Short Wave Groups Research Articles

The influence of wave groups and wave-swash interactions on sediment transport and bed evolution in the swash zone

Large scale laboratory measurements of sediment dynamics in the swash zone are presented. Two bichromatic wave group conditions were generated, having the same energy content but different wave group period (Tg=15.0 s and 27.7 s). For the shortest wave group, due to bore focusing, the shoreline fluctuates predominantly at the Tg time scale, showing a large runup and the presence of wave–swash interactions with strong momentum exchange. In contrast, for the longer wave groups, the swash excursion is dominated by the individual waves. The uprush generally promotes onshore sediment advection with consequent erosion at the rundown location but accretion close to the runup. On the contrary, the backwash promotes seaward sediment advection and accretion at the rundown location. The presence of repeated wave–swash interactions modifies these patterns slightly. A wave overrunning a previous uprush promotes a reduction in onshore sediment advection while weak wave–backwash interactions reduce seaward advection. Consequently, the measured sediment dynamics shows stronger intra–swash cross–shore sediment advection for the swash events produced by the short wave groups. Measurements of the sheet flow layer near the shoreline show that for the shortest wave groups the vertical structure of the concentration is influenced by horizontal advection, leading to large sheet-flow layer thickness. However, for the longer wave groups, the local vertical exchange of sediment in the sheet–flow layer is dominant, with the presence of a pick–up and mirroring upper layer similar to oscillatory sheet–flow measurements. These results reaffirm the important effects of the wave group structure and the wave–swash interactions on the swash zone sediment dynamics and beach face evolution.

Breakpoint Forcing Revisited: Phase Between Forcing and Response

AbstractUsing the breakpoint forcing model, for long wave generation in the surf zone, expressions for the phase difference between the breakpoint‐forced long waves and the incident short wave groups are obtained. Contrary to assumptions made in previous studies, the breakpoint‐forced long waves and incident wave groups are not in phase and outgoing breakpoint‐forced long waves and incident wave groups are not π out of phase. The phase between the breakpoint‐forced long wave and the incident wave group is shown to depend on beach geometry and wave group parameters. The breakpoint‐forced incoming long wave lags behind the wave group, by a phase smaller than π/2. The phase lag decreases as the beach slope decreases and the group frequency increases, approaching approximately π/16 within reasonable limits of the parameter space. The phase between the breakpoint‐forced outgoing long wave and the wave group is between π/2 and π and it increases as the beach slope decreases and the group frequency increases, approaching 15π/16 within reasonable limits of the parameter space. The phase between the standing long wave (composed of the incoming long wave and its reflection) and the incident wave group tends to zero when the wave group is long compared to the surf zone width. These results clarify the phase relationships in the breakpoint forcing model and provide a new base for the identification of breakpoint forcing signal from observations, laboratory experiments and numerical modeling.

Therapeutic heat and cryotherapy increases knee range of movement on hamstring muscles of healthy volunteers

Purpose: To investigate the effects of heat (surface and deep) and cold on the range of motion of the knee. Methods: A total of 40 volunteers were randomly allocated into four groups, with 10 participants in each group. The control group had no intervention, the infrared group received an application of surface heat conducted through an infrared device, the shortwave group received deep heating through a shortwave device, and the cryotherapy group had ice packs placed on them. A blind measurer performed the flexibility evaluation using a goniometer coupled to a board that evaluated range of movement of the knee. Data were statistically analysed by one-way analysis of variance and Tukey's comparison (for comparison between groups) and paired t-student tests (for before and after comparisons) to determine differences between groups, with a significance level of p<0.05. Findings: The infrared, cryotherapy and shortwave groups showed an increase in the range of motion compared with the control group. It was observed that the control and infrared groups showed no significant differences before and after application (p>0.05). However, the cryotherapy and shortwave groups demonstrated an effective increase (p<0.05). Conclusions: The three heating and cooling techniques caused a favourable increase of range of movement compared with no intervention. However, the shortwave and cryotherapy interventions were more effective in increasing the knee joint's range of motion.

Improving predictions of swash dynamics in XBeach: The role of groupiness and incident-band runup

In predicting storm impacts on sandy coasts, possibly with structures, accurate runup and overtopping simulation is an important aspect. Recent investigations (Stockdon et al., 2014; Palmsten and Splinter, 2016) show that despite accurate predictions of the morphodynamics of dissipative sandy beaches, the XBeach model (Roelvink et al., 2009) does not correctly simulate the individual contributions of set-up, and infragravity and incident-band swash to the wave run-up. In this paper we describe an improved numerical scheme and a different way of simulating the propagation of directionally-spread short wave groups in XBeach to better predict the groupiness of the short waves and the resulting infragravity waves. The new approach is tested against field measurements from the DELILAH campaign at Duck, NC, and against video-derived runup measurements at Praia de Faro, a relatively steep sandy beach. Compared to the empirical fit by Vousdoukas et al. (2012) the XBeach model performs much better for more extreme wave conditions, which are severely underestimated by existing empirical formulations.For relatively steep beaches incident-band swash cannot be neglected and a wave-resolving simulation mode is required. Therefore in this paper we also test the non-hydrostatic, wave-resolving model within XBeach for runup and overtopping against three datasets. Results for a high-quality flume test show non-hydrostatic XBeach predicts the run-up height with good accuracy (maximum deviation 15%). A case with a very shallow foreshore typical for the Belgian coast at Wenduine was compared against detailed measurements. Overall the model shows correct behavior for this case. Finally, the model is tested against a large number (551) of physical model tests of overtopping from the CLASH database. For relatively high overtopping discharges the non-hydrostatic XBeach performs quite well, with increasing accuracy for increasing overtopping rates. However, for relatively low overtopping rates of less than 10–20 l/m/s, the model systematically underestimates measured overtopping rates.

Numerical investigation of infragravity wave amplifications during harbor oscillations influenced by variable offshore topography

The infragravity (IG) period oscillations inside an elongated rectangular harbor near the offshore fringing reef induced by normal-incident bichromatic short wave groups are simulated using a fully nonlinear Boussinesq model, FUNWAVE 2.0. Based on an IG wave separation procedure, this article presents a systematical investigation on how the maximum IG period component amplitude, the bound and free IG waves, and their relative components inside the harbor change with respect to the plane reef-face slope and the incident short wave amplitude under the condition of the 2nd to the 5th modes. For the given harbor and the ranges of the reef-face slope and the incident short wave amplitude studied in this paper, it is shown that both the maximum IG period component amplitude and the free IG wave component amplitude inside the harbor fluctuate widely with the reef-face slope, and their changing trends with the reef-face slope are almost identical with each other, while the bound IG waves inside the harbor seem insensitive to it. Both the maximum IG period component amplitude and those of the bound and free IG standing waves inside the harbor change cubically with the incident short wave amplitude.

Efeito agudo da crioterapia e diatermia na flexibilidade e força muscular de isquiotibiais

Objetivo: Verificar o efeito agudo da crioterapia e da diatermia por ondas curtas na flexibilidade e força muscular de isquiotibiais de adultas jovens.Materiais e Métodos: Quarenta e cinco voluntárias foram randomizadas em grupo controle, grupo crioterapia e grupo diatermia por ondas curtas. Os sujeitos foram submetidos a uma única aplicação de crioterapia ou diatermia por ondas curtas. Foram avaliadas, pré e pós intervenção, a flexibilidade através do banco de Wells e do ângulo de extensão ativa do joelho, e a força muscular através da dinamometria. As variáveis foram analisadas por meio do teste t de Student e ANOVA.Resultados: Verificou-se um aumento significativo da flexibilidade dos isquiotibiais, tanto através do banco de Wells (24,50±6,88 cm para 26,87±8,02 cm) (p=0,002), quanto na extensão ativa do joelho (162,60±7,76 graus para 165,53 ± 6,38 graus) (p=0,015) no grupo diatermia. O grupo crioterapia mostrou melhora da flexibilidade no banco de Wells (23,27±6,33 cm para 25,53±6,13 cm) (p=0,002). Não ocorreu aumento significativo da força muscular em nenhum dos grupos de intervenção. Não foi verificada diferença entre os grupos do estudo.Conclusão: Tanto a diatermia quanto a crioterapia melhoraram, de forma aguda, a flexibilidade dos isquiotibiais em mulheres adultas jovens e saudáveis. A termoterapia através da diatermia por ondas curtas mostrou-se mais efetiva nessa melhora. Ambos os recursos não alteraram a força muscular produzida pelos isquiotibiais.

Diffraction Characteristics of Small Fault ahead of tunnel face in coal roadway

Small fault ahead of the tunnel face in coal roadway is the important hidden hazard factor of coal and gas outburst accidents. The study of small fault prediction has important practical significance, which is the urgent demand of coal mine safety production. The diffraction of breakpoint can be used to identify the fault. However, unlike surface seismic exploration, the diffraction is with approximately horizontal incidence when the advanced detection is carried out in the roadway. The common advanced detection system is mainly as the reference of traffic tunnel, without considering the influence of low-velocity coal seam. Considering the influence of an acoustic wave of the roadway cavity and channel wave of the coal seam, the advanced detection model of small fault ahead of tunnel face is established. Diffraction advanced observation system in which sources located in front of tunnel face is constructed, and the numerical calculation of the high-order staggered-grid finite difference is carried out. The simulation results show that: Compared with the data collected by reflection observation system, in seismic records acquired by diffraction observation system, the suppression effect of acoustic wave is appeared. The diffracted P-wave of the breakpoint of component X is clear with strong energy and short-wave group. Multiple diffractions of the breakpoint are not found, but the multiple diffraction of tunnel face endpoint is obvious. The difference between breakpoint diffraction and multiple diffractions of the endpoint is clear, and diffracted P-wave of the breakpoint is easy to identify. The multiple reflected channel wave between the fault and the tunnel face is very obvious, and the reflected channel wave of small fault is so hard to identify. Migration results show that the imaging resolution of diffracted P-wave of small fault is higher than the reflected channel wave, and breakpoint location of imaging is consistent with the actual model.

Dissipation of incident forced long waves in the surf zone—Implications for the concept of “bound” wave release at short wave breaking

A review of laboratory data sets on surf beat is presented, with a focus on the dissipation of long wave energy in the surf zone. It is frequently assumed that incident forced long waves, or “bound” long waves, are released from short wave groups when the short waves break, subsequently propagating to the shore as a free wave. Free long waves may additionally be generated by the moving short wave breakpoint. Convincing evidence of the release of forced long waves as a result of short wave breaking is lacking, while there appears to be strong evidence to the contrary from a range of recent laboratory experiments. The data from the laboratory experiments are also consistent with field observations of strong nearshore dissipation of long waves. These data are also consistent with Longuet-Higgins and Stewart (1962), who suggest that the forced long wave may reduce in amplitude following short wave breaking, not that it might be released as a free wave. In contrast, forced long waves can be progressively “released” from the groups when the short waves are in shallow water, since these conditions correspond to those where the forced long wave satisfies the free wave dispersion relationship. This frequently occurs prior to short wave breaking for mild wave conditions, but here it is shown that these conditions are not usually satisfied at the short wave breakpoint for storm conditions. Energy transfers between free and forced waves are also discussed with regard the data. A surf beat similarity parameter that incorporates both relative beach slope and short wave steepness is suggested, which distinguishes between different long wave forcing regimes inside the surf zone.

Generation, Transformation, and Scattering of Long Waves Induced by a Short-Wave Group over Finite Topography

Abstract Second-order analytical solutions are constructed for various long waves generated by a gravity wave train propagating over finite variable depth h(x) using a multiphase Wentzel–Kramers–Brillouin (WKB) method. It is found that, along with the well-known long wave, locked to the envelope of the wave train and traveling at the group velocity Cg, a forced long wave and free long waves are induced by the depth variation in this region. The forced long wave depends on the depth derivatives hx and hxx and travels at Cg, whereas the free long waves depend on h, hx, and hxx and travel in the opposite directions at . They interfere with each other and generate free long waves radiating away from this region. The author found that this topography-induced forced long wave is in quadrature with the short-wave group and that a secondary long-wave orbital velocity is generated by variable water depth, which is in quadrature with its horizontal bottom counterpart. Both these processes play an important role in the energy transfer between the short-wave groups and long waves. These behaviors were not revealed by previous studies on long waves induced by a wave group over finite topography, which calculated the total amplitude of long-wave components numerically without consideration of the phase of the long waves. The analytical solutions here also indicate that the discontinuity of hx and hxx at the topography junctions has a significant effect on the scattered long waves. The controlling factors for the amplitudes of these long waves are identified and the underlying physical processes systematically investigated in this presentation.

Experimental and numerical study of the effect of variable bathymetry on the slow-drift wave response of floating bodies

An experimental campaign is reported on the slow-drift motion of a rectangular barge moored at different positions along an inclined beach, at waterdepths ranging from 54 cm to 21 cm, and submitted to irregular beam seas. The beach is achieved by inclining the 24 m long false bottom of the tank at a slope of 5%, from a depth of 1.05 m. The slow-drift component of the measured sway motion is first compared with state-of-the-art calculations based on Newman’s approximation. At 54 cm depth a good agreement is obtained between calculations and measurements. At 21 cm depth the Newman calculations exceed the measured values. When the flat bottom setdown contribution is added up, the calculated values become 2 to 3 times larger than the measured ones. A second-order model is proposed to predict the shoaling of a bichromatic sea-state propagating in varying water-depth. This model is validated through comparisons with an extension of Schäffer’s model for a straight beach [Schäffer HA. Infragravity waves induced by short-wave groups. J Fluid Mech 1993;247:551–88] and with a fully nonlinear Boussinesq model. It appears that the long wave amplitude is much less than predicted by the flat bottom model, and that its phase difference with the short wave envelope also deviates from the flat bottom model prediction. As a result of this phase shift the actual second-order wave loads can be lower than predicted by Newman’s approximation alone. Application of the shoaling model to the barge tests yields a notably better agreement between numerical and experimental values of its slow-drift sway motion.

Reynolds averaged Navier–Stokes modelling of long waves induced by a transient wave group on a beach

This paper presents the numerical modelling of the cross shore propagation of infragravity waves induced by a transient focused short wave group over a sloping bottom. A dataset obtained through new laboratory experiments in the wave flume of the University of Cantabria is used to validate the Reynolds averaged Navier–Stokes type model IH-2VOF. A new boundary condition based on the wave maker movement used in the experiments is implemented in the model. Shoaling and breaking of short waves as well as the enhancement of long waves and the energy transfer to low-frequency motion are well addressed by the model, proving the high accuracy in the reproduction of surf zone hydrodynamics. Under the steep slope regime, a long wave trough is radiated offshore from the breakpoint. Numerical simulations conducted for different bottom slopes and short wave steepness suggest that this low-frequency breakpoint generated wave is controlled by both the bed slope parameter and the Iribarren number. Moreover, the numerical model is used to investigate the influence that a large flat bottom induces on the propagation pattern of long waves.

Calculations of kinematics underneath measured time histories of steep water waves

The present paper is concerned with the problem of estimating fluid particle velocities underneath a measured wave profile at a single spatial position. Second-order calculations are compared with measurements of wave particle kinematics underneath both irregular waves (Skjelbreia et al. (1991) [17]) and focused wave groups (Johannessen & Swan (2001) [16]). It is found that second-order theory is capable of describing the kinematics at the free surface very accurately provided that the local underlying regime of free waves can be identified. At the free surface, estimates of the crest velocities are nearly independent of the cut-off frequency even for broad continuous spectra. Since the velocities at the free surface can be calculated accurately, it is found that the simplest and most reliable method to obtain the velocities below the surface is to use the exponentially decaying velocity potential directly also above the still water level. In a continuous spectrum, the solution will necessarily break down for large enough frequencies but since the velocities at the surface are known, this is strictly an interpolation and the frequency cut-off may be controlled. A directional wave field is not defined uniquely from measurements of the surface elevation at one spatial position. Comparisons between measurements of steep directional wave groups and calculations of unidirectional waves based on the measured surface elevation, however, indicate that the unidirectional case may provide very useful predictions also for short crested wave groups.

Generation mechanism of an alongshore bar on a sandy beach slope

A model explaining the mechanism of alongshore bar formation from the point of view of the sediment balance in the surf zone is considered. A cloud of suspended matter that appears during wave breaking is transported shoreward and simultaneously sediments forming a vertical material flux directed to the bottom (S). Simultaneously, an undertow generates a horizontal offshore flux of suspended matter qx. Under these conditions, the sediment balance is determined by the equality of the flux -S and the gradient dqx/dx. The bottom profile satisfying the balance equation is a bar profile with the crest at the point of the flux maximum -S. The model predicts a concave profile of the seaside slope and a concave-convex profile of the slope in the trough. A conclusion is reached on the basis of the calibration and verification of the model based on the field data that the suggested mechanism manifests itself differently in the outer and inner zones of the coastal zone. In the inner zone, the horizontal size of the bar is determined by the length of short wind waves, while, in the outer one, it is determined by the length of the infragravity waves related to the groups of short waves. It is shown that the model can be applied to estimate the parameters of the largest bar in the inner part of the coastal zone.

Influence of wind on extreme wave events: experimental and numerical approaches

The influence of wind on extreme wave events in deep water is investigated experimentally and numerically. A series of experiments conducted in the Large Air–Sea Interactions Facility (LASIF-Marseille, France) shows that wind blowing over a short wave group due to the dispersive focusing of a longer frequency-modulated wavetrain (chirped wave packet) may increase the time duration of the extreme wave event by delaying the defocusing stage. A detailed analysis of the experimental results suggests that extreme wave events may be sustained longer by the air flow separation occurring on the leeward side of the steep crests. Furthermore it is found that the frequency downshifting observed during the formation of the extreme wave event is more important when the wind velocity is larger. These experiments have pointed out that the transfer of momentum and energy is strongly increased during extreme wave events.Two series of numerical simulations have been performed using a pressure distribution over the steep crests given by the Jeffreys sheltering theory. The first series corresponding to the dispersive focusing confirms the experimental results. The second series which corresponds to extreme wave events due to modulational instability, shows that wind sustains steep waves which then evolve into breaking waves. Furthermore, it was shown numerically that during extreme wave events the wind-driven current could play a significant role in their persistence.

Revisiting Horizontal Diffusion of Perturbations over Terrain for NCEP RSM

˙The perturbation in the National Centers for Environmental Prediction (NCEP) Regional Spectral Model (RSM) is defined by the difference between the RSM and its outer model, such as the NCEP global model, on the same given coordinate surfaces. This perturbation is dominated by the difference between terrains of the RSM and the global model if model terrain exists over the domain. After being transformed into spectral space, this difference in terrains is characterized by two distinct groups of coefficients i.e., long-wave and short-wave groups. The long-wave group is considerably larger in amplitude than the short-wave group, and considered to be the cause of error in horizontal diffusion of perturbations on sigma surfaces. A higher order of diffusion and diffusion without long waves on sigma surfaces with perturbations are formulated to investigate the possibility of using diffusion on sigma surfaces. In a typical case, erroneous circulation occurred when fourth-order diffusion on a sigma surface was used; however, reasonable circulation was simulated with second-order diffusion on the pressure surface. Nevertheless, diffusion on a pressure surface is a non-economical method in spectral modeling. The results of sixth- and eighth-order horizontal diffusions of perturbations and no-diffusion on the group of long waves for all orders (second, fourth, sixth, and eighth) on sigma surfaces did not show errone

On the role of the Jeffreys' sheltering mechanism in sustaining extreme water waves

The effect of the wind on sustaining extreme water waves is investigated experimentally and numerically. A series of experiments conducted in the Large Air–Sea Interactions Facility (LASIF) showed that a wind blowing over a strongly nonlinear short wave group due to the linear focusing of a modulated wave train may increase the life time of the extreme wave event. The experiments suggested that the air flow separation that occurs on the leeward side of the steep crests may sustain longer the maximum of modulation of the focusing–defocusing cycle. Based on a Boundary-Integral Equation Method and a pressure distribution over the steep crests given by the Jeffreys' sheltering theory, similar numerical simulations have confirmed the experimental results. To cite this article: J.-P. Giovanangeli et al., C. R. Mecanique 334 (2006).

Wave–Current Interactions in Finite Depth

Abstract The energy, momentum, and mass-flux exchanges between surface waves and underlying Eulerian mean flows are considered, and terms in addition to the classical wave “radiation stress” are identified. The formulation is made in terms of the vertically integrated flow. The various terms are identified with other analyses and interpreted in terms of physical mechanisms, permitting reasonable estimates of the associated depth dependencies. One term is identified with the integrated “CL vortex force” implemented, for example, in simulations of Langmuir circulation. However, as illustrated with a simple example of steady refraction across a shear zone, other terms of the same order can significantly alter the results. The classic example of long waves forced by short-wave groups is also revisited. In this case, an apparent singularity arising in shallow water is countered by finite-amplitude dispersion corrections, these being formally of the same order as the forced long-wave response, and becoming significant or dominant as shallow water is approached.

Long wave generation by the shoaling and breaking of transient wave groups on a beach

This paper presents new laboratory data on the generation of long waves by the shoaling and breaking of transient-focused short-wave groups. Direct offshore radiation of long waves from the breakpoint is shown experimentally for the first time. High spatial resolution enables identification of the relationship between the spatial gradients of the short-wave envelope and the long-wave surface. This relationship is consistent with radiation stress theory even well inside the surf zone and appears as a result of the strong nonlinear forcing associated with the transient group. In shallow water, the change in depth across the group leads to asymmetry in the forcing which generates significant dynamic setup in front of the group during shoaling. Strong amplification of the incident dynamic setup occurs after short-wave breaking. The data show the radiation of a transient long wave dominated by a pulse of positive elevation, preceded and followed by weaker trailing waves with negative elevation. The instantaneous cross-shore structure of the long wave shows the mechanics of the reflection process and the formation of a transient node in the inner surf zone. The wave run-up and relative amplitude of the radiated and incident long waves suggests significant modification of the incident bound wave in the inner surf zone and the dominance of long waves generated by the breaking process. It is proposed that these conditions occur when the primary short waves and bound wave are not shallow water waves at the breakpoint. A simple criterion is given to determine these conditions, which generally occur for the important case of storm waves.

Resonant response of harbours to short-wave groups

A non-linear short-wave propagation model is used for the simulation of low-frequency waves induced by short-wave groups. The model is based on the higher order Boussinesq-type equations for the propagation of breaking and non-breaking waves in nearshore areas. The 2DH (two horizontal dimensions) Boussinesq model is used to calculate the resonant response of harbours due to bound waves generated by short-wave groups. The results are compared with experimental data available in the literature. In these experiments, bound long waves are generated by carrier bichromatic short waves, which form regular wave groups. The results of the model were found to be in good agreement with the experimental data. The 1DH Boussinesq model is applied in the surf zone to simulate surf beat generation by a time-varying breakpoint and the reflected long wave induced by bichromatic wave groups. A new breaking criterion is introduced, based on the relative trough Froude number. Model generation of the surf beat is also shown to be in good agreement with experimental data.

Resonant response of harbours to short-wave groups

Resonant response of harbours to short-wave groups