Surface Wave Train Research Articles

Reduction of Drag Coefficient Due To Misaligned Wind‐Waves

AbstractRecent field observations suggest that the air‐sea momentum flux (or the drag coefficient) is significantly reduced when the dominant wind‐forced surface waves are misaligned from local wind. Such conditions may occur under rapidly changing strong winds (such as under tropical cyclones) or in coastal shallow waters where waves are refracted by bottom topography. A recent Large Eddy Simulation (LES) study also shows that the drag coefficient is reduced by a misaligned strongly forced wave train (with a small wave age of 1.37). In order to investigate more realistic field conditions, this study employs LES to examine the effect of a misaligned (up to 90°) surface wave train over a wide range of wave age up to 10.95. For all wave ages examined, the drag coefficient is reduced compared to the flat surface condition when the misalignment angle exceeds around 22.5°–45°. The drag reduction may occur even if the form drag of the wave train is positive.

Buried object localization by spectral analysis of surface wave reflections

A proposed method of buried object localization, based upon spectral analysis of surface wave reflections, is investigated numerically. This arises from a hypothesis to the effect that reflectivity would be maximized at some intermediate wavelength, shorter ones associated with disturbances too shallow to substantially excite the object as a secondary (reflecting) source, and longer ones with disturbances involving such volumes of earth in motion that the object become insignificant as a reflector. Discernment of that intermediate wavelength of maximum reflectivity might, thereby, provide an index of the object’s depth. Horizontal distance from echo return time, and azimuth from phase array techniques, could complete a localization methodology. Presented, accordingly, are 2D FEA simulations, in which narrow-banded surface wave trains are excited by a point source on the surface of an elastic medium, a void provided at some horizontal distance and depth, the strength of reflected surface motions thereafter examined in relation to frequency. These bear out the hypothesis, finding maximal reflectivity for a surface wavelength about two-thirds of the object depth. Proposed is that this could serve as the basis for a horizontal stand-off detection method, especially for applications like landmines, for which it may be undesirable to scan from above.

Radial and azimuthal seismic anisotropy in NW South America: Insights into crustal deformation and mantle flow using ambient noise and surface wave tomography

We illuminate the crustal and upper mantle structure of the northwestern corner of South America by mapping radial and azimuthal seismic anisotropy. Radial anisotropy is inferred from the discrepancy between VSV and VSH polarized S-velocities in horizontally propagating Rayleigh and Love waves, respectively. First, short-period (7–35 s) phase and group velocities are estimated from ambient noise cross-correlations, and long-period (40–170 s) group velocities are determined from fundamental-mode, surface-wave trains from earthquake sources at regional and teleseismic epicentral distances. Dispersion velocities are then tomographically inverted to develop maps of group velocity variation for periods between 7 and 170 s including azimuthal velocity dependence. We observe that positive anisotropy in the upper crust is related to thick Quaternary sequences in sedimentary basins, while negative anisotropy is found beneath active volcanoes and igneous-metamorphic terrains. Negative anisotropy features observed in the lower crust beneath the Eastern Cordillera suggest the existence of sill-like intrusions that penetrate the lower crust, thus supporting underplating mechanisms. Our study reveals SW-NE oriented fast axes of azimuthal anisotropy beneath the Eastern Cordillera, which strongly suggest the presence of shear zones within the fold and thrust belt system. Notably, the fast axes align parallel to the regional faults in the area, indicating a significant role in controlling faulting processes. Finally, we observe a wide trench-parallel zone of azimuthal anisotropy beneath the Nazca Plate, the Panama Block, and the Caribbean, which we associate with subslab mantle flow.

The <i>n</i>th-order self-resonance law of single wave train for surface capillary-gravity waves in deep water

Wave-wave resonance mechanism plays a fundamental and prominent role in the process of energy transfer and distribution, whether it is in microscopic or macroscopic matter. For the most extensive and intuitive ocean surface wave motion on earth, it is bound to be even more so. Can we extract the general wave-wave resonance law from it, especially the most special and brief resonance law for single wave train? To this end, according to a set of classical methods proposed by Phillips for initiating modern water wave dynamics with the specific 4-wave resonance conditions, and starting from the basic governing equations of ocean deep-water surface capillary-gravity waves, the first-order differential equation, and the second-, third- and fourth-order integral differential ones, which are becoming more and more complex but tend to be complete, of the Fourier components of free surface displacement are respectively given by the Fourier-Stieltjes transformation and perturbation method. Under a set of symbol system, which is self-created, self-evident and concise, these equations are solved in turn to obtain the first-order free surface displacement of single wave train, the Fourier coefficients of the second-, third- and fourth-order non-resonant and resonant free surface displacements, and the second-, third- and fourth-order resonant conditions, thus leading to the general nth-order self-resonance law of single wave train. This completely reveals the rich connotation of single wave resonance dynamics of ocean surface capillary-gravity waves, effectively expands the application range of the classical single wave resonance solutions given by Phillips for ocean surface gravity waves, lays the foundation for depicting single and multiple resonance interaction mechanisms of double and multi-wave trains of ocean surface waves, and so provides a typical example for the exploration of single-wave resonance law in all wave fields.

Eruption sequence of the 2022 Hunga Tonga-Hunga Ha'apai explosion from back-projection of teleseismic P waves

The explosive eruption occurred at Hunga Tonga-Hunga Ha'apai on January 15, 2022, generating atmospheric waves, meteotsunamis, tsunamis, and seismic waves recorded worldwide. Energetic signals of seismic surface waves indicate multiple explosive events, but the detailed eruption episodes are hard to unravel from dispersive long-period surface waves. In this study, we performed the back-projection (BP) analysis using the teleseismic P-waves to clarify the sequence of multiple explosive eruptions. The BP results successfully detected the locations and timing of multiple explosions even though P-waves from each eruption were overlapped and masked by other seismic signals and noises. The results suggest that the series of explosive eruptions can be divided into two parts of eruption sequences. The first sequence started at 04:02 UTC, escalated into major explosions at 04:15 UTC and 200 - 300 s afterward, and lasted at least until 04:35 UTC. The second sequence began about 4 hours later (08:26 UTC) and continued for about 6 - 7 minutes, including a massive eruption at 08:31 UTC. The estimated origin times of each eruption episode determined in this study are consistent with successive arrivals of long-period surface wave trains at frequencies higher than 10 mHz. The time intervals of explosive eruptions in the first sequence suggested that the significant explosive eruptions intermittently occurred at around 270 - 280 s intervals. This interval is nearly equivalent to the eigenfrequencies of the atmospheric resonant oscillation with the Earth at 3.7 mHz. Since the observed amplitude spectra of this eruption exhibit a conspicuous spectral peak at 3.7 mHz, our BP results indicate that the eruption cycle may be synchronized with the eigen-period of the atmosphere-lithosphere coupled mode.

Determination of intraplate focal mechanisms with the Brazilian Seismic Network: A simplified Cut-and-Paste approach

The feasibility of a simplified Cut-and-Paste approach (CAP) for routine determination of intraplate earthquake mechanisms in Brazil is demonstrated with data acquired by the Brazilian Seismographic Network (RSBR). Our approach models three-component seismic recordings through: (i) computation of synthetics seismograms with a single, average velocity model, and (ii) independent alignment of observed and synthetic waveforms through waveform cross-correlation. No partitioning of regional waveforms into their corresponding body- and surface-wave trains is considered. The empirical alignment successfully accounts for lateral variations along specific source-station paths, along with location uncertainties and timing errors, and effectively augments the number of waveforms available for inversion. The performance of the proposed approach is demonstrated through modeling of two recent intraplate earthquakes: the Mw 4.4 2017 Maranhão earthquake and the Mw 4.1 2020 Amargosa earthquake. For the Maranhão event, we obtain a strike-slip focal mechanism (340° ± 0°, 70° ± 0°, 0° ± 0°) and a centroid depth of 9 km with magnitude of Mw 4.4, fully consistent with previous studies. For the Amargosa earthquake, we obtain a normal-fault mechanism (20° ± 4.6°, 60° ± 16.9°, -30° ± 14.4°) with a preferred centroid depth of 10 km, which is in general agreement with P-wave polarity data and the orientation of the nearby Salvador Shear Zone. We thus conclude that our simplified CAP approach is an effective tool for modeling regional waveforms in Brazil and, most likely, in sparse networks in general.

Response regimes in the fluid–structure interaction of wall turbulence over a compliant coating

The interaction between a turbulent boundary layer flow and compliant surfaces is investigated experimentally. Three viscoelastic coatings with different material stiffnesses are used to identify the general surface response to the turbulent flow conditions. For the softest coating, the global force measurements show two obvious regimes of interaction with an indicated transition at $U_b/C_t\sim 3.5$ , where $U_b$ is the bulk flow velocity and $C_t$ is the coating shear velocity. The one-way coupled regime shows friction values comparable to those of the rigid wall, while the two-way coupled regime indicate a significant increase in fluid friction. Within the one-way coupled regime for $U_b/C_t>1.2$ , the flow measurements show a low level of two-way coupling represented by the change of the velocity profile as well as the increase in the Reynolds stresses in the near-wall region. This is supported by the surface deformation measurements. Initially, the turbulent flow structures induce only an imprint on the coating surface, while a change in surface response occurs when the surface wave propagation velocity $c_w$ equals the shear wave velocity of the coating $C_t$ (i.e. $c_w/C_t\sim 1$ ). Above $U_b/C_t>1.2$ , a growth in wavelength is observed with increasing flow velocity, most probably due to the surface wave formation generated downstream the pressure features of the flow. The surface response is stable and correlates with the high-intensity turbulent pressure fluctuations in the turbulent boundary layer, with a wave propagation velocity $c_w\sim 0.7\unicode{x2013}0.8$ $U_b$ . Within the two-way coupled regime, additional fluid motions and a downward shift in the logarithmic region of the velocity profile are observed due to substantial surface deformation and confirm the frictional drag increase. Another type of surface response is initiated by phase-lag instability in combination with surface undulations that start to protrude the viscous sublayer, where the propagation velocity of surface wave trains is $c_w\sim 0.17\unicode{x2013}0.18$ $U_b$ .

Reynolds stress turbulence modelling of surf zone breaking waves

Computational fluid dynamics is increasingly used to investigate the inherently complicated phenomenon of wave breaking. To date, however, no single model has proved capable of accurately simulating the breaking process across the entirety of the surf zone for both spilling and plunging breakers. The present study newly considers the Reynolds stress–$\omega$turbulence closure model for this purpose, where$\omega$is the specific dissipation rate. Novel stability analysis proves that, unlike two-equation closures (at least in their standard forms), the stress–$\omega$model is neutrally stable in the idealized potential flow region beneath surface waves. It thus naturally avoids unphysical exponential growth of turbulence prior to breaking, which has plagued numerous prior studies. The analysis is confirmed through simulation of a progressive surface wave train. The stress–$\omega$model is then applied to simulate a turbulent wave boundary layer, demonstrating superior accuracy relative to a two-equation model, especially during flow deceleration. Finally, the stress–$\omega$model is employed to simulate spilling and plunging breaking waves, with seemingly unprecedented accuracy. Specifically, the present work marks the first time that a single turbulence closure model collectively: (1) avoids turbulence over-production prior to breaking, (2) accurately predicts the breaking point, (3) provides reasonable evolution of turbulent normal stresses, while also (4) yielding accurate evolution of undertow velocity structure and magnitude across the surf zone, for both spilling and plunging cases. Differences in the predicted Reynolds shear stresses (hence flow resistance) are identified as key to the improved inner surf zone performance, relative to a state-of-the-art two-equation model.

Instability of the realizable k– ε turbulence model beneath surface waves

Recent research has proved that most widely used two-equation turbulence closure models are unconditionally unstable in regions of nearly potential flow having finite strain, as commonly found beneath non-breaking surface waves. In this work, we extend such analysis to consider the popular realizable k–ε turbulence model. It is proved that this model, unlike all others thus far analyzed, is only conditionally unstable in such regions due to the addition of viscosity in the ε dissipation term. A method for formally stabilizing the model in the problematic regions is likewise developed. The results of the analysis, using both standard and stabilized turbulence closures, are confirmed via numerical simulations of progressive surface wave trains using a computational fluid dynamics model. Important qualitative differences are likewise demonstrated in simulations involving spilling breaking waves. (In the above, k is the turbulent kinetic energy density, and ε is the turbulence dissipation rate.)

Water Wave Scattering by a Bottom-Standing Thick Rectangular Barrier in the Presence of an Ice Cover

The problem of scattering of a normally incident surface wave train by an obstacle in the form of a thick rectangular vertical bottom-standing barrier submerged in finite-depth water with a free surface is extended here with an ice cover modelled as a thin uniform elastic plate. The problem is reduced to a set of singular integral equations of the first kind. The Galerkin approximation in terms of simple polynomials multiplied by appropriate weight functions whose form is dictated by the behavior of the fluid velocity near the barrier edges is used for solving the integral equations. The reflection and transmission coefficients are obtained numerically, and they are depicted graphically against the wavenumber for various ice cover parameters. It is observed that the barrier thickness plays a significant role in modelling of efficient breakwaters.

Evolution of a pair of random inhomogeneous wave systems over infinite-depth water

A system of two coupled nonlinear spectral transport equations is derived for two obliquely interacting narrowband Gaussian random surface wavetrains, slowly varying in space and time. Using these two equations, stability analysis is performed for two initially homogeneous wave spectra, subject to unidirectional perturbations. We observe that the effect of randomness produces a decrease in the growth rate of instability, but it is higher than the growth for a single wavetrain. The growth rate of instability is observed to decrease with the increase in spectral width. doi:10.1017/S144618111900004X

EVOLUTION OF A PAIR OF RANDOM INHOMOGENEOUS WAVE SYSTEMS OVER INFINITE-DEPTH WATER

A system of two coupled nonlinear spectral transport equations is derived for two obliquely interacting narrowband Gaussian random surface wavetrains, slowly varying in space and time. Using these two equations, stability analysis is performed for two initially homogeneous wave spectra, subject to unidirectional perturbations. We observe that the effect of randomness produces a decrease in the growth rate of instability, but it is higher than the growth for a single wavetrain. The growth rate of instability is observed to decrease with the increase in spectral width.

VS models in the historical centre of Naples (Southern Italy) from noise cross-correlation

Ambient noise measurements have been performed in the historical centre of Naples (Southern Italy) along 40 paths (inter-receiver distances) with a length ranging from ~300 m to ~1550 m, for recording time variable from few hours to several months.Synchronous noise recordings at two receivers, 1-bit normalized, have been cross-correlated in order to estimate the empirical Green's function (surface wave train) of the medium between them. The fundamental-mode Raleigh waves have been extracted at periods ranging from 0.15 s to 1 s by using the frequency-time analysis technique. Average group velocity dispersion curves with error bar have been evaluated along 28 paths and inverted with a non-linear approach to get VS profiles extending to depths of ~50–300 m.Comparison of VS with some deep drillings and two down-hole measurements lets to argue important findings. First of all there is a good agreement with shallow (about 35 m) point down-hole measurements. The historical centre of Naples results to be characterized by a cover of man-made ground and pyroclastics of recent activity with thickness of 15–30 m and VS lower than 400 m/s. The products of the Neapolitan Yellow Tuff eruption have a thickness of about 80 m and are characterized by VS of 500–700 m/s in the shallower, altered and fractured part and of 700–900 m/s in the deeper, compact part. Below them, separated by a thin layer of the Campanian Ignimbrite that cannot be resolved by the data, ancient tuffs or marine sands are present which are locally responsible of velocity decrease. VS of 1100–1300 m/s, ascribable to intercalations of volcanic and sedimentary (marls, conglomerates and marly sands) rocks, are detected at ~200 m depth in the ancient part of the historical centre, rising to ~100 m depth, in the north-east of it.This study also gives an important contribution to microzoning studies. The top of the lithoid Neapolitan Yellow Tuff cannot be considered as the top of the seismic bedrock, being characterized by 500 m/s < VS < 800 m/s. The seismic bedrock with VS ≥ 800 m/s is deeper, sometimes at depths >100 m.

The Effect Of Randomness On The Stability Of Capillary Gravity Waves In The Presence Of Air Flowing Over Water

A nonlinear spectral transport equation for the narrow band Gaussian random surface wave trains is derived from a fourth order nonlinear evolution equation, which is a good starting point for the study of nonlinear water waves. The effect of randomness on the stability of deep water capillary gravity waves in the presence of air flowing over water is investigated. The stability is then considered for an initial homogenous wave spectrum having a simple normal form to small oblique long wave length perturbations for a range of spectral widths. An expression for the growth rate of instability is obtained; in which a higher order contribution comes from the fourth order term in the evolution equation, which is responsible for wave induced mean flow. This higher order contribution produces a decrease in the growth rate. The growth rate of instability is found to decrease with the increase of spectral width and the instability disappears if the spectral width increases beyond a certain critical value, which is not influenced by the fourth order term in the evolution equation.

A previously unreported type of seismic source in the firn layer of the East Antarctic Ice Sheet

AbstractWe identify a unique type of seismic source in the uppermost part of the East Antarctic Ice Sheet recorded by temporary broadband seismic arrays in East Antarctica. These sources, termed “firnquakes,” are characterized by dispersed surface wave trains with frequencies of 1–10 Hz detectable at distances up to 1000 km. Events show strong dispersed Rayleigh wave trains and an absence of observable body wave arrivals; most events also show weaker Love waves. Initial events were discovered by standard detection schemes; additional events were then detected with a correlation scanner using the initial arrivals as templates. We locate sources by determining the L2 misfit for a grid of potential source locations using Rayleigh wave arrival times and polarization directions. We then perform a multiple‐filter analysis to calculate the Rayleigh wave group velocity dispersion and invert the group velocity for shear velocity structure. The resulting velocity structure is used as an input model to calculate synthetic seismograms. Inverting the dispersion curves yields ice velocity structures consistent with a low‐velocity firn layer ~100 m thick and show that velocity structure is laterally variable. The absence of observable body wave phases and the relative amplitudes of Rayleigh waves and noise constrain the source depth to be less than 20 m. The presence of Love waves for most events suggests the source is not isotropic. We propose the events are linked to the formation of small crevasses in the firn, and several events correlate with shallow crevasse fields mapped in satellite imagery.

African clawed toads (Xenopus laevis) sense the distance of lateral line stimuli.

Sighted African clawed toads use their lateral lines to detect stimulus distance, although accuracy and precision are poorer than for stimulus direction. Single surface wave trains elicited discrete turns and/or swims towards the wave origin. Most responses were brief, ending with the toad stationary (70% overall; 54-86% individual toads) or pausing before turning away (11%; 1-24%). Lunges or capturing movements with the arms (13%; 10-22%) also indicated where toads expected to find prey. Overall, 94% (88-100%) of oriented responses had well-defined endpoints. Swim distance--measured as means, medians, and upper and lower quartiles--and the number of bilateral leg kicks increased with stimulus distance. Swim distance also depended upon stimulus angle due to features of turning. Most responses (81%; 62-92%) ended short of the wave origin. Regression slopes were 0.45 ± 0.04 mm/mm for stimulus distances up to 85 mm (ca. 2-3x body lengths), 0.16 ± 0.07 mm/mm for distances of 85-130 mm, and non-significant for larger distances to 220 mm. Slopes were steeper for responses that included lunges or capture movements. In only 15% (3-26%) of responses were both turn direction and swim distance sufficiently accurate for the toad to sweep through the wave origin.

Shallow seismicity, triggered seismicity, and ambient noise tomography at the long-dormant Uturuncu Volcano, Bolivia

Using a network of 15 seismometers around the inflating Uturuncu Volcano from April 2009 to 2010, we find an average rate of about three local volcano-tectonic earthquakes per day, and swarms of 5–60 events a few times per month with local magnitudes ranging from −1.2 to 3.7. The earthquake depths are near sea level, more than 10 km above the geodetically inferred inflation source and the Altiplano Puna Magma Body. The Mw 8.8 Maule earthquake on 27 February 2010 triggered hundreds of earthquakes at Uturuncu with the onset of the Love and Rayleigh waves and again with the passage of the X2/X3 overtone phases of Rayleigh waves. This is one of the first incidences in which triggering has been observed from multiple surface wave trains. The earthquakes are oriented NW–SE similar to the regional faults and lineaments. The b value of the catalog is 0.49, consistent with a tectonic origin of the earthquakes. We perform ambient noise tomography using Love wave cross-correlations to image a low-velocity zone at 1.9 to 3.9 km depth below the surface centered slightly north of the summit. The low velocities are perhaps related to the hydrothermal system and the low-velocity zone is spatially correlated with earthquake locations. The earthquake rate appears to vary with time—a seismic deployment from 1996 to 1997 reveals 1–5 earthquakes per day, whereas 60 events/day were seen during 5 days using one seismometer in 2003. However, differences in analysis methods and magnitudes of completeness do not allow direct comparison of these seismicity rates. The rate of seismic activity at Uturuncu is higher than at other well-monitored inflating volcanoes during periods of repose. The frequent swarms and triggered earthquakes suggest the hydrothermal system is metastable.

Experimental observation of standing interfacial waves induced by surface waves in muddy water

A striking feature has been observed in a laboratory wave tank with a thin layer of clear water overlying a layer of mud. A piston-type wave maker is used to generate long monochromatic surface waves in a tank with a layer of kaolinite clay at the bottom. The wave action on the mud causes the clay particles to rise from the bottom into the water column, forming a lutocline. As the lutocline approaches the water surface, a set of standing interfacial waves form on the lutocline. The interfacial wave directions are oriented nearly orthogonal to the surface wave direction. The interfacial waves, which sometimes cover the entire length and width of the tank, are also temporally subharmonic as the phase of the interfacial wave alternates with each passing surface wave crest. These interfacial waves are the result of a resonant three-wave interaction involving the surface wave train and the two interfacial wave trains. The interfacial waves are only present when the lutocline is about 3 cm of the water surface and they can be sufficiently nonlinear as to exhibit superharmonics and a breaking-type of instability.

Two-dimensionality of gravity water flows of constant nonzero vorticity beneath a surface wave train

We show that a free surface water flow of constant nonzero vorticity beneath a wave train and above a flat bed has to be two-dimensional and the vorticity must have only one nonzero component which points in the horizontal direction orthogonal to the direction of wave propagation. The obtained results are of relevance to studies of resonant wave train interactions in flows of constant nonzero vorticity: in contrast to irrotational flows, all wave trains have to propagate in the same direction. An important practical aspect of these considerations lies in that wave trains of constant vorticity model the interaction of swell with tidal currents, negative vorticity being appropriate for the flood current and positive vorticity for the ebb current.

On near‐source earthquake triggering

When one earthquake triggers others nearby, what connects them? Two processes are observed: static stress change from fault offset and dynamic stress changes from passing seismic waves. In the near‐source region (r ≤ 50 km for M ∼ 5 sources) both processes may be operating, and since both mechanisms are expected to raise earthquake rates, it is difficult to isolate them. We thus compare explosions with earthquakes because only earthquakes cause significant static stress changes. We find that large explosions at the Nevada Test Site do not trigger earthquakes at rates comparable to similar magnitude earthquakes. Surface waves are associated with regional and long‐range dynamic triggering, but we note that surface waves with low enough frequency to penetrate to depths where most aftershocks of the 1992 M = 5.7 Little Skull Mountain main shock occurred (∼12 km) would not have developed significant amplitude within a 50‐km radius. We therefore focus on the best candidate phases to cause local dynamic triggering, direct waves that pass through observed near‐source aftershock clusters. We examine these phases, which arrived at the nearest (200–270 km) broadband station before the surface wave train and could thus be isolated for study. Direct comparison of spectral amplitudes of presurface wave arrivals shows that M ∼ 5 explosions and earthquakes deliver the same peak dynamic stresses into the near‐source crust. We conclude that a static stress change model can readily explain observed aftershock patterns, whereas it is difficult to attribute near‐source triggering to a dynamic process because of the dearth of aftershocks near large explosions.