A Modified Form of Mild-Slope Equation with Weakly Nonlinear Effect

Nonlinear effect is of importance to waves propagating from deep water to shallow water.Thenon-linearity of waves is widely discussed due to its high precision in application.But there are still someproblems in dealing with the nonlinear waves in practice.In this paper,a modified form of mild-slope equa-tion with weakly nonlinear effect is derived by use of the nonlinear dispersion relation and the steady mild-slope equation containing energy dissipation.The modified form of mild-slope equation is convenient to solvenonlinear effect of waves.The model is tested against the laboratory measurement for the case of a submergedelliptical shoal on a slope beach given by Berkhoff et al,The present numerical results are also comparedwith those obtained through linear wave theory.Better agreement is obtained as the modified mild-slope e-quation is employed.And the modified mild-slope equation can reasonably simulate the weakly nonlinear ef-fect of wave propagation from deep water to coast.     

Experimental impact cratering: A summary of the major results of the MEMIN research unit

This paper reviews major findings of the Multidisciplinary Experimental and Modeling Impact Crater Research Network (MEMIN). MEMIN is a consortium, funded from 2009 till 2017 by the German Research Foundation, and is aimed at investigating impact cratering processes by experimental and modeling approaches. The vision of this network has been to comprehensively quantify impact processes by conducting a strictly controlled experimental campaign at the laboratory scale, together with a multidisciplinary analytical approach. Central to MEMIN has been the use of powerful two-stage light-gas accelerators capable of producing impact craters in the decimeter size range in solid rocks that allowed detailed spatial analyses of petrophysical, structural, and geochemical changes in target rocks and ejecta. In addition, explosive setups, membrane-driven diamond anvil cells, as well as laser irradiation and split Hopkinson pressure bar technologies have been used to study the response of minerals and rocks to shock and dynamic loading as well as high-temperature conditions. We used Seeberger sandstone, Taunus quartzite, Carrara marble, and Weibern tuff as major target rock types. In concert with the experiments we conducted mesoscale numerical simulations of shock wave propagation in heterogeneous rocks resolving the complex response of grains and pores to compressive, shear, and tensile loading and macroscale modeling of crater formation and fracturing. Major results comprise (1) projectile–target interaction, (2) various aspects of shock metamorphism with special focus on low shock pressures and effects of target porosity and water saturation, (3) crater morphologies and cratering efficiencies in various nonporous and porous lithologies, (4) in situ target damage, (5) ejecta dynamics, and (6) geophysical survey of experimental craters.     

Thermal regime of the northwest Indian rifted margin – Comparison with predictions

We use a simple approach to estimate the present-day thermal regime along the northwestern part of the Western Indian Passive Margin, offshore Pakistan. A compilation of bottom borehole temperatures and geothermal gradients derived from new observations of bottom-simulating reflections (BSRs) allows us to constrain the relationship between the thermal regime and the known tectonic and sedimentary framework along this margin. Effects of basin and crustal structure on the estimation of thermal gradients and heat flow are discussed. A hydrate system is located within the sedimentary deep marine setting and compared to other provinces on other continental margins. We calculate the potential radiogenic contribution to the surface heat flow along a profile across the margin. Measurements across the continental shelf show intermediate thermal gradients of 38–44 °C/km. The onshore Indus Basin shows a lower range of values spanning 18–31 °C/km. The Indus Fan slope and continental rise show an increasing gradient from 37 to 55 °C/km, with higher values associated with the thick depocenter. The gradient drops to 33 °C/km along the Somnath Ridge, which is a syn-rift volcanic construct located in a landward position relative to the latest spreading center around the Cretaceous–Paleogene transition.     

Variability and propagation of Labrador Sea Water in the southern subpolar North Atlantic

The variability of two modes of Labrador Sea Water (LSW) (upper and deep Labrador Sea Water) and their respective spreading in the interior North Atlantic Ocean are investigated by means of repeated ship surveys carried out along the zonal WOCE line A2/AR19 located at 43–48°N (1993–2007) and along the GOOS line at about 48–51°N (1997–2002). Hydrographic section data are complemented by temperature, salinity, and velocity time series recorded by two moorings. They have been deployed at the western flank of the Mid-Atlantic Ridge (MAR) in the Newfoundland Basin during 1996–2004. The analysis of hydrographic anomalies at various longitudes points to a gradual eastward propagation of LSW-related signals, which happens on time scales of 3–6 years from the formation region towards the MAR. Interactions of the North Atlantic Current (NAC) with the Deep Western Boundary Current (DWBC) close to Flemish Cap point to the NAC being the main distributor of the different types of LSW into the interior of the Newfoundland Basin. Comparisons between the ship data and the mooring records revealed that the mooring sites are located in a region affected by highly variable flow. The mooring time series demonstrate an elevated level of variability with eddy activity and variability associated with the NAC considerably influencing the LSW signals in this region. Hydrographic data taken from Argo profiles from the vicinity of the mooring sites turned out to mimic quite well the temporal evolution captured by the moorings. There is some indication of occasional southward flow in the LSW layer near the MAR. If this can be considered as a hint to an interior LSW-route, it is at least of minor importance in comparison to the DWBC. It acts as an important supplier for the interior North Atlantic, distributing older and recently formed LSW modes southward along the MAR.     

DARCY'S COEFFICIENT OF PERMEABILITY AS SYMMETRIC TENSOR OF SECOND RANK

Synopsis

The dynamic equation of motion that governs the laminar flow of water through soils is the empirical equation of Darcy. According to Darcy's equation the velocity of the flowing water is proportional to the hydraulic gradient under which the water is flowing, with the constant of proportionality being the coefficient of permeability. The interesting question arising is whether or not the coefficient of permeability is a scalar quantity (having only a magnitude) or a vector (having both magnitude and direction). It is proved, in the present paper, that the permeability coefficient is neither a scalar nor a vector but a symmetric tensor of second rank. The fact that the permeability tensor is symmetric gives rise to great simplifications and permits a simple graphical construction of the tensor ellipsoid. Having the tensor ellipsoid, the determination of the direction at which the water will flow under a known imposed hydraulic gradient can be found graphically. In case of isotropic soils (the permeability coefficient has the same value along any direction) the ellipsoid reduces to a sphere and the tensor becomes a scalar. In the general case of anisotropic soils the permeability tensor is an entity with nine elements, six of which are independent representing pure extension or contraction along the three principal coordinate axes, thus transforming the permeability sphere into an ellipsoid and vice versa. It should be noted that in anisotropic soils the only directions along which the flow takes place in the direction of the hydraulic gradient are those of the principal axes of the tensor ellipsoid.

Permeability tests were conducted on anisotropic sandstone samples taken at different directions with respect to rectangular coordinates. The permeability coefficient values plotted on a two-dimensional polar coordinate graph paper give rise to an ellipse substantiating therefore the tensor concept of the permeability coefficient. The graphical construction of the tensor ellipse and the use of it in order to obtain the direction of flow by knowing the direction of the hydraulic gradient is also shown.     

Australia's great comet hunter

John Tebbutt was Australia's pre-eminent 19th-century astronomer who discovered two great comets of that century. Ragbir Bathal tells his story.