Waves in a viscous fluid on a rotating sphere

Summary In this note the waves in a viscous fluid rotating on a sphere has been studied. The solution contains unknown constants which may be evaluated in particular cases applying the boundary conditions.     

The initial cooling of pahoehoe flow lobes

 In this paper we describe a new thermal model for the initial cooling of pahoehoe lava flows. The accurate modeling of this initial cooling is important for understanding the formation of the distinctive surface textures on pahoehoe lava flows as well as being the first step in modeling such key pahoehoe emplacement processes as lava flow inflation and lava tube formation. This model is constructed from the physical phenomena observed to control the initial cooling of pahoehoe flows and is not an empirical fit to field data. We find that the only significant processes are (a) heat loss by thermal radiation, (b) heat loss by atmospheric convection, (c) heat transport within the flow by conduction with temperature and porosity-dependent thermal properties, and (d) the release of latent heat during crystallization. The numerical model is better able to reproduce field measurements made in Hawai'i between 1989 and 1993 than other published thermal models. By adjusting one parameter at a time, the effect of each of the input parameters on the cooling rate was determined. We show that: (a) the surfaces of porous flows cool more quickly than the surfaces of dense flows, (b) the surface cooling is very sensitive to the efficiency of atmospheric convective cooling, and (c) changes in the glass forming tendency of the lava may have observable petrographic and thermal signatures. These model results provide a quantitative explanation for the recently observed relationship between the surface cooling rate of pahoehoe lobes and the porosity of those lobes (Jones 1992, 1993). The predicted sensitivity of cooling to atmospheric convection suggests a simple field experiment for verification, and the model provides a tool to begin studies of the dynamic crystallization of real lavas. Future versions of the model can also be made applicable to extraterrestrial, submarine, silicic, and pyroclastic flows. Received: 26 November 1994 / Accepted: 1 December 1995     

Toothpaste lava: Characteristics and origin of a lava structural type transitional between pahoehoe and aa

Toothpaste lava, an important basalt structural type which illustrates the transition from pahoehoe to aa, is particularly well displayed on the 1960 Kapoho lava of Kilauea Volcano. Its transitional features stem from a viscosity higher than that of pahoehoe and a rate of flow slower than that of aa. Viscosity can be quantified by the limited settling of olivine phenocrysts and rate of flow by field observations related to the low-angle slope on which the lava flowed. Much can be learned about the viscosity, rheologic condition, and flow velocity of lavas long after solidification by analyses of their structural characteristics, and it is possible to make at least a semiquantitative assessment of the numerical values of these parameters.     

The emplacement of pahoehoe toes: field observations and comparison to laboratory simulations

We observed active pahoehoe lobes erupted on Kilauea during May-June 1996, and found a range of emplacement styles associated with variations in local effusion rate, flow velocity, and strain rate. These emplacement styles were documented and quantified for comparison with earlier laboratory experiments.At the lowest effusion rates, velocities, and strain rates, smooth-surfaced lobes were emplaced via swelling, where new crust formed along an incandescent lip at the front of the lobe and the rest of the lobe was covered with a dark crust. At higher effusion rates, strain rates and velocities, lobes were emplaced through tearing or cracking. Tearing was characterized by ripping of the ductile crust near the initial breakout point, and most of the lobe surface was incandescent during its emplacement. This mechanism was observed to generate both smooth-surfaced lobes, and, when the lava encountered an obstacle, folded lobes. Cracking lobes were similar to those emplaced via tearing, but involved breaking of a thicker, brittle crust at the initial breakout of the lobe and therefore required somewhat higher flow rates than did tearing. Cracking lobes typically formed ropy folds in the center of the lobe, and smooth margins. At the highest effusion rates, strain rates, and flow velocities, the lava formed open channels with distinct levees.The final lobe morphologies were compared to results from laboratory simulations, which were designed to infer effusion rate from final flow morphology, to quantitatively test the laboratory results on the scale of individual natural pahoehoe lobes. There is general agreement between results from laboratory simulations and natural lavas on the scale of individual pahoehoe lobes, but there are disparities between laboratory flows and lava flows on the scale of an entire pahoehoe lava flow field.Editorial responsibility: A. Woods     

Preferred aspect ratios of convection in a strongly temperature and pressure dependent viscous fluid

If it is assumed that mantle convection is shallow, i.e. limited to an upper layer of ～700 km, then the extent of surface plates must be such that aspect ratios are noticeably large, in contrast to many laboratory and numerical experiments. A rheology which depends strongly on temperature and pressure is provided as an explanation of why this may occur. The aspect ratio, it is suggested, is preferentially large because of the unwillingness of the stiff plates to subduct, which raises the problem of how subduction occurs. A hypothesis is proposed that this is caused by viscous heating in the asthenosphere, and the preferred aspect ratio is large enough such that partial melting takes place underneath the sinking slab, causing it to sink by releasing the sub-lithospheric pressure so that a transverse buckling may occur.     

Slow motion of a viscous conducting fluid past ellipsoids in the presence of a toroidal magnetic field

Summary An attempt has been made here, to obtain solutions for the velocity and magnetic field, for a flow past an ellipsoid, in the presence of a toroidal magnetic field, when magnetic Reynold number and Hartman number are small.     

On the steady mass transport induced by wave motions in a viscous rotating fluid

Abstract

The steady second-order motion induced by a first-order wave motion in a homogeneous, viscous and rotating fluid is examined. If the wave motion produces a steady Ekman layer suction by non-linear interactions, this suction must induce a steady component of interior, relative vorticity parallel to the axis of rotation in order to conserve mass. A boundary value problem for the determination of the induced, steady interior mass transport velocity is presented. The mass transport induced by a Kelvin wave is examined as an illustration and possible application of the theory.     

On unsteady flow of a viscous fluid between two parallel plates under variable surface charges

Summary The equations of electricity and the equations of hydrodynamics have been used to solve the problem of unsteady flow of a viscous fluid under variable surface charges.     

Analytical study on accelerating falling of non-spherical particle in viscous fluid

Unsteady motion of a vertically falling non-spherical particle has attracted considerable attention due to its frequent applications in nature and industry.A series of semi-analytical methods have been used to raise the results＇ accuracy as well as widening the region of convergence.The current study pursued a new analytical solution for the unsteady motion of a rigid non-spherical particle in a quiescent Newtonian fluid,based on the Optimal Homotopy Analysis Method.With a view towards obtaining the highest level of accuracy and ensuring the convergence of the analytical results,the averaged residual errors were obtained and minimized.In addition to flexibility,it was also proven that the proposed method can lead to completely reliable and precisely accurate results.Based on the series solution,the effects of physical parameters on the terminal settling velocity（i.e.the greatest velocity that a falling body may reach）and the acceleration time（i.e.the time that a particle reaches the settling velocity） are investigated.     

Towards realistic minimum-cost optimization of viscous fluid dampers for seismic retrofitting

This paper presents an effective approach for achieving minimum cost designs for seismic retrofitting using viscous fluid dampers. A new and realistic retrofitting cost function is formulated and minimized subject to constraints on inter-story drifts at the peripheries of frame structures. The components of the new cost function are related to both the topology and to the sizes of the dampers. This constitutes an important step forward towards a realistic definition of the optimal retrofitting problem. The optimization problem is first posed and solved as a mixed-integer problem. To improve the efficiency of the solution scheme, the problem is then re-formulated and solved by nonlinear programming using only continuous variables. Material interpolation techniques, that have been successfully applied in topology optimization and in multi-material optimization, play a key role in achieving practical final design solutions with a reasonable computational effort. Promising results attained for 3-D irregular frames are presented and compared with those achieved using genetic algorithms.     

黏滞阻尼器对拉索参数振动的控制分析

提出采用黏滞阻尼器对拉索参数振动进行控制,建立了黏滞阻尼器控制拉索参数振动的运动方程。从频域和时域以及起振幅值等角度,研究了最优黏滞阻尼器对不同垂度拉索参数振动的控制效果;此外,还研究了最优黏滞阻尼器安装位置对拉索参数振动控制效果的影响。研究表明,黏滞阻尼器可以有效控制拉索的参数振动,控制效果与拉索的激励幅值、最优阻尼器的安装位置和斜拉索的垂度有关。激励幅值越大,控制效果一般越差;最优阻尼器的安装位置越靠近跨中,则控制效果越好;黏滞阻尼器对大垂度拉索的控制效果不及对小垂度拉索的控制效果。     

A simplified two-component model for the lateral growth of pahoehoe lobes

Unconfined pahoehoe lobes, composed of networks of numerous pahoehoe toes, often show a transverse profile with central thickening and crude bilateral symmetry. The overall widths of individual lobes are often relatively constant compared to the large diversity in widths of individual toes. These observations collectively suggest that there is a lateral self-confinement mechanism at the scale of a lobe. Although previous correlated random walk models successfully address the nature of this mechanism, the underlying physical processes are still not clearly understood. Here, we propose a simplified two-component model for the lateral self-confinement mechanism. The model assumes that the surface crust retains an inner hot core until its overpressure surpasses the strength of the crust. It also assumes that fracturing of the crust occurs at the top of the flow where the crust has the weakest strength, and then a breakout of the hot core spills out to form a new flow unit. Episodic fracturing and subsequent coalescence of multiple toes form a broad lobe, which is then considered theoretically to behave as a single large flow unit. Although simplified, the model can determine the inflated thickness necessary to fracture the crust and the width scale of the lateral spreading with a self-confinement effect. The model also provides theoretical support for the correlated random walk model for pahoehoe emplacement.     

Spongy pahoehoe in Hawaii: A study of vesicle-distribution patterns in basalt and their significance

A well-defined pahoehoe lava type that is very common medially and distally in Hawaii is characterized by a high concentration and fairly uniform distribution of spherical or near-spherical vesicles. Measurements of vesicle sizes and concentrations have been made on ten of these spongy pahoehoe lava flow-units. The vesicles increase in size toward the middle, accompanied by a moderate increase in lava porosity. The close approach to bilateral symmetry on either side of the horizontal median plane and the common occurrence of a median gas blister shows that no significant upward movement of vesicles occurred, suggesting that the lava possessed a yield strength and was more or less static. Olivine phenocrysts when present are, however, concentrated in the lower half of the same flow units, showing that the lava previously lacked a significant yield strength. The vesicles are regarded as early, inherited from the vent, but the size characteristics of the vesicle population are a late-formed feature. Vesicles grew in static lava mostly by coalescence, and it is postulated that coalescence was promoted by the presence of abundant diktytaxitic voids which punctured the walls of contiguous vesicles. Zones in which the vesicle concentration is lower and the vesicles are larger and strongly deformed interrupt the symmetry of some spongy pahoehoe units, and gas blisters higher than the median plane occur in many examples. These zones are interpreted to result from late-stage shearing, and point to a mechanism by which vesicles may be eliminated from a lava.     

含两项不混合/单项黏性流体孔隙介质分界面上反透射系数特征研究

弹性孔隙介质分界面上的反透射系数特征,在岩性划分、流体识别、储层边界判识等方面有重要的应用.本文研究上层为含两项不混合黏性流体孔隙介质、下层为含单项黏性流体孔隙介质分界面上的反透射理论.首先根据两种孔隙介质分界面上的能量守恒得到边界条件,再将波函数、位移、应力与应变关系代入边界条件,推导出完全连通孔隙情况下,第一类纵波入射到孔隙介质分界面上的反透射系数方程.通过建立砂岩孔隙介质模型,分别分析不同孔隙流体类型、不同含油饱和度及不同入射角情况下,各类波的反透射系数特征.研究表明,第二、三类纵波反透射系数数值比第一类纵波小多个数量级,且两者对入射角的变化不敏感,但对孔隙流体性质、含油饱和度的变化较敏感,而横波反透射系数特征恰好与此相反;第一类纵波反透射系数特征比较复杂,入射角、孔隙流体的性质及含油饱和度的变化都对其产生影响.不同孔隙流体弹性物性的差异、孔隙介质中含油饱和度的变化及不同入射角引起垂向和切向应力分量的变化都会影响各类波的反透射系数特征,分析这些特征可以为研究储层含油气性提供理论基础.

     

Three-dimensional numerical model for the evolution of convection in a layer of a viscous fluid with six floating continents

A three-dimensional model is developed for describing the long-term evolution of the mantle convection with six continents, which includes the formation and breakup of a supercontinent. In contrast to the theory of floating continents [Trubitsyn, 2000; 2008], in which the drift was calculated from a system of convection equations for the mantle and the Euler equations for the continents, in the present work the continental motion is described in terms of a set of floating markers, which have anomalously high viscosity and are driven by the currents.     

大吨位双出杆粘滞阻尼器开发的数值模拟与实验研究

阐述了大吨位双出杆粘滞阻尼器开发的数值与实验研究结果.基于硅油的幂律特性,通过对硅油介质的流态分析,介绍了非牛顿幂律流体模型对粘滞阻尼器耗能和阻尼出力的影响,与粘滞阻尼器的分析模型和计算公式.在商用流体软件平台上利用动网格技术对样品粘滞阻尼器阻尼出力进行了计算;综合实验研究结果,最终确定了大吨位土木用粘滞阻尼器设计的经验方法.另一方面,实验曲线和数值曲线基本吻和,验证了通过数值手段对粘滞阻尼器的出力特性进行预分析,从而提高开发精度、指导产品设计和缩短产品的开发周期的可行性.     

含黏性流体孔隙介质分界面上反透射系数特征研究

地下岩石由岩石骨架和孔隙流体组成,通常流体含黏性.地震波在地下介质中传播时受岩石骨架和黏性流体的影响会呈现出复杂的变化.本文将流、固体位移和应力连续作为边界条件,推导出含黏性流体孔隙介质分界面上反透射系数方程;通过建立上层为饱油、下层为饱盐水的砂岩孔隙介质模型,开展反透射系数特征研究,分别分析不同频率、不同黏滞系数条件下,含黏性流体孔隙介质分界面上反透射系数随入射角的变化.研究表明,孔隙介质分界面上和等效介质分界面上的反透射系数分别随入射角的变化趋势基本一致,说明方程推导和数值计算的正确性;快纵波反透射系数受频率、流体黏性的影响较小,而快横波反透射系数在一定入射角范围内受频率、流体黏性的影响比较大;由于黏性孔隙流体的作用,慢纵波和慢横波的反透射系数受入射角、频率及流体黏性的影响都很大.

     

Supporting brace sizing in structures with added linear viscous fluid dampers: A filter design solution

Viscous fluid dampers have proved to be effective in suppressing unwanted vibrations in a range of engineering structures. When dampers are fitted in a structure, a brace is typically used to attach them to the main structure. The stiffness of this brace can significantly alter the effectiveness of the damper, and in structures with multiple dampers, this can be a complex scenario to model. In this paper, we demonstrate that the effects of the brace compliance on the damper performance can be modelled by way of a first‐order filter. We use this result to formulate a procedure that calculates the stiffness required by the supporting brace to provide a specified effectiveness of the damping action. The proposed procedure assumes that viscous dampers have been sized in a previous design step based on any optimal methodology in which, as is usually the case, the presence of supporting braces and their dynamic effects were neglected. Firstly considering a one degree‐of‐freedom system, we show that the proposed method ensures a desired level of damper efficiency for all frequencies within a selected bandwidth. Then the analysis is extended to the case of multi‐degree‐of‐freedom systems to show that the design criteria can be applied in a straightforward and successful manner to more complex structures. © 2014 The Authors. Earthquake Engineering & Structural Dynamics published by John Wiley & Sons Ltd.     

The onset of convection in a rotating layer of viscous fluid with an imposed magnetic field: the dependence on the prandlt numbers

The onset of Boussinesq convection in a horizontal layer of an electrically conducting incompressible fluid is considered. The layer rotating about a vertical axis is heated from below; a vertical magnetic field is imposed. Rigid electrically insulating boundaries are assumed. The loss of stability of the trivial steady state, which occurs as the Rayleigh numbers increase, can be accompanied by the development of a monotonic or an oscillatory instability, depending on the parameter values of the problem at hand (the Taylor number, the Chandrasekhar number, the kinematic and the magnetic Prandtl numbers). When the instability is monotonic, the emerging convective rolls themselves are also unstable if the Taylor number is sufficiently large (the so-called Küppers-Lortz instability takes place). In the present work it is studied how the critical value of the Rayleigh number, the type of the trivial steady state instability, and the critical value of the Taylor number for the Küppers-Lortz instability depend on the kinematic and the magnetic Prandtl numbers. We consider the values of the Prandtl number not exceeding 1, which is typical for the outer core of the Earth.