A two-dimensional horizontal wave propagation and mud mass transport model

The present study offers a two-dimensional horizontal wave propagation and morphodynamic model for muddy coasts. The model can be applied on a general three-dimensional bathymetry of a soft muddy coast to calculate wave damping, fluid mud mass transport and resulting bathymetry change under wave actions. The wave propagation model is based on time-dependent mild slope equations including the wave energy dissipation due to the wave-mud interaction of bottom mud layers as well as the combined effects of the wave refraction, diffraction and breaking. The constitutive equations of the visco-elastic–plastic model are adopted for the rheological behavior of fluid mud. The mass transport velocity within the fluid mud layer is calculated combining the Stokes’ drift, the mean Eulerian velocity and the gravity-driven mud flow. The results of the numerical model are compared against a series of conducted wave basin experiments, wave flume experiments and field observations. Comparisons between the computed results with both the field and laboratory data reveal the capability of the proposed model to predict the wave transformation and mud mass transport.     

An analysis of wave dissipation at the Hendijan mud coast, the Persian Gulf

Effects of non-rigid muddy bed on the wave climate at the Hendijan coast along the northwestern part of the Persian Gulf have been examined through field measurements and numerical wave transformation modeling. The field survey included measurements of wave characteristics at an offshore and a nearshore station, and mud sampling to obtain the thickness of the fluid mud layer and its rheological properties. Comparisons of wave spectra at the two stations show energy dissipation along the wave trajectory with higher dissipation in the wave period band around 6?s, because depending on the site a given frequency band tends to be more effective in wave–mud interaction. Dissipation induced by the non-rigid bed is introduced into the REF/DIF wave transformation model through the application of viscoelastic constitutive equations for fluid mud. Numerical outputs of the nearshore wave height, for which the viscoelastic parameters included in the model were obtained independently from oscillatory frequency-sweep tests, are found to be comparable with measured values at the nearshore station. This implies that the model is useful for estimating the design wave conditions in the study area.     

A comparative study on the rheology and wave dissipation of kaolinite and natural Hendijan Coast mud, the Persian Gulf

The objective of this paper is to investigate the rheological behavior of kaolinite and Hendijan mud, located at the northwest part of the Persian Gulf, and the dissipative role of this muddy bed on surface water waves. A series of laboratory rheological tests was conducted to investigate the rheological response of mud to rotary and cyclic shear rates. While a viscoplastic Bingham model can successfully be applied for continuous controlled shear-stress tests, the rheology of fluid mud displays complex viscoelastic behavior in time-periodic motion. The comparisons of the behavior of natural Hendijan mud with commercial kaolinite show rheological similarities. A large number of laboratory wave-flume experiments were carried out with a focus on the dissipative role of the fluid mud. Assuming four rheological models of viscous, Kelvin-Voigt viscoelastic, Bingham viscoplastic, and viscoelastic-plastic for fluid mud layer, a numerical multi-layered model was applied to analyze the effects of different parameters of surface wave and muddy bed on wave attenuation. The predicted results based on different rheological models generally agree with the obtained wave-flume data implying that the adopted rheological model does not play an important role in the accuracy of prediction.     

Interactions among waves,current, and mud: Numerical and laboratory studies

Interactions between waves, current, mud and turbulence are very complicated in the coastal and estuarine turbid waters. It is still necessary to improve our understanding of the fundamental physical processes governing the cohesive sediment transport in the coastal and estuarine waters. A numerical model is developed to study the interactions among waves, current, and mud. An eddy viscosity model for wave and current is proposed in order to close the equations of wave motion or of current motion in a combined flow, respectively. The equations of mud transport are derived based on the visco-elastic properties of mud. Coupling the equations of wave motion or of current motion for water layer with those of mud layer can give (1) wave height; (2) distributions of current velocities in the water layer; (3) distributions of transport velocities at the water–mud interface; and (4) distributions of mass transport velocities within the mud layer. These modeled results are in a reasonable agreement with experimental results. Results suggest that (1) the rate of wave attenuation increases in the opposing currents (currents against in the direction in which the waves propagate) and decreases in the following currents (currents in the same direction as that in which the waves propagate); (2) the opposing currents would have more significant effects on the rate of wave height attenuation than the following currents; (3) the effect of current on the rate of wave attenuation on the muddy bottom is larger than that on the rigid bottom; (4) mud transport rate increased in the following currents but decreased in the opposing currents; and (5) the rate of wave height attenuation on the mud bottom is one order of magnitude larger than that on the rigid bottom.     

Dynamic response of an offshore pile to pseudo-Stoneley waves along the interface between a poroelastic seabed and seawater

A coupled model is developed to investigate the dynamic interaction between an offshore pile, a porous seabed and seawater when subjected to the pseudo-Stoneley wave along the seabed and the seawater interface. The pile and the seabed are treated as the porous medium governed by Biot's theory, while the seawater is considered as an acoustic medium and is described by the conventional Helmholtz equation. The free field solution of the incident pseudo-Stoneley wave is obtained using Biot's theory and the potential method. Based on the boundary element method (BEM) for the porous medium and the acoustic medium, three BEM formulations are constructed for the pile, the seabed and the seawater, respectively, which are combined together using the continuity conditions between the pile, the seabed and the seawater to formulate the coupled model for the system. As shown in numerical examples, when the system is subjected to the pseudo-Stoneley wave, the maximum pore pressure of the seabed usually occurs at the region near the interfaces between the seabed and the seawater.     

EVOLUTION EQUATIONS FOR NONLINEAR WAVES IN TWO-LAYER FLUID SYSTEM OF WATER AND SOFT MUD

LINTRODUCTIONSoftmudhaVebeenfoundinmanycoasts,rivers,andeStheriesallovertheworld.ThemutUaleffectSofpropagatingwavesandsoftmudseedbedshavebeendiscussedbymostinveshgatorsbasedonlinearwavetheory.Buttheinteractionbetweenwaterwaveandsoftmudisnonlinear.OneaPProachisthePe~ationmethod,usedbyPeregrine(1967).AlternativeformofBoussunesqeqUationsisderiVedbyusingthevelocityatanarbitrarydistancefromthestillwaterlevelasthevelocityvariableinsteadofthecommonlyuseddepth-averagedvelocitybyNWogU(1993).…     

Wave-induced steady streaming,mass transport and net sediment transport in rough turbulent ocean bottom boundary layers

The interaction between two important mechanisms which causes streaming has been investigated by numerical simulations of the seabed boundary layer beneath both sinusoidal waves and Stokes second order waves, as well as horizontally uniform bottom boundary layers with asymmetric forcing. These two mechanisms are streaming caused by turbulence asymmetry in successive wave half-cycles (beneath asymmetric forcing), and streaming caused by the presence of a vertical wave velocity within the seabed boundary layer as earlier explained by Longuet-Higgins. The effect of wave asymmetry, wave length to water depth ratio, and bottom roughness have been investigated for realistic physical situations. The streaming induced sediment dynamics near the ocean bottom has been investigated; both the resulting suspended load and bedload are presented. Finally, the mass transport (wave-averaged Lagrangian velocity) has been studied for a range of wave conditions. The streaming velocities beneath sinusoidal waves (Longuet-Higgins streaming) is always in the direction of wave propagation, while the streaming velocities in horizontally uniform boundary layers with asymmetric forcing are always negative. Thus the effect of asymmetry in second order Stokes waves is either to reduce the streaming velocity in the direction of wave propagation, or, for long waves relative to the water depth, to induce a streaming velocity against the direction of wave propagation. It appears that the Longuet-Higgins streaming decreases as the wave length increases for a given water depth, and the effect of wave asymmetry can dominate, leading to a steady streaming against the wave propagation. Furthermore, the asymmetry of second order Stokes waves reduces the mass transport (wave-averaged Lagrangian velocity) as compared with sinusoidal waves. The boundary layer streaming leads to a wave-averaged transport of suspended sediments and bedload in the direction of wave propagation.     

Fluidization and representative wave transformation on muddy beds

Irregular wave-induced mud fluidization and wave spectrum transformation on muddy profiles are studied through representative wave technique. The constitutive equations of visco-elastic model are adopted for the rheological behavior of fluid mud, while the behavior of stationary mud is assumed to be elastic. A set of representative waves are employed to investigate wave–mud interaction. The results are verified using real field data. Comparing the performance of common representative waves, it is concluded that the phenomena can be better predicted by root mean square wave.     

Implementation of viscoelastic mud-induced energy attenuation in the third-generation wave model,SWAN

The interaction of waves with fluid mud can dissipate the wave energy significantly over few wavelengths. In this study, the third-generation wave model, SWAN, was advanced to include attenuation of wave energy due to interaction with a viscoelastic fluid mud layer. The performances of implemented viscoelastic models were verified against an analytical solution and viscous formulations for simple one-dimensional propagation cases. Stationary and non-stationary test cases in the Surinam coast and the Atchafalaya Shelf showed that the inclusion of the mud-wave interaction term in the third-generation wave model enhances the model performance in real applications. A high value of mud viscosity (of the order of 0.1 m²/s) was required in both field cases to remedy model overestimation at high frequency ranges of the wave spectrum. The use of frequency-dependent mud viscosity value improved the performance of model, especially in the frequency range of 0.2–0.35 Hz in the wave spectrum. In addition, the mud-wave interaction might affect the high frequency part of the spectrum, and this part of the wave spectrum is also affected by energy transfer from wind to waves, even for the fetch lengths of the order of 10 km. It is shown that exclusion of the wind input term in such cases might result in different values for parameters of mud layer when inverse modeling procedure was employed. Unlike viscous models for wave-mud interaction, the inverse modeling results to a set of mud parameters with the same performance when the viscoelastic model is used. It provides an opportunity to select realistic mud parameters which are in more agreement with in situ measurements.     

Sand–mud morphodynamics in a short tidal basin

The influence of sand and mud transport on the morphological behaviour of a short tidal basin is investigated in this paper. For this purpose, a morphological model is applied in which sand and mud transport are included and the temporal and spatial bed composition variations are taken into account. Initially, the morphological development shows a sand wave near the entrance of the basin and a mud deposition wave more landward. A quasi equilibrium bed level profile is found after a long period (order century) with a sandy bed surface over almost the entire basin and only a small muddy area near the landward end. The dimensionless ratio between the deposition and erosion flux turns out to be a crucial parameter for the understanding of the observed behaviour. Comparison with previous studies on short tidal basins for sand indicates only that the presence of mud in a combined sand mud model does not change the equilibrium bed level profile considerably for the applied parameter settings herein, but drastically decreases the morphological time scale. Comparison between model results and field data of the Wadden Sea suggests that the obtained bed level and bed composition profile are realistic, indicating that the process-based sand mud model is a first step towards a better understanding of sand mud distributions in tidal basins.Responsible Editor: Jens Kappenberg     

A study of dissipation of wind-waves by mud at Cassino Beach,Brazil: Prediction and inversion

The impact of a non-rigid seafloor on the wave climate at Cassino Beach, Brazil, May–June 2005 is studied using field measurements and a numerical wave model. The measurements consist of wave data at four locations; rheology and mud thickness from grab samples; and an estimate of the horizontal distribution of mud based on echo-soundings. The dissipation of waves by a non-rigid bottom is represented in the wave model by treating the mud layer as a viscous fluid. Applied for 431 time periods, the model without this type of dissipation has a strong tendency to overpredict nearshore wave energy, except during a period of large storm waves. Two model variations which include this dissipation have a modest tendency to underpredict the nearshore wave energy. An inversion methodology is developed and applied to infer an alternate mud distribution which, when used with the wave model, yields the observed waveheights.     

Role of basic rheological models in determination of wave attenuation over muddy seabeds

Among rheological models for estimating the rate of dissipation of non-breaking waves in muddy seabeds, those representing viscoelastic and poroelastic behaviors are used widely. In that regard, the dependence of the wave attenuation coefficient derived from basic rheological representations of mud behavior is examined on a cursory basis. For wave attenuation due to viscoelastic muds, results based on a semi-analytical model incorporating the effects of typically thin mud layers are summarized. This and an existing model for poroelastic beds are tested against selective laboratory data. Relying on these tests, it is emphasized that fluid-like mud should be modeled as a viscoelastic fluid medium, and that only non-fluid beds can be modeled as poroelastic media. Mechanisms for energy dissipation depend on bed compactness specified by the solids volume fraction, porosity or density, and on a characteristic Péclet number defined in terms of particle size, permeability and wave frequency. Due to the role of the latter parameter, for simulation of wave attenuation the chosen rheological model for a bed of given compactness must be applicable over the expected range of wave frequency.     

Erosion and accretion processes in a muddy dissipative coast,the Chao Phraya River delta,Thailand

Seasonal variation in seabed elevation in the muddy intertidal zone of the Chao Phraya River delta, an area of serious coastal erosion for 40 years, was assessed using information on waves and tides predicted by numerical simulations. The study area is under the influence of the Southeast Asian monsoon climate and lies in the innermost part of a sheltered gulf, across which a low‐gradient slope has developed. Observations, aimed at evaluating the effectiveness of a prototype breakwater on mitigating coastal erosion, indicated that the seasonal variation in the seabed elevation, typically about 30 cm, was caused primarily by seasonal changes in wave direction and height. The breakwater seems to have contributed to a net rise in the seabed level at sites behind the structure. Seabed erosion was most apparent during the northeast monsoon, when waves are weak. Erosion under this low wave energy state was attributed to the combined effect of wave breaking and the low tidal level. A difference in the observed seabed accretion rate between the transitional intermonsoon period and the succeeding southwest monsoon period was attributed to the direction of the wave energy flux; offshore sediments seem to have been supplied efficiently to the study area by waves during the transitional period. Another potential cause of seabed erosion and accretion during the wet southwest monsoon season was the discharge of water and sediments from local canals associated with intense tropical rainfall; this discharge seems to be linked to land use in the coastal area. The results of this study show the importance of monitoring across‐shore sediment transport for better understanding of coastal erosion processes. Copyright © 2010 John Wiley & Sons, Ltd.     

A field study of coastal dynamics on a muddy coast offshore of Cassino beach,Brazil

Mud deposits near sandy beaches, found throughout the world, are of scientific and societal interest as they form important natural sea defenses by efficiently damping storm waves. A multi-national field experiment to study these phenomena was performed offshore Cassino beach in southern Brazil starting in 2004. This experiment aimed to investigate the formation of an offshore mud deposit, to characterize wave attenuation over potentially mobile muddy bottoms, and to evaluate the performance of models for wave transformation over heterogeneous beds through the measurement of water waves, near-bottom currents, bathymetry, and changes in bottom sediment characteristics. The main instrumentation was a set of wave sensors deployed in a transect from the shoreline across sandy and muddy deposits offshore to a depth of 25 m. Additional sensors, including current meters and optical backscatter sensors, were concentrated at stations in the middle of the mud deposit and in the surf zone to document aspects of the wave boundary layer and lutocline dynamics. This fieldwork also involved the geological and geotechnical characterization of the mud deposit using seismic equipment, echo-sounders, cores, surficial sampling and an in-situ density meter. These sediment samples were subsequently analyzed for density, grain size distribution, mineralogy, rheology and sedimentary structures. In addition, video and radar monitoring equipment were installed to measure the long-term aspects of surf zone damping by fluid mud and any associated morphodynamic responses. This paper provides a summary of environmental conditions monitored during the experiment and describes the major findings of the various investigations. Although data collection was more difficult than anticipated and dramatic wave attenuation involving the onshore transport of fluid mud into the surf zone region was not observed during the instrumented interval, the new methodologies developed and comprehensive observations obtained during this effort are being used to improve our understanding of shoaling wave dynamics and sediment transport in the coastal zone in regions with significant cohesive sediment deposits.     

A quantitative examination of modern sedimentary lithofacies formation on the glacially influenced Gulf of Alaska continental shelf

Continental-shelf lithofacies are described from a series of cores collected in the northern Gulf of Alaska, a high-energy paraglacial shelf experiencing rapid rates of sediment accumulation. Short-lived tracers (²³⁴Th and chlorophyll-a) indicate that during the annual peak in fluvial sediment input (summer), biologic sediment mixing coefficients in the surficial seabed are generally lower than other coastal environments (<20 cm² yr⁻¹) and mixing extends downward <10 cm.²¹⁰Pb geochronology indicates that sediment accumulation rates (time scales of 10–100 yr) are 0.1–3 cm yr⁻¹. The measured bioturbation and accumulation rates lead to predictions of moderate to bioturbated lithofacies, as observed. Primary depositional fabric is preferentially preserved where sediment accumulation rates >2 cm yr⁻¹ and non-steady sediment deposition occurs. Depositional fabric is also observed in strata at 50–100 m water depths and is similar in appearance to beds that may form through deposition of wave-induced fluid-mud flows, which have been observed forming on other shelves with moderate to high wave energy. Five general lithofacies can be identified for the study area: inner-shelf sand facies, interbedded sandy mud facies, moderate-to-well-bioturbated mud facies, gravelly mud facies, and Tertiary bedrock facies. The moderate-to-well-bioturbated mud facies is areally dominant, representing over 50% of the shelf area, although roughly equal volumes (∼0.4 km³) of strata with some preservation of primary fabric are annually accumulating. Lithofacies on this paraglacial shelf generally resemble mid- and low-latitude allochthonous shelf strata to a much greater degree than Holocene glacimarine strata formed on shelves dominated by icebergs and floating ice shelves. Paraglacial strata may be differentiated from non-glacial shelf strata by lower organic carbon concentrations, a relatively lower degree of bioturbation, and increased preservation of primary depositional fabric.     

Erodibility of soft freshwater sediments in Markermeer: the role of bioturbation by meiobenthic fauna

The Markermeer is a large and shallow man-made freshwater lake in the Netherlands, characterized by its high turbidity. As part of a study aiming to mitigate this high turbidity, we studied the water–bed exchange processes of the lake’s muddy bed. The upper centimeter’s–decimeter’s of the lake bed sediments mainly consists of soft anoxic mud. Recent measurements have proved the existence of a thin oxic layer on top of this soft anoxic mud. This oxic layer, which is much easier to be eroded than the anoxic mud, is believed to be related with Markermeer’s high-turbidity levels. Our hypothesis is that the thin oxic layer develops from the anoxic mud, enhanced by bioturbation. Actually, we will demonstrate that it is the bioturbated state of the bed that increases its erodability, and not the oxidation state of the sediments. In particular, we will refer to bioturbation caused by meiobenthic fauna. The objective of this study is therefore to determine the influence of the development of the thin oxic layer on the water–bed exchange processes, as well as to establish the role of bioturbation on those processes. This is done by quantifying the erosion rate as a function of bed shear stresses, and at different stages of the development of the oxic layer. Our experiments show that bioturbation increases the rate at which Markermeer sediments are eroded by almost an order of magnitude. The short-term fine sediment dynamics in Markermeer are found to be driven by the complex and highly dynamic interactions between physics, chemistry, and biology. Finally, the long-term fine sediment dynamics are driven by the erosion of the historical deposits in the lake’s bed, which is only possible after bioturbation, and which leads to an increase of the stock of sediments in the lake’s muddy bed.     

Mass transport in a thin layer of power-law mud under surface waves

The mass transport velocity in a two-layer system is studied theoretically. The wave motion is driven by a periodic pressure load on the free water surface, and mud in the lower layer is described by a power-law rheological model. Perturbation analysis is performed to the second order to find the mean Eulerian velocity. A numerical iteration method is employed to solve the non-linear governing equation at the leading order. The influence of rheological properties on fluid motion characteristics including the flow field, the surface displacement, the mass transport velocity, and the net discharge rates are investigated based on theoretical results. Theoretical analysis shows that under the action of interfacial shearing, a recirculation structure may appear near the interface in the upper water layer. A higher mass transport velocity at the interface does not necessarily mean a higher discharge rate for a pseudo-plastic fluid mud.     

Geochemical characteristics of deposits from the 2011 Tohoku‐oki tsunami at Hasunuma,Kujukuri coastal plain,Japan

We examined the geochemical characteristics and temporal changes of deposits associated with the 2011 Tohoku‐oki tsunami. Stable carbon isotope ratios, biomarkers, and water‐leachable ions were measured in a sandy tsunami deposit and associated soils sampled at Hasunuma, Kujukuri coastal plain, Japan, in 2011 and 2014. At this site, the 2011 tsunami formed a 10–30 cm ‐thick layer of very fine to medium sand. The tsunami deposit was organic‐poor, and no samples contained any detectable biomarkers of either terrigenous or marine origin. In the underlying soil, we identified hydrocarbons and sterols derived from terrestrial plants, but detected no biomarkers of marine origin. In the samples collected in 2011, concentrations of tsunami‐derived water‐leachable ions were highest in the soil immediately beneath the tsunami deposit and then decreased gradually with depth. Because of its finer texture and higher organic content, the soil has a higher water‐holding capacity than the sandy tsunami deposit. This distribution suggests that ions derived from the tsunami quickly penetrated the sand layer and became concentrated in the underlying soil. In the samples collected in 2014, concentrations of water‐leachable ions were very low in both soil and sand. We attribute the decrease in ion concentrations to post‐tsunami rainfall, seepage, and seasonal changes in groundwater level. Although water‐leachable ions derived from seawater were concentrated in the soil beneath the tsunami deposit following the tsunami inundation, they were not retained for more than a few years. To elucidate the behavior of geochemical characteristics associated with tsunamis, further research on organic‐rich muddy deposits (muddy tsunami deposits and soils beneath sandy tsunami deposits) as well as sandy tsunami deposits is required.     

A study of the crustal structure beneath the Himalayas from body waves

Summary The crustal structure beneath the Himalayas has been investigated using body wave data from near earthquakes having epicentres over the Himalayas and recorded by the observatories situated over, or very near, the foothills of the mountains. A three-layered crustal model, without the top sedimentary layer, with velocities for theP wave group in Granite I, Granite II and the Basaltic layer as 5.48, 6.00 and 6.45 and for theS wave group as 3.33, 3.56 and 3.90 km/sec respectively, has been interpreted. The upper mantle velocity for theP wave has been observed to be 8.07 km/sec and for theS wave as 4.57 km/sec. Average thickness for the Granite I layer has been computed as 22.7 km, for the Granite II layer as 16.3 km and for the Basaltic layer as 18.7 km. Crustal and sub-crustal velocities indicate a lower trend under the mountain. A thicker crust has been obtained beneath the Himalayas.