Electromagnetic propagation in periodic porous structures

A variational technique is employed to compute approximate propagation constants for electromagnetic waves in a dielectric structure which is periodic in the X−Y plane and translationally invariant in the Z-direction. The fundamental cell, in the periodic structure, is composed of a pore and the surrounding host media. The pore is a circle of radius R₀ filled with a dielectric ε₁ and the host dielectric characterized by ε₂. The size of the cell is characterized by the length A which is R₀.

Two limiting cases are considered. In the first, the pore size is assumed to be much smaller than the wavelength; this limit is motivated by microwave heating of porous material. The approximate propagation constants are explicitly computed for this case and are shown to depend upon the two dielectric constants, the relative areas of the two regions in the cell, and on a modal number. They are not given by a simple mixture formula.

In the second limit, the pore size is taken to be of the same order as the wavelength; this limit is motivated by the propagation of light in a holey fiber. In this case our argument directly yields the dispersion relationship recently derived by Ferrando et al. [Opt. Lett. 24 (1999) 276], using intuitive and physical reasoning. Thus, our method puts theirs into a mathematical framework from which other approximations might be deduced.     

Transmission in a rectangular waveguide loaded with an arbitrary number of capacitive screens

Summary Green's theorem is applied to individual domains consisting of the walls of a rectangular waveguide and two neighbouring slotted capacitive screens. In addition this theorem is applied to the two end domains, that is, the one containing the incident field and the other containing the transmitted field only. Using the continuity of the electromagnetic field intensities in the slits, a system of simultaneous integral equations is obtained in terms of field intensity functions within the slits. By a change of variables a system of ² linear algebraic equations is derived, and formulae for the principal mode transmission and reflection coefficients are given to any approximation desired. Conditions for a full transmission are derived, especially to a first order approximation. Some applications with regard to the filter properties of the waveguide system are discussed and the theory developed is compared with measurements.     

Generalized Born scattering in anisotropic media

The Born scattering approximation has been widely used in seismology to study scattered waves, and to linearize the propagation problem for inversion. The standard Born theory requires the model be separated into a smooth, reference model and a perturbation. Scattering occurs from the pertubation. In the distorted Born approximation, when the reference model is inhomogeneous, the reference Green's functions are normally not known exactly, but the error in these Green's functions is rarely quantified. In this paper, we generalize Born scattering theory to include the errors in the Green's functions explicitly, and obtain scattering integrals from these errors. For forward modelling, there is no need to separate the model into a reference and perturbation part - approximate Green's functions in the true model can be used to calculate the scattered signals.

The theory is developed for inhomogeneous, anisotropic media. Asymptotic ray theory results are suitable approximate Green's functions for the generalized Born scattering theory. The error terms are simple, easily calculated and included in the scattering integrals. Various applications of generalized Born scattering theory have already appeared in the literature, e.g. quasi-shear ray coupling, and this paper is restricted to an improved and more complete theoretical development. Further applications will appear elsewhere.     

A general correlation for the local loss coefficient in Newtonian axisymmetric sudden expansions

Results from numerical simulations and guidance from an approximated corrected-theory, developed by Oliveira and Pinho (1997), (Oliveira, P.J. and Pinho, F.T. 1997. Pressure drop coefficient of laminar Newtonian flow in axisymmetric sudden expansions. Int. J. Heat and Fluid flow 18, 518–529) have been used to arrive at a correlation expressing the irreversible loss coefficient for laminar Newtonian flow in axisymmetric sudden expansions. The correlation is valid for the ranges 1.5 < D₂/D₁ < 4 and 0.5 < Re < 200 with errors of less than 5%, except for 25 < Re < 100 where the error could be as much as 7%. The recirculation bubble length is also presented for the same range of conditions and the pressure recovery coefficient was calculated for Reynolds numbers above 15.     

Time-domain electromagnetic scattering by open ended circular waveguide and related structure

The axial electromagnetic backscattering by four objects characterized in part by either a circular aperture or circular conducting surface is studied. Impulse response waveforms for finite and open circular waveguides, a circular loop and a thin circular disc are synthesized from exact and/or approximate frequency domain scattering data. Complex natural resonances of the four objects are compared to illustrate similar and dissimilar features. For the open circular waveguide it is demonstrated that approximate scattering solutions for loaded guides in the resonance region can be obtained by properly combining low and high frequency estimates.     

Isoenstrophy points and surfaces in turbulent flow and mixing

Vorticity ω magnitude is measured by the enstrophy field ω². Equations describing the motion of surfaces of constant enstrophy, and lines and points of extreme enstrophy, are derived. The purpose is to develop better tools for studies of small scale processes of turbulence and turbulent mixing.     

Solutions of some classes of second order non-linear ordinary differential equations

A second order non-linear ordinary differential equation satisfied by a homogeneous function of u and v where u is a solution of the linear equation ÿ + p(t)ÿ + r(t)y = 0 and v = ωu, ω being an arbitrary function of t, is obtained. Defining ω suitably in two specific cases, solutions are obtained for a non-linear equation of the form ÿ + p(t)ÿ + q(t)y = μÿ²y^{−1 +} f(t)yⁿ where μ ≠ 1, n≠ 1. Applying our results, some classes of equations of the above type possessing solutions involving two or one or no arbitrary constants are derived. Some illustrative examples are also discussed.     

Spline function approximation in discrete mechanics

It is shown that the fundamental equations in discrete mechanics are consistency relations for a parametric spline function approximation. The formula which relates displacement and acceleration is of O((Δt)² and unconditionally stable in the sense of Dahlquist. This method is equivalent to two first order difference equations which relate velocity and acceleration, and displacement and velocity.     

Time reversal super resolution in randomly layered media

In this paper we extend previous work on time reversal in randomly layered media [J.-P. Fouque, J. Garnier, A. Nachbin, K. Sølna, Time reversal refocusing for point source in randomly layered media, Wave Motion 42 (2005) 238–260]. We consider first the case of an active source embedded below the surface in a finely layered random medium. We carry out time reversal with a time reversal mirror placed at the surface and we consider here the case where this mirror is larger than the carrier wavelength. In contrast with the situation addressed in our previous paper, where the size of the mirror was comparable to the wavelength, we show that multi-pathing dramatically enhances the effective aperture of the mirror so that super resolution at the location of the source can be obtained. In other words, the focal spot radius of the refocused field obtained in the case of a multiply scattering medium is much smaller than the spot size obtained in the case of a homogeneous medium. This super resolution effect is obtained by time-reversing the long incoherent waves generated by the multiple scattering due to the thin layers. We also give an application to the problem of focusing on a passive scatterer buried in the random medium and illuminated by a source at the surface.     

Conjugate natural convection from an array of discrete heat sources: part 2 — a numerical parametric study

Coupled conduction and natural convection transport within a discretely heated cavity have been investigated numerically. One vertical wall of the cavity is composed of discrete, isoflux heat sources mounted in a substrate of finite thermal conductivity. The opposite vertical wall and the horizontal walls are assumed to be isothermal and adiabatic, respectively. The governing steady-state partial differential equations for the fluid and solid region are solved simultaneously using a control volume formulation, coupled with an additive correction multigrid procedure that increases the convergence rate of the solution. The fluid Prandtl number and heater/fluid thermal conductivity ratio are fixed at 25 and 2350, respectively, corresponding to a dielectric fluid (FC-77) and heaters manufactured from silicon. With increasing modified Rayleigh number (10⁴ < Ra_Lz^* < 109), the cavity flow becomes more boundary layer-like along the vertical walls, and multiple fluid cells develop in the central region. Thermal spreading in the substrate increases with decreasing modified Rayleigh number and with increasing values of the substrate/fluid thermal conductivity ratio (10⁻¹ <- R_s ≤ 10³). For large R_s, the discrete heat sources lose their thermal identity, and the streamlines and isotherms resemble those associated with a differentially heated cavity. Thermal spreading in the substrate also has a significant effect on circulation in the cavity and on maximum surface temperatures.     

Pressure spectra in homogeneous low Reynolds number turbulent shear flow subjected to weak rotation

In this paper, pressure spectra have been derived from the authors’ model (Eur. J. Mech., B/Fluids 12 (1) (1993) 31–42) developed by means of rapid distortion theory (RDT) of homogeneous low Reynolds number turbulent shear flow subjected to weak rotation. The combined effects of uniform shear dU₁/dx₂ and weak rotation Ω₃ on the evolution of pressure spectra have been examined in terms of the rotation number 2Ω₃/(dU₁/dx₂). It is found that the system rotation exhibits the opposite effect on the pressure field as compared with the influence of rotation on the velocity fluctuations.     

DNS of heat transfer in turbulent and transitional channel flow obstructed by rectangular prisms

Direct numerical simulation (DNS) of heat transfer in a channel flow obstructed by rectangular prisms has been performed for Re_τ = 80–20, where Re_τ is based on the friction velocity, the channel half width and the kinematic viscosity. The molecular Prandtl number is set to be 0.71. The flow remains unsteady down to Re_τ = 40 owing to the disturbance induced by the prism. For Re_τ = 30 and 20, the flow results in a steady laminar flow. In the vicinity of the prism, the three-dimensional complex vortices are generated and heat transfer is enhanced. The Reynolds number effect on the time-averaged vortex structure and the local Nusselt number are investigated. The mechanism of the heat transfer enhancement is discussed. In addition, the mean flow parameters such as the friction factor and the Nusselt number are examined in comparison with existing DNS and experimental data.     

Taylor-Görtler disturbances in thin film flow: a perturbation method

The theory of Görtler-like instability of Eagles (Phys. Fluids 31 (1988) 1386) is extended to the next order of approximation in δ^1/2, where δ is a measure of the thickness of the film compared to the radius of curvature of the bed, which varies slowly on the scale 1/δ. A convenient way of calculating the modified growth rate is described and applied to eight examples with modified neutral curves being obtained. In some cases the effects are strongly stabilizing and in other cases they are strongly destabilizing.     

Inertial instability of the Stewartson -layer

Inertial stability of a vertical shear layer (Stewartson E^1/4-layer) on the sidewall of a cylindrical tank with respect to stationary axisymmetric perturbations is inverstigated by means of a linear theory. The stability is determined by two non-dimensional parameters, the Rossby number Ro = U/2ΩL and Ekman number E = v/ΩH², where U and L = (E/4)1/4H are the characteristic velocity and width of the shear layer, respectively, Ω the angular velocity of the basic rotation, v the kinematic viscosity and H the depth of the tank.

For a given Ekman number, the flow is more unstable for larger values of the Rossby number. For E = 10⁻⁴, which is a typical value of the Ekman number realized in rotating tank experiments, the critical Rossby number Ro_c for instability and the critical axial wavenumber m_c non-dimensionalized by L⁻¹ are found to be 1.3670 and 8.97, respectively. The value of Ro_c increases and that of m_c decreases with increasing E.     

空化器出水非定常垂直空泡的研究

对空化器朝水面高速运动产生的非定常垂直空泡进行了理论研究. 建立了受水面和重力影响下的水下垂直空泡长度变化数学方程, 从方程中导出了非定常垂直空泡长度计算公式, 利用公式计算了空化器出水后空泡从脱落、收缩到溃灭的时间. 对带空化器的航行体, 公式还可以计算脱落空泡溃灭高压作用在航行体上的位置, 最后给出了避免溃灭高压作用在航行体上的条件和判据.     

Impedance at a rough waveguide boundary

The impedance at the randomly rough upper boundary of an ocean waveguide is derived. The sound speed of the waveguide is an arbitary function of depth. The boundary surface height is assumed to be a statistically homogeneous Gaussian process. Integral equations for the Green's function and its normal derivative on the boundary are derived. These are solved to second order in the surface interaction. The result is a rational approximation to the impedance in terms of the wave guide Green's function and the statistical properties of the surface. The special cases of small and large roughness as well as that of a constant sound speed profile are presented. For simplicity we restrict the analysis to a semi-infinite waveguide where the waveguide Green's function vanishes at the surface (Dirichlet problem).     

On the radiation properties of an asymmetric cylinder

The radiation properties of an asymmetric cylinder, formed by slicing a circular cylinder with a plane making an angle π/2 − Λ with the cylinder axis, are investigated as a model problem of relevance to noise emission by novel aeroengine intakes. We consider the scattering of incident duct modes and use asymptotic analysis in the limit Λ 1; the unsteady flow then comprises an inner incompressible region around the cylinder rim and an outer region comprising the rest of space, and the radiation in the outer region is determined using the method of matched asymptotic expansions. From this we are able to conclude that the correction to the radiation directivity is O(Λ), whilst the correction to the total integrated sound power reaching infinity is much weaker, and is in fact only O(Λ²).