mid-Atlantic Bight, in the northwestern Pacific at Kamchatka, the Seyshelles-Mascarene bottom rise, and some regions of the open ocean where the intense short-period IWs occur. Comparative analysis of the intense IWs observed in the Mid-Atlantic Bight and at Kamchatka revealed similarity and difference in the IW field in these regions differing by their bottom topography. Most of the observed trains in the Mid-Atlantic Bight propagate shoreward from the shelf break in the form of soliton packets or solibores and do not occur seaward from the shelf. The soliton trains in the northwestern Pacific at Kamchatka are common not only at the shelf edge but also in deep water where they propagate in various directions that seem to be related to the supercritical steepness and complicated form of the continental slope. Observation of generation and evolution of the IW trains at the Seyshelles-Mascarene bottom rise where huge internal solitons have been encountered has shown that the undular bore generated at the lee side of the bottom rise gradually evolves in a train of solitons with the trailing linear waves. Large solitons are generated also in deep water as a result of ray propagation of the internal tide emanated from the rise as happens in the Bay of Biscay. Certain consequences of the IW interaction with the background current leading to intensification of the high-frequency waves were observed in several regions of the open ocean. Revealed dependency of the intense wave propagation direction on the current direction, and closeness of the wave frequency to the frequency at which the waveguide steeply tapers may be regarded as clear evidences for the important role which currents play in the IW intensification.

Measurements in the macro-tidal Daly Estuary show that the presence of an undular tidal bore contributed negligibly to the dissipation of tidal energy. No recirculation bubble was observed between a trough and the following wave crest in the lee waves following the undular bore. This differs to stationary undular bores in laboratory experiments at larger Froude numbers where a recirculation bubble exists. Secondary motions and the turbulence generated by the undular bore had no measurable influence on the sediment transport. This situation contrasts with the intense sediment resuspension observed in breaking tidal bores. The tidally averaged sediment budget in the Daly Estuary was controlled by the asymmetry of tidal currents. The undular bore may widen the river by breaking along the banks that it undercuts, leading to bank slippage. A patch of river-wide macro-turbulence of 3-min duration occurred about 20 min after the passage of the bore during accelerating tidal currents.

Results are presented from a recent experiment in Knight Inlet, British Columbia, focusing on the generation and propagation of nonlinear internal waves near the sill during ebb tide. High–quality echo–sounder and velocity measurements were obtained in a novel fashion, using instrumentation carried aboard a small inflatable boat. Complementing these data, a set of photographic images of the surface signature of the internal waves was acquired from both a fixed mountainside location and a helicopter. These photographs situate the observations within the larger–scale structure of the internal response found in the inlet. The observations reveal the development of strongly nonlinear internal waves on a bore occurring upstream of the sill crest. As the tidal flow relaxes, these waves propagate upstream, at first slowly, and later rapidly against the gradually waning flow. A simulation of wave generation with a fully nonlinear numerical model is discussed. The simulation shows that upstream influence, associated with the rapidly increasing tidal forcing, leads to formation of an undular bore upstream of the sill crest. As the tidal flow relaxes, the bore subsequently evolves into a group of upstream–propagating solitary–like internal waves. Taken together, the observations and numerical simulation describe a process for the generation of nonlinear internal waves involving upstream influence, which likely has application in other environments for stratified flow over topography.

During the INTIFANTE 99 experiment in July 1999, observations were made of a prominent internal undular bore off Cape Sines, Portugal. The feature was always present and dominant in a collection of synthetic aperture radar (SAR) images of the area covering the period before, during and after the trial. During the trial, rapid dissemination of SAR data to the survey ship enabled assessment of the progression of the feature, and the consequent planning of a survey of the bore coincident with a new SAR image. Large amplitude internal waves of 50 m amplitude in 250 m water depth, and 40 m in 100 m depth, were observed. The images show that the position of the feature is linked to the phase of the tide, suggesting an internal tide origin. The individual packets of internal waves contain up to seven waves with wavelengths in the range of 500–1500 m, and successive packets are separated by internal tide distances of typically 16–20 km, suggesting phase speeds of 0.35–0.45 m s−1. The internal waves were coherent over crest lengths of between 15 and 70 km, the longer wavefronts being due to the merging of packets. This paper uses the SAR data to detail the transformation of the wave packet as it passes across the continental slope and approaches the coast. The generation sites for the feature are discussed and reasons for its unusually large amplitude are hypothesised. It is concluded that generation at critical slopes of the bathymetry and non-linear interactions are the likely explanations for the large amplitudes.

Observations are presented of nonlinear internal waves on the outer New England continental shelf during the summer Shelfbreak Primer study conducted between July 26 and August 5, 1996. Current and temperature measurements were made with an upward looking acoustic Doppler current profiler (ADCP) located on the 147 m isobath near the shelfbreak and three vertical thermistor moorings located upshelf. Data from the ADCP and two nearby thermistor chains show energetic internal tides propagating at roughly 0.9 m s 21 to the north-northwest, nearly perpendicular to the local topography with 10 -15 cm s 21 horizontal currents and 15-30 m vertical displacements. These waves evolve rapidly within a 5.8 km range into an undular internal tidal bore. Cross-isobath barotropic tidal currents, responsible for generating the internal tides are in the 5-12 cm s 21 range. The bore formation is highly variable. There is evidence of a correlation between internal tide steepening and a shelfbreak front jet orientation that is oppositely directed to the internal tide propagation. There is no correlation between steepening and the jet's vertical shear. Statistics of the undular bores show rms travel time fluctuations from 0.8 to 1.7 hours and average tidal bore durations from 12 to 9 hours. The average undular bore speed is 0.9 m s 21 , with an rms fluctuation of 0.4 m s 21 . The number of high-frequency waves in the bore varies from 0 to 8 near the shelfbreak and increases to 30 waves 26.7 km upshelf. The observed distribution function of temporal spacing between high-frequency internal waves is spread between 4 and 20 min.

The development of an undular bore is governed by the regularised long wave equation. A Petrov-Galerkin B-spline finite element method for its solution is set up. The numerical model is validated by showing that it models well the motion of a single solitary wave. The development of an undular bore is studied through computer simulation.

Freshwater outflows from estuarine systems carry nutrients, sediments, larvae and other materials into the coastal ocean where they mix into ambient ocean water. Loch Etive is one such estuary on the west coast of Scotland that is fed by a large rainfall catchment area, and from which the outflow is strongly modulated on a tidal basis. Freshwater leaves the loch on the ebbing tide in a pulse released into the coastal ocean as a thin layer, the leading edge of which develops into an undular bore or a train of internal solitary waves with strong mixing and associated entrainment. A Hydroid 600 m depth-rated AUV equipped with a forward-mounted microstructure sensing package has been used in conjunction with moored measurements to study the dynamics of thin freshwater layers that are regularly released into the coastal ocean. During observations conducted in winter 2009 and spring 2010 we observed turbulent bores and internal solitary waves in Ardmucknish Bay, near the entrance to Loch Etive. The passage of the bores and internal solitary waves of depression were associated with downward vertical movement of near-surface water and turbulent mixing that was enhanced above background by over 2 orders of magnitude.

Scale parameters of large tsunamis suggest that non-linearity of waves is important only within a short distance of about a half wavelength from the shoreline.The Carrier-Greenspan transformation of the non-linear shallow-water equations on a uniformly sloping beach is elucidated to give a set of linear equations analogous to the linearized equations of the original non-linear equations, and an explicit form of the wave-breaking criterion is given.Although a weak bore (or an undular bore) may be formed close to shore if the head wave of a tsunami is a positive wave, there may be no bore formation at all if the negative wave forms the front.The maximum run-up of a tsunami is caused mostly by the non-breaking wave enhanced by the effect of bay resonance.

[1] The shoaling of the nonlinear internal tide in Massachusetts Bay is studied with a fully nonlinear and nonhydrostatic model. The results are compared with current and temperature observations obtained during the August 1998 Massachusetts Bay Internal Wave Experiment and observations from a shorter experiment which took place in September 2001. The model shows how the approaching nonlinear undular bore interacts strongly with a shoaling bottom, offshore of where KdV theory predicts polarity switching should occur. It is shown that the shoaling process is dominated by nonlinearity, and the model results are interpreted with the aid of a two-layer nonlinear but hydrostatic model. After interacting with the shoaling bottom, the undular bore emerges on the shallow shelf inshore of the 30-m isobath as a nonlinear internal tide with a range of possible shapes, all of which are found in the available observational record.

An X-band marine radar on Windmill Hill, Gibraltar, was used to monitor the propagation of internal waves in the Strait of Gibraltar during March, April, and June 1986. Surface roughness features of the waves were observed out to a range of ∼15 km. From photographic images of the radar screen, the positions of image features were measured manually using a digitizing table, and these data were then computer processed to give wave arrival times and phase speeds. During most tidal cycles, an internal undular bore generated at Camarinal Sill was observed to pass eastward (A-waves). These occurred throughout the experiments although less frequently near neap tides. The time of travel to Gibraltar varied significantly, so that the bore arrived between four and nine hours after high water. Arrival times were found to be closely related to the amplitude of the upper layer tidal current. This current had a strong diurnal component, which was manifested as an inequality between the arrival times of success...

During the summer, nonlinear internal waves (NLIWs) are commonly observed propagating in Massachusetts Bay. The topography of the area is unique in the sense that the generation area (over Stellwagen Bank) is only 25 km away from the shoaling area, and thus it represents an excellent natural laboratory to study the life cycle of NLIWs. To assist in the interpretation of the data collected during the 1998 Massachusetts Bay Internal Wave Experiment (MBIWE98), a fully nonlinear and nonhydrostatic model covering the generation/shoaling region was developed, to investigate the response of the system to the range of background and driving conditions observed. Simplified models were also used to elucidate the role of nonlinearity and dispersion in shaping the NLIW field. This paper concentrates on the generation process and the subsequent evolution in the basin. The model was found to reproduce well the range of propagation characteristics observed (arrival time, propagation speed, amplitude), and provided a coherent framework to interpret the observations. Comparison with a fully nonlinear hydrostatic model shows that during the generation and initial evolution of the waves as they move away from Stellwagen Bank, dispersive effects play a negligible role. Thus the problem can be well understood considering the geometry of the characteristics along which the Riemann invariants of the hydrostatic problem propagate. Dispersion plays a role only during the evolution of the undular bore in the middle of Stellwagen Basin. The consequences for modeling NLIWs within hydrostatic models are briefly discussed at the end.

A tidal bore is a hydrodynamic discontinuity propagating upstream in an estuarine zone with a funnel shape as the tide starts rising under spring tidal conditions. The transient sediment motion beneath tidal bores was investigated in laboratory under controlled flow conditions by measuring simultaneously the fluid and sediment particle velocities. Although no sediment transport was observed in the initially steady flow and in undular bores, a transient sheet flow motion was observed beneath the breaking bores. The sediment transport was initiated during the passage of the bore roller toe by the large longitudinal pressure gradient force, and the sediment particles were subjected to large horizontal accelerations. About 5 % of all particles were accelerated in excess of 1 g. The sediments were advected upstream with an average velocity close to the instantaneous fluid velocity. The time evolution of instantaneous particle velocity for each trajectory was analysed, using the starting point of particle trajectory corresponding to the entrainment point, and the end point to the particle stoppage point. The present data provided some quantitative data in terms of force terms acting on sediment particles beneath a tidal bore and their trajectory characteristics.

My long-term goals for this research project are to understand the interaction of stratified flow with topography with an emphasis on those flows relevant to coastal oceans and marginal seas. The specific objectives of the last year have been a study of two related problems in the general area of time-dependent rotating hydraulics and nonlinear waves. The first is a study of the fully nonlinear dam break problem in a rotating channel. One focus of this work has been to study the characteristics and dynamics of the shocks and bores. The second project is an extension of Long's (1954, 1970) classic problem of upstream influence and the establishment of hydraulically controlled flows in rotating channels. Both of these projects have been on single-layer flows, though the long-term goal is to extend the work to two-layer systems. The work on the hydraulics of rotating flows adds to the understanding of the role of straits and sills in regulating flow within and between abyssal basins, marginal seas, etc. The work on the dynamics of shocks and bores in rotating flows is applicable not only the issue of time-dependence in rotating hydraulic flows, but also to nonlinear wave dynamics in straits and coastal zones, including the dynamics of the marine boundary layer along the California coast. Though the focus to date has been on single layer flows, the results gained so far should help in the interpretation of stratified flows. It is also worth pointing out that the fully nonlinear shocks and bores are the hydrostatic limit of the (typically) weakly nonlinear solitary wave and undular bore solutions. As such they may provide information on the initial, or boundary, conditions which result in solitary waves in the far field.

Potential tsunami generated in the Okinawa Trench or the Manila Trench may attack the southeast coast of China. The continental shelves with extremely gentle slope in the China Seas affect the evolvement of tsunami waves. In this paper, we carry out the simulation of tsunami propagation based on the fully nonlinear and highly dispersive Boussinesq model, which could describe the nonlinearity and dispersion of water waves quite well. So the undulation characters could be well presented. In terms of the real topographies of the East China Sea and the South China Sea, we take some typical profiles to simulate the hypothetical tsunamis generated in the Okinawa Trench and the Manila Trench. Different waveforms in the near shore regions are obtained. The N-shape tsunami waves will evolve into long wave trains, undular bores or solitons near the coastal area. The numerical results of the near shore waveform provide essential conditions for the further studies of tsunami runup and inundation.

Recent observations of the coastal impact of large tsunamis (e.g., Indian Ocean 2004; Tohoku 2011) and related numerical and theoretical works have made it increasingly clear that tsunami waves arrive nearshore as a series of long waves (so-called N-waves) with, often, the superposition of undular bores around each crest. Such wave trains are much more complex and very much in contrast with the solitary wave paradigm which for a long time was the accepted idealization of tsunami waves in both experimental and numerical work. The dissipation associated with these breaking bores can be very large, particularly over a wide and shallow continental shelf such as along the east coast of North America, particularly for the shorter waves associated with tsunamis generated by Submarine Mass Failures (SMFs). In this paper, we perform numerical simulations of tsunami coastal impact in the context of both idealized laboratory experiments and several tsunami case studies. We attempt to clarify the key physical processes at play in such cases, and discuss the parameterization of long wave dissipation and implications for models of coastal tsunami hazard assessment.

This paper presents the results of a field expedition mounted in late September/early October 1979 to investigate the structure and origin of the “morning glory” of the Gulf of Carpentaria in northern Australia. The morning glory is a line wind squall, accompanied by a pressure jump, and often by a long roll-cloud or series of such clouds. It frequently occurs in the early morning, especially in October, in the Gulf area. A light aircraft, fitted with a temperature and humidity probe, was flown in two glories to determine their thermodynamic structure, and wind fields wore obtained principally by tracking pilot balloons using the double theodolite method. Data also were obtained from a network of surface stations, recording wind velocity and pressure, installed at locations across Cape York Peninsula, which is believed to be the area of genesis. The morning glory is identified as an internal undular bore propagating on the nocturnal and/or maritime inversion. Its origin appears to lie frequently ...

The curious undular bore// Propagates onward to shore// The energy flies// From low freqs to high// Until the wavefront is no more

Several studies have reported the development of undular bores over fringing coral reefs (e.g, Gallagher, 1976; Nwogu and Demirbilek, 2010) but the importance of this phenomenon for reef hydrodynamics has never been studied. Yet, the transformation of a long wave (e.g., swell or infragravity wave) into an undular bore leads to significant modifications of the wave field. The formation of undulations is for example associated to a significant increase of the leading bore height. Moreover, if the undulations have enough time to develop (i.e. if the reef flat is wide enough), the initial long wave will ultimately split into a series of solitons (e.g., Grue et al., 2008). All this is likely to affect wave run-up. As reeffronted coastlines are particularly vulnerable to flooding, a good understanding of long wave transformation over the reef flat, including their possible transformation into undular bores, is crucial. In this study, we investigate undular bore development over reef-type profiles based on a series of laboratory experiments. More specifically, we aim to characterize the conditions under which undular bores develop, and analyse how their development affect the hydrodynamics at the toe of the reef-lined beach and the resulting wave run-up.

Using the laser-induced fluorescent method, the transition process from bore to runup mode, i.e., “bore collapse,” is investigated experimentally. The observed process appears to be different from both previous analytical and numerical predictions. The results indicate that momentum exchange takes place between the incident bore and the quiescent water body along the shoreline. Turbulence generated in a bore nearshore is highly three-dimensional and sporadic. Very close to the shore, turbulence is advected with the bore front, and consequently, the bore collapse process involves strong turbulent action onto the dry beach bed.