Non-linear dispersive waves with a small dissipation

The general theory of Whitham for slowly-varying non-linear wavetrains is extended to the case where some of the defining partial differential equations cannot be put into conservation form. Typical examples are considered in plasma dynamics and water waves in which the lack of a conservation form is due to dissipation; an additional non-conservative element, the presence of an external force, is treated for the plasma dynamics example. Certain numerical solutions of the water waves problem (the Korteweg-de Vries equation with dissipation) are considered and compared with perturbation expansions about the linearized solution; it is found that the first correction term in the perturbation expansion is an excellent qualitative indicator of the deviation of the dissipative decay rate from linearity.

A method for deriving necessary and sufficient conditions for the existence of a general uniform wavetrain solution is presented and illustrated in the plasma dynamics problem. Peaking of the plasma wave is demonstrated, and it is shown that the necessary and sufficient existence conditions are essentially equivalent to the statement that no wave may have an amplitude larger than the peaked wave.

A new type of fully non-linear stability criterion is developed for the plasma uniform wavetrain. It is shown explicitly that this wavetrain is stable in the near-linear limit. The nature of this new type of stability is discussed.

Steady shock solutions are also considered. By a quite general method, it is demonstrated that the plasma equations studied here have no steady shock solutions whatsoever. A special type of steady shock is proposed, in which a uniform wavetrain joins across a jump discontinuity to a constant state. Such shocks may indeed exist for the Korteweg-de Vries equation, but are barred from the plasma problem because entropy would decrease across the shock front.

Finally, a way of including the Landau damping mechanism in the plasma equations is given. It involves putting in a dissipation term of convolution integral form, and parallels a similar approach of Whitham in water wave theory. An important application of this would be towards resolving long-standing difficulties about the "collisionless" shock.

The choice of a suitable sampler for benthic macroinvertebrates in deep rivers

Both chemical and biological methods are used to assess the water quality of rivers. Many standard physical and chemical methods are now established, but biological procedures of comparable accuracy and versatility are still lacking. This is unfortunate because the biological assessment of water quality has several advantages over physical and chemical analyses. Several groups of organisms have been used to assess water quality in rivers and these include Bacteria, Protozoa, Algae, macrophytes, macroinvertebrates and fish. Hellawell (1978) provides an excellent review of the advantages and disadvantages of these groups, and concludes that macroinvertebrates are the most useful for monitoring water quality. Although macroinvertebrates are relatively easy to sample in shallow water (depth < 1m), quantitative sampling poses more problems than qualitative sampling because a large number of replicate sampling units are usually required for accurate estimates of numbers or biomass per unit area. Both qualitative and quantitative sampling are difficult in deep water (depth > 1m). The present paper first considers different types of samplers with emphasis on immediate samplers, and then discusses some problems in choosing a suitable sampler for benthic macroinvertebrates in deep rivers.

Topic 1. Some steric-height features of the water off the Pacific coast of Canada; Topic 2. Possible warming of the water at station P in the northeast Pacific during 1956-1984 [abstract]

TOPIC 1: In terms of seasonal scale, temperature effect dominates the annual change of steric height in the open ocean whereas salinity effect controls it along the continental shelf. Large portion of the annual change of height relative to the 1000-db surface is contained in the upper 100m layer. However, in interannual scale large anomalies of steric height in the open ocean, are more often than not, caused by halosteric rather than thermosteric effect. At least in the open ocean the heights are almost totally determined by the behavior of deep water. Their interannual variability appears to be related to the cumulative effect of Eckman pumping. TOPIC 2: There is a "trend" that over the past 28 years the water at Station P has warmed. Least-square analysis indicates that this warming may be significant but shortening of the time-series data by approximately 10 years fails to show that this is the case. These "trends" have to be interpreted with care. The warming may be "apparent" in that it is not indicated clearly in the deep isopynal surfaces which, during the above period, have deepened. Thus warming at the isobaric surfaces may be the effect of the downward migration of the isopynal surfaces.

Resiliencia en crestas de arrecifes coralinos del este del golfo de Batabanó, Cuba, y factores determinantes probables

RESUMEN Se comparó el grado de resiliencia de seis crestas arrecifales del este del golfo de Batabanó, Cuba. Tres fueron del norte del golfo de Cazones (Tramo Norte) y las restantes, del oeste de Cayo Largo (Tramo Sur). Las del primer tramo fueron las de faro Cazones, Norte de la cresta de cayo Diego Pérez y de faro Diego Pérez. Las otras tres fueron las de cayo Rico, arrecifes Los Ballenatos y arrecifes Hijos de Los Ballenatos. Se emplearon los indicadores biológicos del Protocolo AGRRA. El Tramo Norte presentó las crestas más resilientes, sobre todo la de faro Cazones. Las del Tramo Sur no exhibieron resiliencia. Fueron varios e interrelacionados, los factores aparentemente más determinantes en la resiliencia. Entre estos, cuatro se consideraron como fuerzas motrices: resguardo contra el oleaje, circulación habitual giratoria ciclónica en la ensenada de Cazones, entrada de nutrientes provenientes tanto de la ciénaga de Zapata como de aguas profundas, y abundancia del erizo herbívoro Diadema antillarum. Los demás factores, desencadenados por los anteriores y también interrelacionados, fueron, al parecer la menor afectación por oleaje y sedimentos, estabilización de fragmentos vivos de coral, índices favorables de macroalgas bentónicas, cierta retención de nutrientes y plancton, más alimentación heterotrófica de los corales, mayor auto reclutamiento de corales y del erizo Diadema; mejores condiciones para el asentamiento y viabilidad de los reclutas, y para el recapamiento de corales; mayor crecimiento y recuperación de los corales y mejores condiciones térmicas contra el blanqueamiento de corales ABSTRACT The degree of resilience of six reef crest sites was compared at the east of the Gulf of Batabano, Cuba. Three of them were located north of the Gulf of Cazones (Northern Stretch), while the remaining ones were west of Cayo Largo (Southern Stretch). Those of the Northern Stretch were “Faro Cazones”, north of the crest of cayo Diego Pérez and “Faro Diego Pérez”. The remaining sites were those of the cayo Rico, Los Ballenatos reefs, and Hijos de Los Ballenatos reefs. The AGRRA biological indicators were applied. The Northern Stretch presented the most resilient crests, mainly that of “Faro Cazones”. Those of the Southern Stretch did not reveal signs of resilience. Several interrelated factors were apparently more linked to resilience. Four of them were considered as driving forces: shelter from waves, usual cyclonic revolving water circulation in the Ensenada de Cazones, nutrient input from the Zapata swamp and deep water, and the abundance of the herbivore sea urchin Diadema antillarum. Triggered by these driving forces, the remaining factors apparently were less effect of waves and sediments, stabilization of live coral fragments, favorable benthic macro-algae indices, some retention of nutrient and plankton, increased coral heterotrophic feeding; better conditions for recruit settlement and viability, and for coral re-sheeting; faster coral growth and recuperation and better thermal conditions against coral bleaching.

Simplifying mooring analysis for deepwater systems using truncation

Over recent years academia and industry have engaged with the challenge of model testing deepwater structures at conventional scales. One approach to the limited depth problem has been to truncate the lines. This concept will be introduced, highlighting the need to better understand line dynamic processes. The type of line truncation developed here models the upper sections of each line in detail, capturing wave action and all coupling effects with the vessel, terminating to an approximate analytical model that aims to simulate the remainder of the line. A rationale for this is that in deep water transverse elastic waves of a line are likely to decay before they are reflected at the seabed because of nonlinear hydrodynamic drag forces. The first part of this paper is centered on verification of this rationale. A simplified model of a mooring line that describes the transverse dynamics in wave frequency is used, adopting the equation of motion of an inextensible taut string. The line is submerged in still water, one end fixed at the bottom the other assumed to follow the vessel response, which can be harmonic or random. A dimensional analysis, supported by exact benchmark numerical solutions, has shown that it is possible to produce a universal curve for the decay of transverse vibrations along the line, which is suitable for any kind of line with any top motion. This has a significant engineering benefit, allowing for a rapid assessment of line dynamics - it can be useful in deciding whether a truncated line model is appropriate, and if so, at which point truncation might be applied. This is followed by developing a truncation mechanism, formulating an end approximation that can reproduce the correct impedance, had the line been continuous to full depth. It has been found that below a certain length criterion, which is also universal, the transverse vibrational characteristics for each line are inertia driven. As such the truncated model can assume a linear damper whose coefficient depends on the line properties and frequency of vibration. Copyright © 2011 by the International Society of Offshore and Polar Engineers (ISOPE).

Faecal pellets in deep marine soft clay crusts: Implications for hot-oil pipeline design

In recent years, the presence of crusts within near surface sediments found in deep water locations off the west coast of Angola has been of interest to hot-oil pipeline designers. The origin for these crusts is considered to be of biological origin, based on the observation of thousands of faecal pellets in natural crust core samples. This paper presents the results of laboratory tests undertaken on natural and faecal pellet-only samples. These tests investigate the role faecal pellets play in modifying the gemechanical behaviour of clayey sediments. It is found that faecal pellets are able to significantly alter both the strength and the average grain-size of natural sediments, and therefore, influence the permeability and stiffness. Hot-oil pipelines self-embed into and subsequent shear on crusts containing faecal pellets. Being able to predict the time required for installed pipelines to consolidate the underlying sediment and thus, how soon after pipe-laying, the interface strength will develop is of great interest to pipeline designers. It is concluded from wet-sieving samples before and after oedometer tests, that the process of pipe laying is unlikely to destroy pellets. They will therefore, be a major constituent of the sediment subject to soil-pipeline shearing behaviour during axial pipe-walking and lateral buckling. Based on the presented results, a discussion highlighting the key implications for pipeline design is therefore provided. Copyright © 2011 by ASME.

Decay of vibrations along deepwater mooring lines

Model tests for global design verification of deepwater floating structures cannot be made at reasonable scales. An overview of recent research efforts to tackle this challenge is given first, introducing the concept of line truncation techniques. In such a method the upper sections of each line are modelled in detail, capturing the wave action zone and all coupling effects with the vessel. These terminate to an approximate analytical model, that aims to simulate the remainder of the line. The rationale for this is that in deep water the transverse elastic waves of a line are likely to decay before they are reflected at the seabed. The focus of this paper is the verification of this rationale and the ongoing work, which is considering ways to produce a truncation model. Transverse dynamics of a mooring line are modelled using the equations of motion of an inextensible taut string, submerged in still water, one end fixed at the bottom the other assumed to follow the vessel response, which can be harmonic or random. Nonlinear hydrodynamic damping is included; bending and VIV effects are neglected. A dimensional analysis, supported by exact benchmark numerical solutions, has shown that it is possible to produce a universal curve for the decay of transverse vibrations along the line, which is suitable for any kind of line with any top motion. This has a significant engineering benefit, allowing for a rapid assessment of line dynamics - it is very useful in deciding whether a truncated line model is appropriate, and if so, at which point truncation might be applied. Initial efforts in developing a truncated model show that a linearized numerical solution in the frequency domain matches very closely the exact benchmark. Copyright © 2011 by ASME.

Turbulent flow structure in experimental laboratory wind-generated gravity waves

This paper is the third part of a report on systematic measurements and analyses of wind-generated water waves in a laboratory environment. The results of the measurements of the turbulent flow on the water side are presented here, the details of which include the turbulence structure, the correlation functions, and the length and velocity scales. It shows that the mean turbulent velocity profiles are logarithmic, and the flows are hydraulically rough. The friction velocity in the water boundary layer is an order of magnitude smaller than that in the wind boundary layer. The level of turbulence is enhanced immediately beneath the water surface due to micro-breaking, which reflects that the Reynolds shear stress is of the order u *w 2. The vertical velocities of the turbulence are related to the relevant velocity scale at the still-water level. The autocorrelation function in the vertical direction shows features of typical anisotropic turbulence comprising a large range of wavelengths. The ratio between the microscale and macroscale can be expressed as λ/Λ=a Re Λ n, with the exponent n slightly different from -1/2, which is the value when turbulence production and dissipation are in balance. On the basis of the wavelength and turbulent velocity, the free-surface flows in the present experiments fall into the wavy free-surface flow regime. The integral turbulent scale on the water side alone underestimates the degree of disturbance at the free surface. © 2012 Elsevier B.V.

Short and long waves over a muddy seabed

The available experimental results have shown that in time-periodic motion the rheology of fluid mud displays complex viscoelastic behaviour. Based on the measured rheology of fluid mud from two field sites, we study the interaction of water waves and fluid mud by a two-layered model in which the water above is assumed to be inviscid and the mud below is viscoelastic. As the fluid-mud layer in shallow seas is usually much thinner than the water layer above, the sharp contrast of scales enables an approximate analytical theory for the interaction between fluid mud and small-amplitude waves with a narrow frequency band. It is shown that at the leading order and within a short distance of a few wavelengths, wave pressure from above forces mud motion below. Over a Much longer distance, waves are modified by the accumulative dissipation in mud. At the next order, infragravity waves owing to convective inertia (or radiation stresses) are affected indirectly by mud motion through the slow modulation of the short waves. Quantitative predictions are made for mud samples of several concentrations and from two different field sites.

Benthic foraminifera and bottom water evolution in the middle-southern Okinawa Trough during the last 18 ka

A piston sediment core E017 from the middle-southern Okinawa Trough was investigated. A preliminary study of the deep-water evolution since 18 cal. ka BP was performed based on the quantitative census data of benthic foraminiferal fauna, together with planktonic foraminiferal oxygen and carbon isotope, AMS(14)C dating, and the previous results achieved in the southern Okinawa Trough. The result shows that the benthic fauna was dominated by Bulimina aculeata (d'Orbigny), Uvigerina peregrina (Cushman), Hispid Uvigerina and Uvigerina dirupta (Todd) during the glaciation-deglaciation before 9.2 cal. ka BP, while Epistominella exigua (Brady), Pullenia bulloides (d'Orbigny), Cibicidoides hyalina (Hofker), Sphaeroidina bulloides (d'Orbigny) and Globocassidulina subglobosa (Brady) predominated the fauna in the post-glacial period after 9.2 cal. ka BP. The benthic foraminifera accumulation rate (BFAR), paleoproductivity estimates and benthic foraminiferal assemblage conformably indicate that surface water paleoproductivity and organic matter flux during the glaciation-deglaciation were higher than those of the post-glacial period in the middle-southern Okinawa Trough, and gradually enhanced from the southern to the central Okinawa Trough during the glaciation-deglaciation, which could be caused by the discrepancy of the terrigenous nutrients supply. High abundances of E exigua, an indicator of pulsed organic matter input, after 9.2 cal. ka. BP may indicate that the intensity of seasonally riverine pulsed flux during the post-glacial period was stronger than that of the glaciation-deglaciation period, and the seasonal influx in the central trough might be stronger than in the south. The temporal distributions of the typical species indicating bottom water oxygen content and ventilation condition show that the ventilation of the bottom water during the post-glacial period is more active than the glaciation-deglaciation, which reflects that the evolution of the intermediate and deep waters of the northwestern Pacific during the last glaciation has no evident influence on the deep-water of the middle-southern Okinawa Trough. Additionally, the variations in agglutinated benthic foraminiferal abundance and other carbonate dissolution proxies indicate that carbonate dissolution gradually increased since the last 18 ka in the Okinawa Trough and rapidly enhanced at 9.2 cal. ka BP. The modern shallow carbonate lysocline could form at 3 cal. ka BP.

Benthic foraminiferal distribution in surface sediments along continental slope of the southern Okinawa Trough: dependance on water masses and food supply

Benthic foraminiferal analysis of 29 samples in surface sediments from the southern Okinawa Trough is carried out. The results indicate that benthic foraminiferal abundance decreases rapidly with increasing water depth. Percentage frequencies of agglutinated foraminifera further confirm the modem shallow carbonate lysocline in the southern Okinawa Trough. From continental shelf edge to the bottom of Okinawa Trough, benthic foraminiferal fauna in the surface sediments can be divided into 5 assemblages: (1) Continental shelf break assemblage, dominated by Cibicides pseudoungerianus, corresponds to subsurface water mass of the Kuroshio Current; (2) upper continental slope assemblage, dominated by Cassidulina carinata, Globocassidulina subglobosa, corresponds to intermediate water mass of the Kuroshio Current; (3) intermediate continental slope assemblage, dominated by Uvigerina hispida, corresponds to the Okinawa Trough deep water mass above the carbonate lysocline; (4), lower continental slope - trough bottom assemblage, dominated by Pullenia bulloides, Epistominella exigua and Cibicidoides hyalinus, corresponds to deep water mass of the Okinawa Trough; and (5) trough bottom agglutinated assemblage, dominated by Rhabdammina spp., Bathysiphon flavidus, corresponds to I strongly dissolved environment of the trough bottom. The benthic foraminiferal fauna in the southern Okinawa Trough are controlled jointly by water masses and food supply. Water temperature, oxygen concentration and carbonate dissolution of the water masses are important controlling factors especially for the continental shelf break and trough bottom assemblages. The food supply also plays an important role in these benthic foraminiferal assemblages along the western slope. of the Okinawa Trough. Both the abundance and the 5 assemblages of benthic foraminifera correspond well to the organic matter supply along the continental slope and a lateral transport of TSM (total suspended matter) and POC (particulate organic carbon) from the shelf break to the deep water is also an important food supply for benthic fauna in this region.

Strongly nonlinear long interfacial waves in uniform basic flows and their dispersion relationship

In this paper, long interfacial waves of finite amplitude in uniform basic flows are considered with the assumption that the aspect ratio between wavelength and water depth is small. A new model is derived using the velocities at arbitrary distances from the still water level as the velocity variables instead of the commonly used depth-averaged velocities. This significantly improves the dispersion properties and makes them applicable to a wider range of water depths. Since its derivation requires no assumption on wave amplitude, the model thus can be used to describe waves with arbitrary amplitude.

Numerical modeling of water wave interaction with a soft mud bed

A vertical 2-D numerical model is presented for simulating the interaction between water waves and a soft mud bed. Taking into account nonlinear rheology, a semi-empirical rheological model is applied to this water-mud model, reflecting the combined visco-elasto-plastic properties of soft mud under such oscillatory external forces as water waves. In order to increase the resolution of the flow in the neighborhood of both sides of the inter-surface, a logarithmic grid in the vertical direction is employed for numerical treatment. Model verifications are given through comparisons between the calculated and the measured mud mass transport velocities as well as wave height changes.

The nonlinear evolution equation on the shallow water wave

Based on the variation principle, the nonlinear evolution model for the shallow water waves is established. The research shows the Duffing equation can be introduced to the evolution model of water wave with time.

Numerical Simulation of Waves Generated by Seafloor Movements

Waves generated by vertical seafloor movements are simulated by use of a fully nonlinear two-dimensional numerical wave tank. In the source region, the seafloor lifts to a designated height by a generation function. The numerical tests show that file linear theory is only valid for estimating the wave behaviors induced by the seafloor movements with a small amplitude, and the fully nonlinear numerical model should be adopted in the simulation of the wave generation by the large amplitude seafloor movements. Without the background surface waves, many numerical tests on the stable maximum elevations eta(max)(0) are carried out by both the linear theory and the fully nonlinear model. The results of two models are compared and analyzed. For the fully nonlinear model, the influences of the amplitudes and the horizontal lengths on eta(max)(0) are stronger than that of the characteristic duration times. Furthermore, results reveal that there are significant differences between the linear theory and the fully nonlinear model. When the influences of the background surface waves are considered, the corresponding numerical analyses reveal that with the fully nonlinear model the eta(max)(0) near-linearly varies with the wave amplitudes of the surface waves, and the eta(max)(0) has significant dependences on the wave lengths and the wave phases of the surface waves. In addition, the differences between the linear theory and the fully nonlinear model are still obvious, aid these differences are significantly affected by The wave parameters of the background surface waves, such as the wave amplitude, the wave length and the wave phase.