On the response of a Coulomb‐damped poroelastic bed to water waves

Abstract

The problem of forced vibration of a slightly inelastic porous bed by water waves is treated analytically on the basis of a linearized expression of the nonlinear damping term for the grain‐to‐grain friction in bed soils and the linear theory by Biot (1962a [Jour. Appl. Physics, 33:1482–1498]) on the elastic wave propagation in porous media. A dispersion relation of water waves is obtained as a function of wave frequency, water depth, permeability, Poisson's ratio, rigidity, and specific loss of bed soil. Three types of elastic waves are induced in a bed by water waves: a shear wave and a compressional wave in the skeletal frame of soil, and a compressional wave in the pore fluid. The compressional wave, due to the motion of the pore fluid relative to the skeletal frame of soil, is highly damped by the viscosity of pore fluid and only a short range effect near the boundaries of discontinuity, such as a sea‐seabed interface. The seabed response to water waves is characterized by the two Mach numbers, i.e., the ratio of water‐wave speed to shear‐wave speed in soil and the ratio of water‐wave speed to compressional‐wave speed in soil. Most of the water‐wave propagation problems fall into the subsonic flow condition, where elastic waves in the bed travel faster than water waves.

For sandy beds, generally the speeds of compressional and shear waves are much higher than the phase velocity of the water wave. For this case, the solution of the Coulomb‐damped poroelastic bed response presented in this paper approaches the solution of the massless poroelastic bed response in Yamamoto et al. (1978 [Jour. Fluid Mech., 87(1): 193–206]). The damping of water waves due to internal grain‐to‐grain friction is equally or more significant than the damping due to percolation in sand beds.

For clay beds, the speed of the shear wave in soil becomes low and comparable to the phase speed of the water wave. The bed motion for this case is considerably amplified due to the near‐resonance vibration of shear mode of bed vibration. The water wavelength on a clay bed is significantly shortened compared to the water wavelength over a rigid bed. The water wave damping due to internal grain‐to‐grain friction in soil becomes much larger compared to the water wave damping due to percolation in clay beds. Long water waves over a soft clayey bed attenuate within several wavelengths of travel distance.     

Dynamics of elastically moored floating objects

The two-dimensional problem of wave transformation by, and motions of, moored floating objects is solved numerically as a boundary value problem by direct use of Green's identity formula for a potential function. The cross-sectional shape of the floating object, the bottom configuration and the mooring arrangements may be all arbitrary. For a given incident wave, the three modes of body motion, the wave system and mooring forces are all solved at the same time. A laboratory experiment is conducted to verify the theory. Generally good agreements between the theory and experiments are obtained as long as the viscous damping due to flow separation is small. A numerical experiment indicates that a conventional sluck mooring is to worsen the wave attenuation by a floating breakwater and that a properly arranged elastic mooring can considerably improve the wave attenuation by a floating breakwater.     

Helium and carbon isotopes in fluorites: implications for mantle carbon contribution in an ancient subduction zone

The concentrations of helium and carbon in fluorite associated with Cretaceous to Neogene (90–13 Ma) granitic magmatism in the Japanese arc have been measured. Concentrations of Li, U, Th and Gd were measured to correct for secondary generated ³He. The CO₂/³He of fluorites are almost uniform (1.5×10¹⁰–4×10¹⁰) and in fair agreement with the range of present island arc volcanic gases. The calculated mantle C contribution in the Mesozoic subduction zone appear to have been identical to the present one (7–19%) indicating that the C flux from the mantle in supra-subduction zone environments has remained fairly constant during the past 70 million years.     

An analytical and experimental investigation of the effect of impact on coarse granular rocks

SummaryAn Analytical and Experimental Investigation of the Effect of Impact on Coarse Granular Rocks The interaction between metallic strikers and coarse, granular rock, associated with many mechanical rock breaking methods was investigated by theoretical and experimental methods. Cylindrical steel strikers of 12.7 mm diameter with flat, conical and hemispherical tips and masses of about 18.5 g were fired by means of a gas gun at blocks of diorite and spessartite with initial energies ranging from 4 to 34 J, generating substantial fracturing. The damage pattern in the rocks was ascertained, partly with the aid of a scanning electron microscope. A synthetic model consisting of long square bars of cement paste bonded with an adhesive was constructed as a simulator of diorite and tested to further delineate the failure mechanisms in this material.As previously, it was also found here that the geometry of the striker tip significantly affects the damage pattern and extent in diorite. A crucial difference in this pattern was observed between that found in diorite, a coarsegrained rock, and in spessartite, a more finely-grained substance. The crack network in diorite consisted of numerous kinked fractures extending a distance not in excess of 20 grain lengths, whereas only 5 to 7 nearly straight cracks with a length in excess of 20 times the grain size were found in spessartite that appeared to have propagated without regard to the grain packing structure or material defects. The synthetic rock model successfully reproduced the crack pattern found in diorite under impact.An analytical model to predict the region of grain and grain boundary failure incorporating one failure criterion for grains and another for grain boundaries was constructed. The first involved the development of failure surfaces based on an empirical limiting strength analogous to the modified Griffith criterion. Grain boundary failure was stipulated upon attainment of a combination of critical tensile and Coulomb type of shear stress. The model successfully delineated the major features of damage in the synthetic rock and in diorite and established upper bound predictions for the extent of damage.With 19 Figures     

Magnetotail response during a strong substorm as observed by GEOTAIL in the distant tail

Simultaneous energetic particle and magnetic field observations from the GEOTAIL spacecraft in the distant tail (X_GSM -150 Re) have been analysed to study the response of the Earths magnetotail during a strong substorm (AE 680 nT). At geosynchronous altitude, LANL spacecraft recorded three electron injections between 0030 UT and 0130 UT, which correspond to onsets observed on the ground at Kiruna Ground Observatory. The Earths magnetotail responded to this substorm with the ejection of five plasmoids, whose size decreases from one plasmoid to the next. Since the type of magnetic structure detected by a spacecraft residing the lobes, depends on the Z extent of the structure passing underneath the spacecraft, GEOTAIL is first engulfed by a plasmoid structure; six minutes later it detects a boundary layer plasmoid (BLP) and finally at the recovery phase of the substorm GEOTAIL observes three travelling compression regions (TCRs). The time-of-flight (TOF) speed of these magnetic structures was estimated to range between 510 km/s and 620 km/s. The length of these individual plasmoids was calculated to be between 28 Re and 56 Re. The principal axis analysis performed on the magnetic field during the TCR encountered, has confirmed that GEOTAIL observed a 2-D perturbation in the X-Z plane due to the passage of a plasmoid underneath. The first large plasmoid that engulfed GEOTAIL was much more complicated in nature probably due to the external, variable draped field lines associated with high beta plasma sheet and the PSBL flux tubes surrounding the plasmoid. From the analysis of the energetic particle angular distribution, evidence was found that ions were accelerated from the distant X-line at the onset of the burst associated with the first magnetic structure.     

Boltzmann approach to the large-angle cosmic X-ray background fluctuations

Large-angle fluctuations in the cosmic X-ray background are investigated by a new formalism with a simple model of the X-ray sources. Our method is formulated from the Boltzmann equation and a simple extension of the work by Lahav et al. to be applicable to a hyperbolic (open) universe. The low multipole fluctuations due to the source clustering are analysed in various cosmological models in both numerical and analytic ways. The fluctuations strongly depend on the X-ray source evolution model, as pointed out previously. It turns out that the nearby ( z  ≲ 0.1) sources are the dominant contributors to the large-angle fluctuations. If these nearby sources are removed in an observed X-ray map, the dipole (low multipole) moment of the fluctuation drastically decreases. In this case the Compton–Getting effect of an observer's motion can be a dominant contribution to the dipole fluctuation. This feature of fluctuation, relating to the matter power spectrum, is discussed.     

Prediction method of sand-movement direction in rivers by geochemical elements

 The analysis of sand samples by X-ray fluorescent spectroscopy (XRF) gives the ratio of the geochemical elements to construct the sand samples. The application of the ratio matching to sand samples represents the correlation number between two sand samples with respect to geochemical elements. When the correlation number between two sand samples is low, the two samples are not geochemically similar each other. This denotes that the exchange of sand between two sampling points is scarce or the two samples are independent. When the correlation number between two sand samples is high, the two samples are geochemically similar, signifying that the exchange of sand between two sampling points is frequent or there is sand movement between two sampling points. If there exists prominent sand movement in the study area, the correlation number is almost 1 and kilo count number per second of each geochemical element per weight decreases along the flow direction. The decrease is caused by the reduction of sizes and the adherence of dirt on the surface of sand particles. Since the flow direction in rivers is usually the same as the direction of sand movement, it can be verified. This study obtains satisfactory results applying the method of prediction in sand movement to sediments in rivers. Received: 17 May 1995 · Accepted: 14 August 1995     

Evaluation of tidal error in altimetry data in the Asian marginal seas

The magnitude and geographical distribution of the error in the Archiving, Validation and Interpretation of Satellite Oceanographic data (AVISO) altimetry data associated with tidal correction around Asian marginal seas has been revealed. The errors were evaluated by harmonic analysis of the AVISO corrected sea surface heights data (CorSSH). Errors of more than 15 cm of tidal correction were recognized in the western and northern parts of the Yellow Sea, Celebes Sea, Kuril Islands, and the northwestern part of the Okhotsk Sea. It was found that the CorSSH and sea level anomaly (SLA) data downloaded from the AVISO are not available for direct use in those marginal seas. To reduce the tidal correction error, the harmonic constants calculated from the latest tide model and regional tide model were applied as the tidal correction of the Altimetry data. The tidal errors in the Yellow Sea and the northwestern part of the Okhotsk Sea were reduced by approximately 20 cm and 10 cm, respectively. Root mean square differences between the harmonic constants derived from tide models and those derived from altimetry data were calculated. The root mean square differences were large in the Yellow and the Okhotsk Seas. Root sum squares for four principal tidal constituents in the Yellow and East China Seas and Okhotsk Sea were 7.72 cm and 8.36 cm, respectively.     

Development of a Neural Network Algorithm for Retrieving Concentrations of Chlorophyll, Suspended Matter and Yellow Substance from Radiance Data of the Ocean Color and Temperature Scanner

An algorithm is presented to retrieve the concentrations of chlorophyll a, suspended pariclulate matter and yellow substance from normalized water-leaving radiances of the Ocean Color and Temperature Sensor (OCTS) of the Advanced Earth Observing Satellite (ADEOS). It is based on a neural network (NN) algorithm, which is used for the rapid inversion of a radiative transfer procedure with the goal of retrieving not only the concentrations of chlorophyll a but also the two other components that determine the water-leaving radiance spectrum. The NN algorithm was tested using the NASA's SeaBAM (SeaWiFS Bio-Optical Mini-Workshop) test data set and applied to ADEOS/OCTS data of the Northwest Pacific in the region off Sanriku, Japan. The root-mean-square error between chlorophyll a concentrations derived from the SeaBAM reflectance data and the chlorophyll a measurements is 0.62. The retrieved chlorophyll a concentrations of the OCTS data were compared with the corresponding distribution obtained by the standard OCTS algorithm. The concentrations and distribution patterns from both algorithms match for open ocean areas. Since there are no standard OCTS products available for yellow substance and suspended matter and no in situ measurements available for validation, the result of the retrieval by the NN for these two variables could only be assessed by a general knowledge of their concentrations and distribution patterns. This revised version was published online in July 2006 with corrections to the Cover Date.