Stresses produced by a load moving over the rough boundary of a semi-infinite transversely isotropic solid

Summary Stresses produced due to a moving load over the plane surface (supposed to be rough) of a semi-infinite transversely isotropic medium have been calculated in this paper.     

Observations of intensity variations and harmonics of heater induced VLF waves

Very low-frequency (VLF) radio waves have been generated in the ionosphere by the heating facility near Tromsø. VLF signals have been received at Porojärvi (69.17 ° N, 21.47 ° E, L = 6.1), in Northern Finland, about 100 km from the heating transmitter. Three heating experiments were performed under different geophysical conditions and different results were obtained. Signal intensities have been compared with magnetic variations. Correlations and anti-correlations were observed. Several harmonics of the generated signal have generally been found. In some cases when the intensity of the detected VLF signal was low the first harmonic was as intensive as the fundamental frequency. VLF response from Artificial Periodic Inhomogeneities (API) experiment was also observed.     

Stresses produced by a normal load moving over a transversely isotropic layer of ice lying on a rigid foundation

Summary In this paper, the problem of a normal load moving over the surface of a layer of ice, lying on a rigid foundation, has been considered. FollowingHearmon, the ice is taken to be transversely isotropic. Two cases have been considered-in the first case, the rigid foundation is taken to be smooth, and in the second case, it is taken to be in welded contact with the layer of ice. Expressions have been obtained in both cases for the stresses at any point of the layer. From detailed numerical calculations, it has been found that the value of the normal stress at a point directly below the moving load falls of approximately as that of 1/z with increase in the depthz below the surface. On calculating the normal stress at the boundary between the layer of ice and the foundation, it is found that the normal stress falls off rapidly as we move away along the boundary from the point directly below the load.     

Observations on the distribution of dissolved mercury in the ocean

The concentration of dissolved mercury in sea water has been determined in a number of areas in the northern and southern hemispheres and an attempt has been made to correlate the values found for certain areas with natural physical phenomena. The average concentrations found ranged from 11.2 ng l^?1 in the southern hemisphere to 33.5 ng l^?1 for the northern hemisphere; an increase suspected to be the result of dispersion of industrial pollution by jet streams. Local effects including upwelling, volcanic action, land run-off and heavy suspended matter loads are also discussed.     

Note on stresses produced by a shearing force moving over the boundary of a semi-infinite transversely isotropic solid

Summary Two dimensional problem of distribution of stresses produced by a pulse of shearing force moving uniformly on the boundary of a semi-infinite transversely isotropic solid has been studied here. It is observed that the shearing stress in the direction of propagation of pulse attains maximum value at a point directly below the point of application of the shearing force on the boundary.     

On the stresses produced in a liquid-saturated porous solid by normal and tangential forces on a moving strip of finite width

Summary This paper deals with the stresses produced in a semi-infinite liquid-saturated porous solid of the type considered byBiot [1]²), by moving normal and tangential forces acting simultaneously on a moving strip of finite width on the free surface. It has been found that the stresses can be obtained in a closed form. It has also been found that if the velocity of the strip exceeds a certain value, the nature of the stresses changes, and there are discontinuities of stress along certain lines. The results have been applied to study the changes in the stresses produced by moving normal and tangential forces with depth and distance.     

On the stresses produced by a moving stress discontinuity at the boundary between two transversely isotropic media

Summary This paper deals with the stresses produced by a moving stress discontinuity between two semi-infinite transversely isotropic media. The solutions for the stresses have been obtained in simple closed forms for certain types of moving stress discontinuity. Discontinuities in the normal stress as well as in the shear stress has been considered. The case in which one or both of the media are isotropic may be deduced as a special case from the results obtained here.     

Interactions between mean flow and finite-amplitude mesoscale eddies in a barotropic ocean

Abstract

For the purpose of deriving an analytical parametrization, oceanic mesoscale eddies are represented as a horizontally propagating wave field in a non-uniform environment. The mathematical analysis rests upon the assumption of scale disparity between a short eddy scale and a long mean-flow scale. The novelty resides in the treatment of finite-amplitude eddies, which, moreover, form either a band-like or a cell-like pattern. A barotropic ocean is chosen as a first step to illustrate the mathematical analysis, but dissipation is included. The main result is an analytical derivation of a mesoscale-eddy parametrization: the mean-flow equation contains Reynolds-stress terms which are computed from parameters of the eddy field, which, in turn, are predicted by separate evolution equations. Due to restrictive assumptions (barotropy, orthogonal waves,…), the parametrization established here should be viewed only as a first step toward the design of a more practical parameterization for large-scale modelling.     

Spectral analysis of mean flow and turbulence forced by waves in a horizontally homogeneous zone of the Iroise sea

The 1D version of the Model for Applications at Regional Scale is used to parameterize the effects of sea surface waves in 2D in a horizontally homogeneous offshore zone of the Iroise sea. Here we present the first simulation of the Iroise sea including sea surface waves forcing, and more generally, the first study of a boundary layer including the Hasselmann force with a tidal wave. We use a single equation turbulence closure based on a non-local diagnosis for energetic and dissipation length scales. The turbulent energy flux at the surface due to whitecaps and the Hasselmann force induced by Stokes drift are assessed using the whole sea surface waves spectrum given by the Wave Watch Third generation model. The ability of the parameterization to reproduce surface currents over a period of 1 year (2007) is tested with high frequency radar using spectral and time-frequency analysis. One problem with 1D modelling, corresponding to overestimation of current oscillating at inertial frequency is illustrated by comparing 1D and 3D simulations. We found an overall improvement by including the Hasselmann force mainly within the bandwidth of less than one cycle per day to one cycle per day for surface currents. Turbulence is induced by whitecaps decaying rapidly below the ocean surface but the mixed layer below 40 m is deeper due to waves breaking on the sea surface.     

Observations on the flow structures and transport in a simulated warm-core ring in the Gulf of Mexico

This study presents several new observations from the study of a numerically simulated warm-core ring (WCR) in the Gulf of Mexico based on the ECCO2 global ocean simulation. Using Lagrangian coherent structures (LCS) techniques to investigate this flow reveals a pattern of transversely intersecting LCS in the mixed layer of the WCR which experiences consistent stretching behavior over a large region of space and time. A detailed analysis of this flow region leads to an analytical model of the velocity field which captures the essential elements that generate the transversely intersecting LCS. The model parameters are determined from the simulated WCR and the resulting LCS show excellent agreement with those observed in the WCR. The three-dimensional transport behavior that creates these structures relies on the small radial outflow that is present in the mixed layer and is not seen below the pycnocline, leading to a sharp change in the character of the LCS at the bottom of the mixed layer. The flow behavior revealed by the LCS limits fluid exchange between the WCR and the surrounding ocean, contributing to the long life of WCRs. Further study of these structures and their associated transport behavior may lead to further insights into the development and persistence of such geophysical vortices as well as their transport behavior.     

Seasonal replenishment of mercury in a coastal fjord by its intermittent anoxicity

We report the first time-series of seasonal change in the concentration of mercury in sea water, and its speciation and mechanism of replenishment by sulphide chemistry in an intermittently reducing coastal fjord. We observed total Hg levels in sea water as low as 0.3 ng l⁻¹ in the oxygenated waters of Saanich Inlet, British Columbia, as well as a correlation of seasonal buildup of Hg and sulphide in the bottom waters between March and August through diffusive supplies from the anoxic sea water/sediment interface.     

On solitary waves generated by a moving pressure field

Summary The waves generated by a steadily moving two-dimensional pressure distribution are examined using non-linear shallow water theory. The applied pressure is zero ahead of the disturbance, that is in the downstream direction, and is a constantP ₀ in the upstream direction, these regions being joined smoothly by a cubic function.We consider here only the case of supercritical flow in both regions, the solution representing an asymmetric solitary wave travelling with the disturbance. The wave profiles are determined by an iterative method previously employed for non-linear waves. Wave amplitudes and profiles, and the wave drag, associated with each system are computed for various values ofP ₀/Q g h, whereh is the undisturbed depth of water ahead of the wave.The solution obtained reduces to the classical solitary wave of finite amplitude when the applied pressure is everywhere zero.

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Résumé Nous avons calculé les expressions des profils d'ondes solitaires produites par une pression, qui se propagent sur la surface d'une couche d'eau peu profonde avec une vitesseU plus grande que (g h)^1/2. La pression appliquée est nulle en avant de l'onde, elle est une constanteP ₀ en arrière, et entre ces deux régions elle est representée par une fonction cubique. Les profils sont calculés par une methode iterative déjà employée pour des ondes non-linéaires. L'amplitude, le profil et la force ont été evalués pour diverses valeurs deP ₀/Q g h, ouh est la profondeur en avant de l'onde.

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Division of Numerical and Applied Mathematics, National Physical Laboratory.     

热源激发重力波特征以及波流作用的数值模拟研究

本文在二维等温可压大气中引入了一个随时间和空间变化的热源扰动,分别以静止风和中纬1月份月平均向东的纬向风急流为背景,对不同背景下热源激发的重力波的传播详细过程及其特性进行了数值模拟研究.热源激发出来的重力波在初始阶段有很宽的频谱范围,随后由于重力波的传播效应,水平波长和垂直波长分布范围随时间都有所减小.顺风传播的重力波的小尺度和低频部分会容易被急流吸收,从而加强了对流层急流,而逆风传播的重力波更容易上传,会导致中间层区域向西的背景风增强.这体现了低层大气急流对中间层大气风场结构的影响.热源的尺度直接决定激发波的尺度;激发波的垂直尺度和时间尺度对热源的变化比其水平尺度更敏感.     

Increasing temperature and flow management alter mercury dynamics in East Fork Poplar Creek

East Fork Poplar Creek (EFPC) is a mercury (Hg) contaminated creek in east Tennessee, USA. Stream restoration activities included the initiation of a flow management programme in 1996 in which water from a nearby lake was pumped to the head of the creek. We conducted regular water sampling for 2 years along the length of EFPC during active flow management and for 5 years after flow management stopped. Total Hg and total monomethylmercury (MMHg) concentration and flux decreased in the uppermost reaches of EFPC that were closest to the point of water addition. Most water quality parameters, including DOC concentration, remained unchanged after flow management termination. Nevertheless, SUVA₂₅₄, a measure of dissolved organic matter (DOM) composition, increased and coincided with increased dissolved Hg (Hg_D) concentration and flux and decreased Hg solid-water partitioning coefficients throughout EFPC. Higher SUVA₂₅₄ and Hg_D concentration have potential implications for bioavailability and MMHg production. Total and dissolved MMHg concentrations increased in lower reaches of EFPC after the end of flow management and these increases were most pronounced during spring and early summer when biota are more susceptible to exposure and uptake. A general warming trend in the creek after active flow management ended likely acted in concert with higher Hg_D concentration to promote higher MMHg concentration. Total and dissolved MMHg concentrations were positively correlated with water temperature above a threshold value of 10°C. Concentration changes for Hg and MMHg could not be accounted for by changes in creek discharge that accompanied the cessation of flow management. In addition to the changing DOM composition in-stream, other watershed-scale factors likely contributed to the observed patterns, as these changes occurred over months rather than instantaneously after flow management stopped. Nevertheless, similar changes in MMHg have not been observed in a tributary to EFPC.     

Disturbances produced in a visco-elastic medium by transient torsional body forces

Summary The disturbances produced in a semi-infinite visco-elastic medium and in a layer of visco-elastic material resting on a rigid foundation by transient torsional body forces have been considered. Formal solutions have been obtained for a general type of body force, and this solution has been used to obtain the displacements for a transient torsional point source in the case of a semiinfinite medium, and for a cylindrical source of finite dimensions and a line source in the case of the layer of visco-elastic material mentioned above. Solutions have also been obtained for a transient shearing stress applied at the free surface of the layer mentioned above.     

On the disturbance produced in a semi-infinite poroelastic medium by a surface load

Summary Biot's theory of dynamical poroelasticity is used to solve the axisymmetric problem of deformation of a semi-infinite proelastic medium which is subjected to a uniform load within a circular area of its boundary. The solutions valid for large time have been derived. In some limiting cases, the solutions are shown to reduce to those of classical elasticity. The solutions for the point load case have also been deduced. Lastly, the variations with time of the solid displacements, the normal stress and the fluid pressure for the point load case after the arrival of the shear wave are exhibited graphically and the results for the classical case are included for the sake of comparison.