Surface wave propagation in sandy layer overlying a liquid saturated porous half-space and lying under a uniform liquid layer

Dispersion of Rayleigh-type surface waves is studied in a sandy layer under a uniform layer of homogeneous liquid lying over liquid-saturated porous solid half-space. The frequency equation in the form of a ninth-order determinant is obtained and evaluated. Special cases have been deduced and dispersion curves for the phase velocity and wave number have been plotted for a particular model.     

Surface wave propagation in a double liquid layer over a liquid-saturated porous half-space

The frequency equation is derived for surface waves in a liquid-saturated porous half-space supporting a double layer, that of inhomogeneous and homogeneous liquids. Asymptotic approximations of Bessel functions are used for long and short wavelength cases. Certain other problems are discussed as special cases. Velocity ratio (phase and group velocity) is obtained as a function of wavenumber and the results are shown graphically.     

Two dimensional nonlinear wave propagation in a shallow tidal estuary

Summary A study is made of a two-dimensional mathematical model of nonlinear wave propagation in a shallow tidal estuary using an unconditionally stable numerical scheme. The alternative direction implicit scheme is used to investigate the simulation of the flow pattern of the estuary, and to examine the effects of the changes in the bed topography either due to dredging or due to construction of spurs and guidewalls in tidal flows. The Coriolis force due to rotation of the earth is taken into account in the present two-dimensional model. It is shown that the Coriolis force is responsible for the existence of the transverse component of the flow field. The proposed theoretical model is applied to investigate the flow structure in the Hooghly estuary. The computed results are then compared with the observed values in the Hooghly estuary. A stability analysis of the alternative direction implicit scheme is also included.

---

Zweidimensionale nichtlineare Wellenausbreitung in einer Flachwasserflußmündung bei Gezeiten.

Zusammenfassung Es wird ein zweidimensionales mathematisches Modell für die nichtlineare Wellenausbreitung in einer Flachwasserflußmündung mit Gezeiten erarbeitet, das ein stabiles numerisches Verfahren benutzt. Es wird ein implizites Verfahren (alternative direction) gebraucht, um die topographischen Einflüsse des Flußbettes zu simulieren. Die Corioliskraft als Folge der Erddrehung wird bei diesem zweidimensionalen Modell ebenfalls berücksichtigt. Es wird nachgewiesen, daß die Corioliskraft für die transversale Komponente des Stromfeldes verantwortlich ist. Das vorgeschlagene theoretische Modell wird auf die Flußmündung des Hoogly angewendet. Die berechneten Resultate werden mit beobachteten Werten in der Hoogly-Flußmündung verglichen. Eine Stabilitätsuntersuchung des (alternative direction) impliziten Verfahrens wird ebenfalls durchgeführt.

---

---

With 4 Figures     

Experimental investigation on hydrothermal wave in a shallow annular pool

An on-ground experiment was conducted for observation of pattern formation in thermocapillary convection in an annular pool (r_i=20 mm, r_o=40 mm, and depth d=1.4 mm) of silicone oil (0.65 cSt, Pr=10.1). By a shadowgraph technique, curved traveling hydrothermal waves (HTW) were observed in liquid pools differentially heated at the outer wall. The critical temperature differences (ΔT_c) for the incipience of HTW were measured and were semi-quantitatively consistent with our numerical analysis for d=1.0mm and Pr=6.7.     

Parameters of wave instability in a boundary layer

The waves developing in a boundary layer during transition from laminar to turbulent flow are investigated experimentally.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 53, No. 4, pp. 624–629, October, 1987.     

Two-dimensional wave propagation in a micropolar thermo-elastic layer

The object of the present paper is to investigate the 2-dimensional thermo-elastic wave propagation in a micropolar solid layer. The wave velocity equation for the thermo-elastic Rayleigh wave in the micropolar medium has been deduced from the above theory and in the limiting case the wave velocity equation so obtained is in agreement with the corresponding classical problem when the thermal and micropolar effects are vanishingly small.     

层状LiMnO_2的水热合成

采用X射线衍射的方法系统研究了由Mn2O3和LiOH作为反应物时,正交层状LiMnO2的水热合成条件.结果表明,在200℃温度下,Mn3+与Li+的摩尔比小于等于1∶10,反应2 h以上可获得纯的产物.Rietveld分析表明,产物为正交层状结构,空间群为Pmnm,晶胞参数为a=566(3),b=5.751(2),c=2.808(1);晶体结构中,在2a位置有2%~3%的Li+、Mn3+占位无序.对200℃温度下,Mn3+与Li+的摩尔比为1∶10,反应2 h合成的正交层状LiMnO2的电化学性能测试表明,在0.1C的电流下,循环3次后放电容量可达175 mAh.g-1.     

Love wave propagation in a solid with a cold-worked surface layer

In this paper, experiments show Love wave generation along the top surface of used railroad rail, where the shear wave velocity has been slightly reduced by the cold-working of wheel passage for years. The rf pulses used in the experiments have about 10 µs duration and a relatively narrow frequency spectrum. The group velocity of the Love wave is found to have a strong dependence on the carrier frequency over the tested range of 0.45–3.1 MHz. Application of the seismological one-layered model to the experimental measurements yields an NDE technique for the elastic properties and the thickness of the cold-worked surface layer. The results are interpreted on the basis of a destructive observation by micro-Vickers hardness testing.     

Rayleigh wave propagation in a solid with a cold-worked surface layer

The propagation of the Rayleigh surface wave is experimentally studied along the top surface of used railroad rail under conditions where ultrasonic pulses have carrier frequencies ranging from 0.4 to 3.0 MHz and approximately 10 µs duration. The generation of the first higher (M ₂₁ or Sezawa) mode as well as the fundamental (M ₁₁) mode and their dispersion properties are observed. These phenomena are attributable to the presence of the cold-worked surface layer caused by the wheel passage. It is shown that a theoretical model of a single layer overlying a half space, whose elastic constants are determined by a destructive method, yields results which agree with the dispersion curves obtained experimentally. On the basis of this one-layered model, an inversion method to estimate the layer thickness and its elastic constants is discussed.     

Natural convection of a conducting liquid in a spherical layer

A system of differential equations describing the natural convection of the conducting liquid in the earth’s core is solved numerically by the methods of a reference volume and finite differences.     

Thermocapillary instability of a viscoelastic liquid layer

Summary The stability of a layer of viscoelastic fluid heated from below is studied in the case that the instability is driven by surface-tension gradients at the upper surface. The operative parameter for instability is the Marangoni number and the critical value of this parameter is calculated as a function of Prandtl number, heat-transfer coefficient and elasticity parameters. It is shown that when the elasticity is very small instability sets in as steady convection, as for a Newtonian fluid, but at larger elasticities oscillatory convection is the first mode of instability to appear.With 5 Figures     

Two-dimensional wave propagation in a micropolar thermo-elastic layer with stretch

This paper deals with the propagation of 2-dimensional waves in a thermo-elastic micropolar solid layer which can stretch and contract. Thermo-elastic Rayleigh wave velocity equation in the micropolar medium with stretch has been deduced from the above theory. The wave velocity equation obtained is in agreement with the classical result of Rayleigh when the layer is unstretched and thermal and micropolar effects are negligibly small.     

Gas-bubble formation in liquid layer

The dynamics of bubble formation and breakaway when a gas issues into a liquid is considered. The different modes of gas-bubble formation in a liquid layer are indicated. The results of analytic investigation are compared with experimental data.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 6, pp. 1066–1071, December, 1978.     

Stretching of a liquid layer underneath a semi-infinite fluid

Exact similarity solutions of the Navier–Stokes equation are derived describing the flow of a liquid layer coated on a stretching surface underneath another semi-infinite fluid. In the absence of hydrodynamic instability, the interface remains flat as the layer thickness decreases in time. When the physical properties of the fluids are matched, we obtain Crane’s analytical solution for two-dimensional (2D) flow and a corresponding numerical solution for axisymmetric flow. When the rate of stretching of the surface is constant in time, the temporal evolution of the interface between the layer and the overlying fluid is computed by integrating in time a system of coupled partial differential equations for the velocity in each fluid together with an ordinary differential equation expressing kinematic compatibility at the interface, subject to appropriate boundary, interfacial, and far-field conditions. Multiple solutions are found in certain ranges of the density and viscosity ratios. Additional similarity solutions are presented for accelerated 2D and axisymmetric stretching. The numerical prefactors that appear in the analytical expressions for the interface location and wall shear stress are presented for different ratios of the densities and viscosities of the two fluids.     

Resonant wave scattering on a finite supercritical plasma layer

The two-dimensional problem of excitation of a finite supercritical plasma layer by a cylindrical wave has been numerically studied. It is established that the frequency dependence of the excited field intensity has a resonant character for plasma-layer parameters close to values corresponding to a triply degenerate surface wave in the case of an infinite plasma layer. The values of near and far fields at the resonance frequency are calculated.     

Thermal-convective instability in a liquid layer in a system with rotating pivots

The stability of the main stationary liquid motion defined by Dirichlet boundary conditions on lateral surfaces of pivots was considered for a heated layer of a viscous thermal conducting liquid periodically perforated by a set of thin pivots. It was established that at any type of perforation and exceeding the critical Rayleigh number loss of stability is monotonic. In addition, the asymptotics for the critical Rayleigh number were defined at different types of perforation of the liquid layer.     

Spreading of a horizontal layer of non-Newtonian liquid

The flow of a layer of non-Newtonian liquid in an open volume is investigated numerically.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, Np, 6, pp, 950–957, June, 1985.     

Electromagnetic wave propagation in a plane dielectric layer under critical conditions

An exact solution to the problem of a plane wave propagation in a plane-stratified dielectric layer of arbitrary thickness is studied. An approach based on self-consistent finite differences is suggested, replacing the layer by a stack of homogeneous sublayers of variable thickness matched to the local behavior of the permittivity profile. For the region around zero permittivity, it is predicted that small perturbations of the physical parameters of the problem cause qualitative and quantitative changes in the solution. The conditions for the excitation of a surface wave are formulated. Computed data for the wave are presented.     

Boundary layer flow in a thin sheet of viscous liquid

Summary This paper investigates the steady flow of a thin sheet of viscous liquid down a variable incline; the Reynolds numberRe and the Froude numberFr are both large, withFr/Re=0(1). The governing equations are of the boundary layer type, and the Karman-Polhausen method is utilised to describe possible motions. It is found, when the incline becomes increasingly horizontal, that there can exist a point of separation on the bed of the stream; this is accompanied by a rapid rise in the depth of the liquid. The physical explanation is equivalent to that of classical boundary layer theory, except that the role of the pressure gradient in the external flow as the driving force is replaced by that of the force due to gravity.