Review of Global Ocean Intermediate Water Masses: 1.Part A, the Neutral Density Surface (the ‘McDougall Surface’) as a Study Frame for Water-Mass Analysis

This review article commences with a comprehensive historical review of the evolution and application of various density surfaces in atmospheric and oceanic studies. The background provides a basis for the birth of the neutral density idea. Attention is paid to the development of the neutral density surface concept from the nonlinearity of the equation of state of seawater. The definition and properties of neutral density surface are described in detail as developed from the equations of state of seawater and the buoyancy frequency when the squared buoyancy frequency N2 is zero, a neutral state of stability. In order to apply the neutral density surface to intermediate water-mass analysis, this review also describes in detail its practical oceanographic application. The mapping technique is focused for the first time on applying regularly gridded data in this review. It is reviewed how a backbone and ribs framework was designed to flesh out from a reference cast and first mapped the global neutral surfaces in the world’s oceans. Several mapped neutral density surfaces are presented as examples for each world ocean. The water-mass property is analyzed in each ocean at mid-depth. The characteristics of neutral density surfaces are compared with those of potential density surfaces.

Mapping of an Approximate Neutral Density Surface with Ungridded Data

A neutral density surface is a logical study frame for water-mass mixing since water parcels spread along such a surface without doing work against buoyancy restoring force. Mesoscale eddies are believed to stir and subsequently mix predominantly along such surfaces. Because of the nonlinear nature of the equation of state of seawater, the process of accurately mapping a neutral density surface necessarily involves lateral computation from one conductivity, temperature and depth (CTD) cast to the next in a logical sequence. By contrast, the depth of a potential density surface on any CTD cast is found solely from the data on this cast. The lateral calculation procedure causes a significant inconvenience. In a previous paper by present author published in this journal (You, 2006), the mapping of neutral density surfaces with regularly gridded data such as Levitus data has been introduced. In this note, I present a new method to find the depth of a neutral density surface from a cast without having to specify an integration path in space. An appropriate reference point is required that is on the neutral density surface and thereafter the neutral density surface can be de- termined by using the CTD casts in any order. This method is only approximate and the likely errors can be estimated by plotting a scatter diagram of all the pressures and potential temperatures on the neutral density surfaces. The method assumes that the variations of potential temperature and pressure (with respect to the values at the reference point) on the neutral density surface are proportional. It is important to select the most appropriate reference point in order to approximately satisfy this assumption, and in practice this is found by inspecting the θ-p plot of data on the surface. This may require that the algorithm be used twice. When the straight lines on the θ-p plot, drawn from the reference point to other points on the neutral density surface, enclose an area that is external to the clus- ter of θ-p points of the neutral density surface, errors will occur, and these errors can be quantified from this diagram. Examples showing the use of the method are presented for each of the world’s main oceans.

Adiabatic density surface,neutral density surface, potential density surface,and mixing path

In this paper,adiabatic density surface,neutral density surface and potential density surface are compared.The adiabatic density surface is defined as the surface on which a water parcel can move adiabatically,without changing its potential temperature and salinity.For a water parcel taken at a given station and pressure level,the corresponding adiabatic density surface can be determined through simple calculations.This family of surface is neutrally buoyant in the world ocean,and different from other surfaces that are not truly neutrally buoyant.In order to explore mixing path in the ocean,a mixing ratio m is introduced,which is defined as the portion of potential temperature and salinity of a water parcel that has exchanged with the environment during a segment of migration in the ocean.Two extreme situations of mixing path in the ocean are m=0(no mixing),which is represented by the adiabatic density curve,and m=1,where the original information is completely lost through mixing.The latter is represented by the neutral density curve.The reality lies in between,namely,0<m<1.In the turbulent ocean,there are potentially infinite mixing paths,some of which may be identified by using different tracers(or their combinations)and different mixing criteria.Searching for mixing paths in the real ocean presents a great challenge for further research.

An analytical model for predicting sheet springback after V-bending

Springback is caused by the redistribution of stress in sheet material after the tooling is removed. Precise prediction of sheet springback is very important in die design. Based on Hill’s yielding criterion and plane strain condition, an analytical model is proposed in this paper which takes into account the effects of contact pressure, the length of bending arm between the punch and die, transverse stress, neutral surface shifting and sheet thickness thinning on the sheet springback of V-bending. The predicted results by this analytical model indicated that the contact pressure and transverse stress have much effect on the springback when the bending ratio (the ratio of punch radius to sheet thickness) is less than five. The contact pressure declined when the length of bending arm goes up, which means that shorter length of bending arm will result in larger springback. The effect of neutral surface shifting on the springback is less than that of contact pressure and decreases with the bending ratio. However, this research showed that the influence of thickness thinning on the springback can be ignored. Comparison with finite element method (FEM) simu-lating results shows that the predicted results by the analytical model accord well with simulation results by FEM. In addition to that, the bending ability—the limit bending ratio for a given sheet thickness and material properties was also determined.

Closed-form solutions for free vibration of rectangular FGM thin plates resting on elastic foundation

This article presents closed-form solutions for the frequency analysis of rectangular functionally graded material (FGM) thin plates subjected to initially in-plane loads and with an elastic foundation. Based on classical thin plate theory, the governing differential equations are derived using Hamilton's principle. A neutral surface is used to eliminate stretching-bending coupling in FGM plates on the basis of the assumption of constant Poisson's ratio. The resulting governing equation of FGM thin plates has the same form as homogeneous thin plates. The separation-of-variables method is adopted to obtain solutions for the free vibration problems of rectangular FGM thin plates with separable boundary conditions, including, for example, clamped plates. The obtained normal modes and frequencies are in elegant closed forms, and present formulations and solutions are validated by comparing present results with those in the literature and finite element method results obtained by the authors. A parameter study reveals the effects of the power law index n and aspect ratio a/b on frequencies.

Testing the intraplate origin of mega-earthquakes at subduction margins

The disastrous Mw 9.3 （seismic moment 1.0 × 10^30 dyn/cm） earthquake that struck northwest Sumatra on 26 December 2004 and triggered -30 m high tsunami has rejuvenated the quest for identi- fying the forcing behind subduction related earthquakes around the world. Studies reveal that the stron- gest part （elastic core） of the oceanic lithosphere lie between 20 and 60 km depth beneath the upper （- 7 km thick） crustal layer, and compressive stress of GPa order is required to fail the rock-layers within the core zone. Here we present evidences in favor of an intraplate origin of mega-earthquakes right within the strong core part （at the interface of semi-brittle and brittle zone）, and propose an alternate model exploring the flexing zone of the descending lithosphere as the nodal area for major stress accumulation. We believe that at high confining pressure and elevated temperature, unidirectional cyclic compressive stress loading in the flexing zone results in an increase of material yield strength through strain hardening, which transforms the rheology of the layer from semi-brittle to near-brittle state. The increased compres- sive stress field coupled with upward migration of the neutral surface （of zero stress fields） under non- coaxial deformation triggers shear crack. The growth of the shear crack is initially confined in the near-brittle domain, and propagates later through the more brittle crustal part of the descending oceanic lithosphere in the form of cataclastic failure,

Accurate Free Vibration of Functionally Graded Skew Plates

The present study aims to analyze free vibration of thin skew plates made of functionally graded material(FGM)by using the weak form quadrature element method.The material properties vary continuously through the thickness according to a power-law form.A novel FGM skew plate element is formulated according to the neutral surface based plate theory and with the help of the differential quadrature rule.For verifications,Numerical results are compared with available data in literature.Results reveal that the non-dimensional frequency parameters of the FGM skew plates are independent of the power-law exponent and always proportional to those of homogeneous isotropic ones when the coupling and rotary inertias are neglected.In addition,employing the physical neutral surface based plate theory is equivalent to using the middle plane based plate theory with the reduced flexural modulus matrix.